733 308
$.$..*......$*...*..$*...*$$.$.$.$$.$*..$$.....**...$.*..$...$.$.*$*.$.......$**$.$$$$.*$*$***..**.$....*......*.$$$.*..$..$......*$..$.$.*.....*.....$*.....$$.*$.$..$*............**..**$*....$*$$..*...$...$$.*.....*...........$**...*$$..$$$$....$..$.*$..***.........$$$.$..$...*.....**.$*.$$$$...*$.$..**...
*.........*..*..*..*$...$....*$$.......*$$*....$.**.**.......$*$...**..$$*.......*..*.$..$$....$..*.....$.$.......$*.$..$.......$.*.$$.....$$.**..**..$*.....**.$$$.$.*..*..$$..$*...$..$$*...*...*.$*.***.$...$.*$.$$......$$*$$$..$.........*.*.$.......*$*.$.$.$.*.$....*.....$.$.$*..$$..$$$.*...$**..$$..*.*$.*
...$$..*....**.......*.$.*..**.$..**..*$....$*...*$.....$.*.*.....*...$...$.*..$*.$.*...*.$..$.*..****.$.*.....*.*..*.......$....**.*.$$.**.***.*$$$.$*.$..*$*......*....$...$..*.*.......$.*...*$..**$$...$....*$.$.*...$.*$*$..$..$*$...*...*.*..$..$$.**.$$*...$**.$..*..*..$*..............*.......$..$.$..$...*
.$$.*$..$....**.$*..*.*..*....*....$....$$......$$..$$$.....$...*..*.*..$*.$.$.....*.$...$.........$.$..$....$.*...*$.....*$...*.....*..$.$..*...$**...$$.*.$...**.*$*......*$.*..*..*......$.*........*.$..*.**.*.*$$..$.$*$.*.$.*.$**$.*.$*$.**..$**..*.*$.*.....*..$..**..*...$.*...*.*..$.**.*...*$..**.$.*....*
*...*$*$......$...*...*$*$$.*.$..$$...$....$..*.*.$*.$$..$*$.$.....$$.$...*....$.$.$.$..$**..**.*$.$*$*.$.*.*...$**......$..$...**..$...*.*$.$.$*..*$...$.$...$..$....$.*$..*.*..*...$........*....$*.......$....$.$$$.*..$...$*$$.$.$*$.**..$$$....$*.**.*$$.$$..*..$*$*.*....*.***$...........*.**.*....$$.*.$*$..
...*.*...$$*.*.....*...**...*.....$.$**$.$..*.$..$**$...$.$*.$$*.$......$...$....$.*...$$..*..*..$.*.$*.$......$.$...*.....$.$..**..$.$..*..*.$....$....*...**.$..$.*...$..*$...*.*.**..$..**..*.$.*.$*$........$*.$$$*.**..$..*..*$.$*....*..**....$..*.*.$..$$.$*.**...****$*.....$$...$$...$.$.*$$.$.**.$.*..$.$.
..*...*.*..$...$*.$$*..$.$..$*.*....$..**..*.$$$...*.*..$$$.....*.......$...*.*..$$............$.....*....$.$$...*.***.....$$.$$...$.$.*..$.*.*$..*.$..*.$..$..**$.$.*..$**$...*$$$$**....$...$.*$..*.$$*..$*$$.*.........$*.*....$...$*$$**..$$.....$..$*$..$..$...$*.*$.**$..*$*$.......*.......*....$$***...*....
$.*.*$.$.$...*.*..*$....$..*$..**$.$*.....$*..*.....*$........$.*......$.$.....*.*.*.*......$*$.....$$...*$..*...***....*.*......$..$$...$....*...*...$..$.*.....$.$......*$*...*.*..$.$.$$*.........*..*.....$..*.....$*.$.*.....*.*$..$..$*.*.......**..$...$$..*$..$$*..*$...$$**..*.$.....$...*..$...........$.*
$...$$**.**$.*$$...**$..$..$.**$.*$$.......$..*...$*..$*...*$......$...*.*.$*.....$.......***.$$$**.*.*.$$$.*$****..*$$.*...$.$$.**$.$.*...*$**.....*$....*$.*$.$*$.$*.....*$$.$.$.......*$..$.$.*.**..$..$$..$$$*$*..*$..**...*****........$*$$**.*.$***..*..**.$.$**...*........$.$.....*.........$$.**..$...*....
.*.$*..*.**.$..$**..*.$....$$.$.*..$.$$.*..**.$..$$$..*.....$...$*$*.**..$.*.*...*..*$..***.***...$*$.$.$..$...*....**$......$.*$$..$*...*..$*$.$.**$...$.*.*$.....***$..$.$...*$**..$..**.**$**...*.**.$...$...$$.$.....$.$...*....$.$........$..*...*.*...*.$.......$..$.....**.$....*$$.*...$$*..*.....$$...$*.$.
$*....*..$$.$*.$.*$.*.$.*.$..$*$.*.$...$$$.$$.....$$.*$*$.$$$..**.**..$$$..*..$.**.**.$..$*.$..*.......$.*.$*.*$.$$.$......$.*.....$.$.$.$*...*.$.......*..$.$.$*....*..*...**..**$.$.*.*$......*$$.$..$$...**$..**.........$.*..$$$...*$.*$.$......$...*..*.*.....*.*......*$.*..*..$*.**.$*......*..*$..*.......$*
$.$.$......*.$$..**........$..$.*$*$.....$$.*$.$$.$*$$*...*..$.$$.*...$..*....$.....$*.$*..$*..$..*$..$.*...$........$..*$..*...**.**.$$.*.......$.*.$..*.$**.***$.$.........$*$$.$.$$.*.......*..*..*...$$*$....*..*.*$..*..$.$..**.$.$..$$.$*...**.*........$.....*......$*.$*$.$...*.$.*$...$...$....$......$..*.
.*..**..*.*.**.$$.*$.***.*$*...*.$$.*$*$....*..$$.**.*..........*.....**..*.$*....$$..*...$*$*...*..**.*.....$.*$.*$..$.*.**..**$$.*..$*..$....$.*.*....**.$*..***...$*..$*....*.*$..*..$*.....$*.*.$....$.$*.*.*$*.*..$$.....$.$.*.*.*.$.$...$.***....*..*$$.**.*$**.$.$..$*$.....$...*.**$$.$*..**..*.*.$..$...*.*
..*.*$$..**...$*..*..*$*$*$...$..$....$..$..$..$*......$.$$$*.$*..$.....*.....*...$*..*.....*..$.$..$.**.*..*....$$.*$$*..*..$..$..**.*..*$*...$*$*......................$***..**..$....*.*$..*....$*$..*.*.$.....*..........$*......*.....$$*$.$.**..**$$$$$.$.*.$.......$*......*...$.*..*.**.*...$....$......$...
**..*.$$$...$*$..$$$.*.***..*.$*$..$..*...$.*.$$.$...*$.....*.**..$.**.*....$*$...$*$..........*.......$$$.*$*.*.....$$...*....$...$..$....$..*$.**...$.$.....$*$*$....*...$...*.$$***.$..*$*.$.....*$.$.$..*..*..$$.$$**.$$...$.*$..*...$...*...$.....**....$....*.*.*$..*.....$$*..$$*.*.*.*$....***..$*.*....*.*$
*.....*$....$$...*.$$...*..$.$..$.**.$........$**$$$..$.$**..$...$.....$*...*......$....$$..$.$.......*.....$.......*....$.$*$**$..***..$*.*$........*$.$$$$.*...*$.$*.$....*.$*.*.$...*$**$....$*$..*.*...*.*.****...*$*...*.***.$..$..*.*..*.....*.$.*$*$$*.**..$.$.$$..*$..*..$.*$$..$$..*.....*.$*..$$*.**..$...
.*.$..$$.**.$....$*$.....$.......*.*.**$$$*.......**.$...****.*.*...*$.*..$.**.*$*.......$..*.$..*.........$..*$.**$$..$$.....$...*.......*....*..*..$...$.......$..........$.*.$......**.......$...**..$...$....$......$.$.....$.$*.*.****...$.*$.$.*.$..*.*...*..$*.*$*..*..$.*$..*$..*$.*$$$.$..*.*..$***.*...**.
.$.......*...*..$.*..$.....$$*....$$...*..*..***......*$....***$....**$$$.$$...*..$...*..*.*.*.........*.......$.*.....*...........$.*..*.*$$..$**..*....*.*.*..*.*$.$....$$**$..**$.*...*..*.....*.$*.*..$.**..*....**$..*$.$*.$..*...$..*$.....$..$..$*.*..**..$*.......*..*.*$..$.**...*..$$$...$...$$...$...*.$.
..$..**..*....$....$...*.*..*$.*.$.$**.....$*..**..$..*.....**.$.$$.*...*....$.*.$$*.$.*..$.$..$*.....$..$.*$..*$$....*.$...$..$$.......$.$*.*..$.*.*.*....*..*..*.*....$....$.$.....$..*$*...*..**....**...*....$......$$.*.....*.$..*$..$.*.*$*..$$*$.$..$....*$....$...$*.....$.*....$*............$.....*...****
.....$...*..$..*.*$......$**.*.$*$$$....*......*...$.$*$.$$$*....*$$$$.$$..$.*..$..$..$.$.$$*..$...**..*.$..$..*.$.*..$..$.$.......*..*$*$*.$*.$$...*$....*$.*.$.**$....$......$$$*.$*....$*$$..*..*.*.$..**.$.$*.*$*....$...$...*......*...*.*$.$$..$$...*.*.....$*..$.$*..*.$....$.$.$$*..$....*.$..*...$.*.$$....
....$.*........*..$..$$.$*$*..$..$..*...*.........*$..$.....$..*.......*....$$$.$.$.......*$......$*..$$$.....$..*......$$.**..**.$..$$..$....$.$*.$..*.....$...*.$.**....$$....*.$*...*....*..$...*.**....$....**$$*..*$$*.....**.**.*...$...........*..$.**.*..$.....*...$*$.....$*$$..$....$..*.......$..**.$$.*.
**$.....$$$.*..*$.....$*$.......*$$.*$*...**.*...$..$..*$.*.....*.$*.$.**..$..*$*.$$$.**..*.*..*.*....*...*..*.**..*..*.$...*...$.$$..*...*$.*.$..**.*..$....$.....*....$.*..$.$*.$*..*..$..$$.....*....$$.$$.$$.....**.$..$..*$..$$..$.*.....*.*....$.*..$.*..*$$.***.**....*.$.$.$.*...$*...*....*..$..*...$***...
$....$*.$.$.*..*..*$*.*$.$.**.......**..*$**$*.*..*.$..$$$.*.***$$..$$$.$...*.$*$.*.$..$**......$.......$..$*$.$*...$$$.*....*.*..*......**.$....$$....$.*.$$$...****.$*.....$.$..*...*...$*....*..*.*..*....$*....*...*$$$.....***.$.$*........$..***..*$...*.$.......*.*..$.....*..$$....$......$$$.$$.$..$*...$.*
.**$...........$*....*..*..*..*.$...$*........$.$.$.$..*..$.*...$$.......$.$.$.$$..$....$.*$.......*$.*.$.....$..*.....$$**...$.*...$.*...*$..**...$.*....*..$$.$$.*.$****.$.......*..**..*$$...$$.....*..$.$.$$....*$...$..$*.*.....$.*..$***$.$.*.....$*....*.***......$*....$$$.$$.$...$***$$.*.$...**.$$.$*.$.*$
.*..$$......$$......$.*.$.$$..$$*$*...*$...$.*..*...$..$$...*.$.......$..*..$$....$.**$..$..***........*..*..*.***$$...$...*.*..*$..*....**.......$...$..*.....$$$.$....$$*...$$......$.$$.*$..*...$*.$$.$.$..**$.$*..$..*...$*.*.$...$..*$....*$...*..***...*..*..$...*..$$$*.$..*.$$$.$.$...$........*...$*...*..*
...$.$$$.$*.*.*.**.......$$..*.$*$$$....*..**....$...*$..*$$**...$...$$$***..*...$..$.$$.$*....**.$......*...*.*$*....**.$$$.$*..$.......$.$.$$...$.**.....$......$$.$..$*$.$$.*$*$..........$..$...*$*...$*...$$.*...*$...*$*..***.$.$.$..*.....$$$*....$.$.$$..*$.*....$..*...*.*$$..*.$$.*....*..*$..*$$...$..*$.
$...$...$....*$$.$..$$$$$$.***$**$.$.*..*...*.$.*....**$.*..$..*.*....*....*..*..$*$.*..$$.$..$.$*$.$*.$*..$..*.$$***$......$$$$$*$....$.*..$$....$..$..*.*$.....$$$$$..$*$*....$*..*..*..$****$.....*.$.........$...$...*..$....*.*.$*.$$.....*.$.$...*....$.$.$.$.$$..$.*......$....$......$.$$.**..*.**..*.....$*
$.*...$**.$.$...*.**...*..*..$*.$$..$..**..*..*$...$$.$..$..*.$.*...$$.$...$*.**....$*.$$..$.**...$.$...$..$..*.$.*...*..$$$$..*$..$.......$.$.$*...*.$*......$....$$...**....*.$$$......$..**..$...*$.*..$$*$$*...*.$$$.....$.$..$$...$*.*.$.....$.*$.$$*....*.$***........*$....***.*...$$.$.......*..$.*$$*$*...*
$.$$*......$..$...*..$.*..*.........*.*$$**.*$$...$..*...*.*$...$**......$.$.*.$$.*..*.*...*.$..*.....$$$**.*.*...*....$.$.$*..*.$$...*...$$.$...*..$*.$$...$.....**.*.................*...*...$.$*..*.$...*..*..**.$..$.$..$$$...$$*.*....$....*.....$..$....*.***$..*.......$**.*$*.*..**..$$$.$*$.*..$..*...**..$
..$*.$$*.$*...$$.*..$*..$$*$....****..$*.*.**....*.$..$.$..*..$$...$$.*..$..$..$.$$..**......*.*..**.**..$..*..*..$*..$.$....*.$$$$.$.$.*...$*..**.$$..*.....***$.....$.*....$..$*.....*..*...*...*$$..$..*...*...$$..$*........$.$$*...$$..$...$*..$.....*.$$.$.......$......*$.$..$$$..*..$$........*.$.*.$..*.**.
.....*..$..$.$$.*..*.**....$.$**..*..*....**.**.**$$$$*......$*.$......$..$..$$.$*.**.$.$*......**.$$.$$..**...........*$....*.*.*.*....$$.****$*...**$...***..$$.$$.....$*.$.$**.......**$......*..*.***$.$$*$.*....*.*.*...$$...$$.$$$$.$*$...$.*.$...*...$$...$.....*..*..$..$.$..$*$...$.$......$..$..$*....$$$*
...*......$$*.$$..*.$*...$.*.$.$.*......$.*$.....$..$.*.$$.$.*.$..$.*...$$....*.$..$..*...*.*.$........$..$*..$.....*.$*.$*$$*.$...$.**$..$.*.....**....$$*...$$*....$$**...$$$......$.*.......$$.$.$$.**......$**$.*.*$$.$$.....$.*$$.$...$.......$$....*..$...$*.$................*......$.$.$.*$.....$...*....$*.
*.*..*.$$*$$...$..$$......$.$..*$...$....$$.**.$........*$$$...*.$.$*..$...*$.$.*.....*..*...*$..*$$.*.**.*...$.$$..*...**$$.$*..$.$......$.*$...$.$$.$..*$*.$.....$...**.*$**....$*..$*....$.$$$*$$.*..........$....$......$**$.$..$...*$.$.***.**..*.**$**...*$.$*....$.$$.*$$.*.....$$*.......*.....*.$.$..$*.$*.
$**..*$**....*$$.*$.$.$.$.*$.$*$.**.*.*..*$...$*..$.*..*.*....$$*$.$.*...$$.........*$.$.....$.....$***.*$.$..$.**..$*$...$*....$.*$$.*..$.*$..$.$.$...$.*...$$$$..$$.*.$..$...*$**..*.*$$*.*$..$..*.$$*..$$..*.....*.$....$..$...*$......$*....$$........*.$...$*.*...*$$.....$..$$**...*..*$$$*..****..*..*..$.$..
*$....$....*....*........*.........$*$$$*..*..$..*..*..*$***.$*.........**.$.$..*....*$...*$......*$...$$*.*..**...$*$$*..$..$.*..*.$*.*$**.$.....$..*...*$.....*.$...**.*.*..$****$$$*......**$......*.$..$$*.$...*...$.$*...*...$......*..$**.*$.*.....$$.$....*...*......$.*.$*.....$**$.*..*...$**...$...**.*$.*
.*.**......*$..*...*...*.**.$...$**.....$.$..*...$..$.*....*..*.**....$$.$$...$$$.........$$.....$$..$.....$*.$.$$....$..$..$.*$.*..$$*$...*.*$...*.......*.*.....$.$**..$*$.*..$......$..*.*....*$..$...$....$$*$.$*........$*......$.$...$....$....*.......*....*....*..$$$*....$*...**.*.$.....$$$..$*....*...$$$
.*..$*$...$...*......**$***$.....$*....*$.$...*......$.........$$$...$*.*..$.*.$*..**...*$$.***.$.$.$.*....*.*.$.*$......$.$....$..$.$$$..*.*.$..$.*......$...$.*.$...$*..*$$$..$.*.*....*$.........$.$..$$...$...$**.....**.$.$.$..$..$*$...*$$$*.*.$.*$..*.*.*..*..*..$$.*..$....*..*..*...$.$..$*..$.*.$.$...$*..
.$.......$.$$.*.$*.$.*$**.$*.$.*.$**.*.*.*..*$.*..*......$...$...**...$$$.$...*$......$..$.$..***..*.$$..*$...*..$.$...*..*..$....**$.*.....$$*$.*..**..$$.$.*...$....*$***....*....$.$.$**..$.$**.$*.$*$.*.*.**.*..*.*..$..*.$..*.$..*$$..*.$***.*....$$..$*...$$.*$.*..*..*......$*.*...$$...$..***...$....**...$*
.**.$$..$..*...$$.$.$*$*..$..*..*......**...*...$......$.$..$.$.$...$.*.$..$.**.$....$**$*.*.....*.$*.$.$$....*.**.*..*....*....$..$$*.$*..$........$..**....**.*.$..$....$$.*.........*.$.....*.........*.$$**..*..........$*.....*.*..*.$...$..*$**...*$...*..$**.$.....$...$...*.$.*...$***.*..*.*$.*..*.$..*$$..
$..*.*$...*$...$.*...$$.......*$..*$.***.$$.*.$*...$***$*...$*$$......$*.$.$$.*.$$$$*.$*.$....*.$*$*.**.$.*.*..*..*$.*..$.*...**.$.***..$...*..........$$.$....$..*.$$.$$.***.$..**..$..*.$.$$.....$.$..$...**.......***.*.....$$***..$.*....*.*..$.$.**$..$**.*...*....**..$.$....$$.*..*...*$...*...$**......*....
...........*...$...*$...*.$...$..$..$$...**.*$*.$**....*$$.*.*.*$*.......*$.$$**.$**..*.$....*$*.***$.*..*.*..*.......$$*.*$.....*.*...*....$..$.$....$...*..$.....*.*..$..$**..$..$$...$$..$*.$**..**...*$.......*...$...*.$......$.**$.........$...$...$*$.*$...$.$.$..$.*.........*.*..$..$*$..$$....$*.*...*$..*
$$$.....$.*..*.$.$....$$$...........*$...*.........$.$.$.$..*$*.$$*..**....$..$$*$*$.*$*.*.*...*.*..*.....$...*.$*$*$...$$...$*..........$............*.$$..*..$..*$....**$.**.****...***..*.$..$$.$***..*..*...*...*..*$..**.*$..$$$..*.***$.**$$.**$..$.$..$.**..*$*$$.....*$*.....$*.$*$..$*.......*.$...$...$.*.
*$.*$$......*$.*.$.$.*.*..**........$$**.*...$.....$.$.$***..*..$..*.$***.*.$*........*....*.$...$..$**..*.**...$.$$...$.*..$$*$.$*$$...$.$$*$.$...*.$$.....$.$$.....$*.****.....*...$.*$$..*...*$*...*.$.**$.$$....$.....$*$*.*..$....$.$.*$$..*.*$..$$....*$..$.*.$*.$$...*....$*.*........*$*$...*.*.$...*$*..$..
.*.*..*.$....*.$$*..**..*..$...$...*...$..$$$.*$.*...$..$$.$*..*$..$....**$....*.$..*.$*.$..**$.*.....$....$**.*...*$.*..*.*...*$$$$*.**..*...*$$$.$..$$.$.*.*..$..$.*..$*..$*....$.....*..$.*...*$....*...$$**..$...$.*....$....$$......$*.$*.$..$$*.$.$...$.$$$*$.$......*$**.*.$**.....$.**......$...$....$.....*
..$*.$....*...$...*.....*....*.....$.*.$.*$*.$*.*.$.*$*.*$.$$...*..*$..**.*$.$..$**.*.$$.$....*$$*$..*.$.....*...$*.*$*....$...*...**.$..***..$...**....*.*$.*$*$..$.$.$$$.......*.*$.$*$.*$.**.*$**......*...$$$.....*..$...$...*$$$.$$$*...$..$*$....*...$$$**..*$..****$.*$..$.....$...*$...*.$$**.*..$$$$.$.....
.*...*.**$...$..$....$$.*$*.$*...$..*.$....*$**.$$...$$....$..$...*$$$.....$*...*..$.$...*$..*$**$*.*..**$...$.$$*$.$$$$*$*..$.**...$$$.$.*.$$.$.$.*.......*$$*....*..$.*.$...$$..$.*......*...*.*....$$..*.$..***............$.$..$$..**.*.....*.*$...$.$$..$*...$...$....$.$.$.*..*........$.$...$.$...$.$**..*.*.
*....$..*..*...*.*.*$$.*$.$*......$.....*.*..*..*.*.$..*$...$....$.$.*$$.*...*..*..**$...*$....*.*.$*$.*..$...$........$.*..........**.*...$...$..*$..*....*..$$...$$..*..$.***$...***..*.$$*$....**$....**$*..*$*$..$...*.*.*.$.$.*$**.......$.*$....$.*..$*.$.*$..*$.*$.*..$*$*...$$...$*...*....*.*.*.*.*.$.$..$*
.....$.....$..*....$.$......$.$..**.$...$..$.$............*.*.*..$*****.*.*.......*....$......*..$..$$$...$....*$**$..$....$**.*..$...$$$$$.*....*.*$...*.$..$$.*.*$..$*..*$...$$...$*..*.*$$*..*...**$$*.$.$$$$*.$$...$$*$..*.$*.$.$...*..............$$.*..........$*.$$$.*.*.*.*.**.*.....$..*$.....*....*$*.*..$
.....*$*.$...$...$.$*..$$$.$.*.$.......*.*..$.....*...*....$..$$.*.$$.......*$..*$.$*.*..*..$.*$....$.*$$...$$*$**.$$..*..$$*..**.*.$..**$*.*.$..*.$.$.$*....$..$..*$$*........*.*.*.**.*.$..$$......$*..$.*..*...*.......$..$....$...$$*....$....$$*.*.*..*.....$........$.*.$.$..$$..$.........*..$.$.$.*.........
.$.$....$.....*.$.$....***..*...$..$...***.$.$*$.**...$$...*.....$.*..*.$..$$...$.$*$$*.**$*.*.$..$.$..$$$**..$.*.$.*....$**$...$.*$............$*$..$.*..**.*..$...$$$.$.**.*...$$.*.$*$..$...$.....*$*.$..*..$...*.....*..**..$.$$*$$$.$.$$...$*.....**$....$..*.*.*..$*..$*..$.$$.....$...$....$*.*...$...*...*$.
....*.....$.........$$$*.*$*.$...*.....*.**....$.*..*.....**..$.*..*$..........*...*$......**.*.*.$...**.$.$...*..*..$....$$*.*..*$**.......*...*.....*$.*....*.**.*$...$$.$*.$....$*.$$$$*...*$....*$.$.**$**...$$...*......*$.$*$..*...*...*.$.....*...*....*$....$.****.$$$.**.$$.$......$..$....$*$.$....$$$$$.*
*....***$.*$$...*$$*$.*...$..***.*.$.*$.$.$.$..*$.....$$*..$...*$.$.*....$....*.*$$..$.**$..*....$..*....$$...$$..*..**.**.....$..*.*$....*....$*$*.$**.$*..**..*.$..$$.***........****.*.*..*.....$...$$.$.....$.$*........*$.$**..*$.*..*..$$*.$$..$****$*....*$.$$..*..*..$$...$.$...*$*.**......$...*....$.**$..
.$..$.*.*.*$*.$....$.$..**$.*..*$*.*..*...*$..$....$$$$.$..........*.$..**.*.$$*....*.*...........$$$...*.......$*.....*$.*$...$*.**.$$...$.*...........$..$*$$.$*$.$.*.*...$*$..*..$$.$.$.$.*.*...........$*...**...**.$..$*.*$....$$$..$...$.*.$....$*.*..$.$.*.$.$...$...$...$***.*....$....*...*....$.**.*$*...$
...**$..$*....*$..*$$..**.*...**....$*$*$..$.$....*...**..*.$...*$......$$...$*.**....*..$..$.*.$..$$$..$*$**....$$..$.....*.$*$.*..$.$$$...*..*.*..$.$$*.......$.$..*...$...**$$..**...*...$*.$$$.$$*.*....$..**....*...$......*....*.$.*.....*$...$.$**.$..*$.$$......$$.........***.**.**.........$.....$..*.$.*.
...*.$.$***..$$...*.$*..$...$...$....*$*.*.*....**...$....$..*$$...$..$.........$..$..$$..*...$.....*....$*.......$**....$*.*.$$$*.$**..**.....$*........$......$$.*$.....$..$*$*...$$....$....$$......$..*$**$*.$..$....$..$...$*.**..*.$$.$.$..$.......****...$$$$$$$*.*$**..$*.$**....$*.**..$.$*$.$**$.$$*......
.$.*$.$$*.$*....*....*.$.....$.**.**..$...$.*...$*$.$.*.*.*.$.**..$..$.*.....$$.....*...*.*.*........*.....*.**.***.*.**$$.$..*.....*..***..$..$$.$...$.$.**.**$..$..$*$...$*.....*$$*.....$.**.....*..........$..*..*$......*$..$........$...$.**...*.*$*.$..$.$.*...*$...$..**$*.....***.$....$..$$............$..
*.....*...$..*.....***..$$*$.*...$..$..$...$..***...$...*..*$...$.*....*...$.*.....$$$.$.....**...$*.*.....*.**..$*$..*...$$*..$$...$....$.*...$*$.*..$....*...*...$*....$$......$.$$*.*$.$$.*.**.$*$.*..***.....$$...$..$.*.*$.....*..*......*.$..*...$*$......$.*........$$.**......*.$$.$***....*.*.**$$**.......
.$.......*$..$$.*.$$$**$..*..$$...$.*.$**.*...*$..$$*..*...**....$....**..*....*.....$*$.....$$.*...$$$.$.....$....*....*.*.$.*$*...**..*..**..$*..*...$..*.$$...$......$.$.*...**$*.*.$..........*$**..*....*....$..*$..$*$$.$.*.*$$*...$.$.....$.*.$$.....*..$..$$.*.*......**............$$..$....*$....*.*......
...*.....$.*$..*..$$.$*$..$.*.*.......$.$...*....$..$**..*.....*.$...*........**.$*..*.$$..*...*$.*$....*$.$..$...$*.*$$.*$.....*$$*......*.*.....$...$.*...$......$.$..$...*......**$..*...........*.....$*.......$*....$..$...$*$*.$$.......$.*..$.$.*$$.*.*$..$$$..**..$..*$$*..*......*$*.$$.$.**$.*.*.$...$*...
......$.$.*..*.....$....*....$.*$$$$.$.$$.$$..$*.*.*...*$$.**...$....$.*$*$.*..$.$....$..*.*.***..*.*..$..*.$.$$.$*$...$$*..$$*..$*...*..*.$..$..$..*.**.........$.....**$.**..**..$.*...*...*.$$.$..*****.**.*$*...*.*..$.*...*.*.$...$....**......*$$*....$..*..*..$.$$.*....$.$..$...*$.$$.*.$*$...$.$$*.$..*$$*$
.*.$*$..*$**.*..**...$.*.*....*....$**$.*.$......***$*$**..$**....*$$$.$$...$...$**$*.*...**..*.$.$...$..$*$.......**.$....*$***..$.....**...*.*.*.......$.$*....*$*$*.$.......*...*.*..$.$$....$...*.**..$**$.*.*..***..*$.$.$...**.....$..$*..$..*...*.$..*....$.*....$..**.$...*$$$*$.$*.*.$.$..$$*.$*...*..*....
...*...$$.*$$...$$*.**.$$**..$.*..***......**.$.....$.*$$..$.$....*....*.*..*...........*$.*....$.*.$.***$.$.**$.*.*..*..*.*$.*......*..$.*..*.......$.$.$*...**..........*$....$$.*.*......*..$...$....$.$..*...*.*.*$.......$...**...$.............*.*...*.$.$.*....*...$....*.**.$$..*..$$..*.*$......**..$...*.*
.*$*..$.$**..$*$.**$.....$*...*..*...$$.**..*.*........*..*..*..*.....$....***..$....*..*.....$..*$***.$.$.$.....**$*.**....$..*$$.$.....$*..$*.$..$...$*.$.$...$**$.$..$$*...$......$**....$...**..$..$**..*.*$$$.*.$....$$$.$*...*$.*.*.....*......*...*$$.**..$.....$...$.$.*...*.$$..*.*....$....$.*...*..*.$..*
..$.*$....**..*.*.$...*.*..$...*...**...*$.*.*.$..*..$....$.$.$$*.*$*.$....$$.$.....$$*...$.$.*....*$*..*.$...$..*..$.$$.*$.*..$$..$...**..$*...*....$$....$$...****..*$...$$*....$......$.*$$*....$*..........*$$*.....$*$$.......$*..*$...*.**..$.*..$*.$..*$...$.$.*.$*.$...$$$$.$...*....$.*.*.$*$.**..*..$....$
*..*..$*.......$..*.$...$*..*.*..$*$**.$*$..$.......$**.****...**.*..**.$...**...*..*$.*$.$.$..$.$.$........*$..$*...*.*.**.*..*.**..*....*..$.**$..$*$.*.....*....$*.$*..**.*..$$$....**...*..****.$........*$$....$...$$.....**.$.$.....*..**.$$.....*$..$.*$.*.*..*....$*..*.....$.*$..$$$*$*$.*..$.*.$..$.$**...
......$...$..$...*$*...$..........$.$..........*..**.*.**.$*$..*$.$......$.*$.$.$..$..$*..$...$*..**..$.$*$$$*.*.*$.$.$$...$*$$.......***$..*.$..*$$*.$......*$$......*......*..*$.$....$*$*...**...$..$...*.$..$.*.$*$..$*$..*..*...$$**...$..*$.$$$...*......$...*$.........*.*.$.*..*$..*.**.*.$$...$.*....*..**.
$.*..$**.$..$*.*.$...$....*$*.....*.......*....***.$.$**....$$...$.***............$.$**......*.*....$....***..*$.$$.$**..$**..*...$.*.$.......*.*.$..*..*....*.*.....*....*...**.$*.$$**.$**..*$$.*..$..*.$.*....$**.$**$.*...$.*..*..$.*.$$*...*..*...$.....*$$....$$.**$....*.....$**$..*..$.*.........*.**....**$
$...$..*.$.$...$.*..*..*$$..*.$***.*.*.$.*.$..$$**...*.$..$$$$...$*.$*.$.$$.$$.$...*...$.*....*.*$*....$**..$$..$**...*..*.$..*$*...**$.*.$..$....$*..*$$..*.*$...*..***..*$**...**.....*$....$...*..**.$$...**$*......$$*.*.....*......*.*..*$.*..*..*...$..$$.$$*...$.**$..$**.$**....*$*..**$.$..*..**..$..*....$
.....*..$..*.$.***..**..$*$.**.$.....$$..$*$$.....$...$.............*$$.$..$.*......*.....$*......$*.**$...$**.**.**..$*...$$.*$.*.......*.$$*$......*..*.....*.$*.*...***....*.$.$.*..$$.**.$..**..*...$.*$**$......*.*...$.*$......*........*$.....$*$$*.*..$.$.*.*.....$...$........$...*.*..*.*.....*..$*..$.*..
*$*.$$...*..***$.*$$$.$.....$..*.$....**$.....$.*..$$..$..*.**.**$$..*$*.*..*$.*.....$.....*.**$....$$****$...***....$...$$.$..**.$...*...*$**$....*.$..$.*.*.......$$...*..*..$$.*$..*..$...*..$.**..*.**..$...$.....*$*..$..*...*.$***.*.$....*$$$...$.*.....*$..$.*$.$$*.$....$****..$.*.$$.$.....$$.*.$..$.$.**.
.*.$...*$.....*.*$.*..*...*$..**.*$$*...*....$*...$.*.**.$....*..****$$$.$.$.$......$*.....**.$**.......$*$..$.***.....$.$$............**.......$*$...*$.$..*$$.$$...*.$$$.*...$$*......*.*..$$***.$*.$..*$$*..**.......$.....*.$...$.$......$.*..*$.$*......$.$$.......**$...$$..........$...$...*....$$$.**....*.*
...........*..*$.$$......$$.$..$*$..$*...$.$$...$$...$$$$......$.$$..*$*$...*..$....$.....$..$..*..*...*..$.$*.*..**.****.$$$.....**$.**....$......*$.*.......$$...*.*.*$*..$...*...*.$.*$**.$.......*...$..*$$.*.$.*.*$...*..$.*.$...$*$$.*.*..*.$..$.$**..$*.$$...**$.....$$..$.*$$.$.*.$*.....$*.*$..*..$..**.*..
.$.*.$..$$.*.**....$$$...*......*..*...$$$..*....$.**$*.$..$*..*.*.*.*$...*$.$***.*$..**$*.$$*....$$**$***$.*.........**.....$$.....*..*.*...*$.*.*......$*..$.....*......*...*.**.**..*..**.$**$**..$..$$*....$*.$.....$.....$.*.$$...**..*.$..*..**.....*.$$.$....**..........*..*.$.........$$....*..$..$$.*.*.$*
..$*.*.*$*$.**$...$.*$$*...$*.$.$*....*....$$*.*.**.*.*$...*...$.*......$...$*.....*..$$.*.*..$..*$....*..**....*.$...*....$.*...*$..*....*.$.*.*$..*.*.$..**......*$.$$.$$.......$.*.....$*.....*.$$.*$.$*.*..*$*.**.$.**$...*....$.$......$.*....*.*.*..*.$............$*$..........$*..$..$.***.*...$.*..*...$.$.
*...*..$$*****$.$...*.*..*$*.$.*$.$.$......$.*..*.$*$..$.$.........$..$..*...$*...*$$*.$**$.$...$$.....$$.$.**$*..$*....*....*...*$*$.$.......$..**..$...**$.$$....*.$.$$..$...$*...*..$**..*$.....*.*$.$$**.**.$.$..$...*.***$..$.$.$.$.$*.*...*.$*$*$..$..$.....*$$$.$...*..$...*.....$$**..*$.**.*.*$..**...$....
*$....$*$.$.$.*...$.$....$*....$..**$.**..*.$.*.*$$..$...$.*..............$..*$.........*....*.......*..........$$.*......$$.$...$*$*.*...*......*......*.$.$.$$....$.$.*.*.*$...****....*....*$....*$*..*$........*$..*...**...*.$*....*...*...*...*$*..*.$.$*......$$*.*$.$.*$.$*.$$*.*..*$*...$..*..$$*...$.$*$*.
..$$....$....*.**.$.**$*.$..*.$...**..***...$.*.$$.***.*$..*$..$...$.****.$*..*$.*****.$.$....$*...$*$..*.$.*...$..*..*.*$.*$**$.*......$.....$$$..*.*.$...$..$.$$..*..**....$*..*$.$.$*....**.*.*.*...$$*..*....*$.....*$$...*..*$.*.*.*$$$*$...$$$*......$$*.*.$*$*$....*...$*....$$..***.*..$...*....**$.*.*.*...
$.*....$$.**$...$....***$..*$***....*.....$*$$$.$$....*.....*$*..*..$.**...*.....*$.........$.$$*.*.*....**$..$....$*.$*.$*.*.*..*$$$...*.$...*..$$.$$.....$.$.$*$.....$*$.*.........**$....**.*.$**.$..$*..$..$..*$.*..*...$**...$.***$*...$..$$..*.***.***....*.*.*.$*......***$.*$*.....$.....*...$.........$..*.
...$*...$*..*..$*...*......$.........$...$..*.*$$.*..*.$...*...$..*$.*$*...$*...$.$....$.....$$$$$$...$...*....$.*.$.$*$.*....*....$$*$.**...*..*.*$*.*..*$..*.*.*..*.**.**...*...**...$.*.*.*...*.$$...$....$*$..$.$.....**...**...**$.*.*.$$.*.*......$...$..*....*$$....$...*..$....$.........$$$$.**$....$$.$..*
*$..*$*..$$*$....$.**$.**.$$..*.**....$$$....$.*..*...........$*.$....**..$.....*....$$.$.$.$$.*..*.*....$..***.$$.$..$..$....*....$*..*$**....*.$$....$.*.....*$..$.*$$**$*...$*.*....*..*..*$..*$.*.*.*$.$.*...$.$**..$.$.....**..*.$....$....*..$**..*.....$.$.$..*.......$*.$$..*........$$.....*.*....*...*$$..
..$....$$$......$$**.$.*$*.*...**.**.$...$...$*....*.*..**$$..$.*.$$$**$.*$*$$*.$.*$...*...$...*$*$...$*$.....$...$$.$.***.....*.*...*$$$.......**$..$*.**$*.$.**$.....*..........$.$..$.*....***..**.$$*.$....$...$$...$...*$..$......$.$..*..*..............$.....*.$$.*.$$.$....$.**....$*.*$....***$.$*.....$..*
.*......**$..**..**$.$.$$$..*..$.$.*..*........**..$*.......$.$$*$......*.....*...$..$.......$*.$..*.$$.$$**...*.**.......*....*.$$.**$.*..*..*...$$.*.**.$..*.$*.$..$*.*$$$.*.*$$$....$..$...*...*$$*....*..**....$**....$..*..*.$..*.$.$.$$.*..*$.*..$....*.....$...$.*.*.$**$.*..*..$..*..*.*...$...**.$.....**..
..$..$...$$$.**$*..$.*.*..$$..$.*.$.....*....*.*.$**.$...*$.$$.$.$*...*...$...**..*....$$..*..$$***.....$..*$.......$.*.....*$.....$...*.**$**.*..$.....*$.*.*..*.$...$$$*.$$$.$$...***...$.*.$...$$*...*.$..$..$.**.$..$$*.*.*..**...$...**$.*.*$*.$.*.*..*..$$*..$*$$..$..$**..*....$*$.$.......$.*.*.$.$$*$.*.$..
.$....*..*...$.*....*.*..*.*..*.*.$$.$.**.$.**.....$...$..$*.**$.$.*.**$..$......*.**$*....*.**....$**$..$$.$**.*..*.***$*.$**$....$*.*....*..........$.$*...$*...*$*$.$..*..$.$.*..*$$...*.$..$.*.$..*.$*...*...*..**$$**..$$....$...$....*..*.$..$*.$$.*.*...$.$.$*...$$..*.*$.$.*$...*...$$*.*.$...$....*....*...
*$.**$*$.$$$.$..$$..*.....$....*$...$**.....*..$.$**...$$.*.....$$...$.....$.*.*$*...........$..$$.$.$....*.$..*.$..$*$$*..$..$...$.....$...$$$*$.$....$..*$*.*$**$$.......*...$*$***$*.$**$$$$...*$.*$..*..*.....*.......$$.$....**...*...**.....*.$$.....*.......$*..***.*$**..**.*.*....$.*...$.*....**..$.....$.
*$*..*$.*...***$$$..*.*$$..$.....$.$..****.*....$$.$.**..*$.....$*$....*.**..$*....*..*...*.$**$..*$..*.*..*...*..***....$.$.*$$.*$*...*$*.$.$*..$$....$$.$.$.*.....$*....*...*$.$.**$.....*$....$*.$*.*....*..*$.$*..*.*..$*.$.*$..$.$*...$..$....$..$$*$$$..$...*.*$*$.*.$$.*...$*...$.**$.*$$.$$.$$**.$$*..$..$..
..*$*.$.*.$.*...*$..$**.$...$...*..*..*...$*.$*.....$*...*.*$$$*.*$*.*...$..$..$..$..$...$......**..$.....***$*$..$.....*.....*..$*...*..$.$**.$.**..$......*...$....**..$...........*....*...$.....*..*$*.$...*....$$$..$**$$*......$$*..*.$*$*$....$.**.$*..*$.....$*..*.*.*.$.......$*.....*$..$..$$$*.$......$.$
.***...$..$.$...$.$..$.*$.*.....$$*..*$*.$....*.*..$.**.*......$....*.....***................$$...$$.*.**....$..*.$**.*$.$..$.**....**....$$$.$$.$$..**.....*....**...*..$.*$.$..$.*..*...$$..$..$$**...*$*$.$..$.$.$.$.....$.*.*.**$...$..$.*$$.$..**..*.*...*$..**..*.*...*..$.*....$$.***...$..*..$...$....$...$.
**...**.*.....$.*.*..**.$.$$.*$.$$.$...$......*.*$*$$.....$$$..*....*.*..$$..*$....$$...*.*$.*..*..*..$.....**.$*$*$*.$...**..$*.*...$.$...$..***.$$.*......$*.$.$..*..**$.....****..$..$$*.........$.*..$..$.$..$.*....$..$.....$$..**..*$.........$.$.**.$$*$...$**$..$..$.$$.**.*.***..*..$..*......*.$$$.$$*...*
.$...*..$$.$..*.*....$**.........*****.*.....**..*..*$.*$...*$..**.$.*....$...$**$..*...*...*.$$$.*......*$...$.$*....$.*.*.$*.....*.*.*$..***.....$.**.*.....$.$.*$...$.$..$$..$..$..*.....$...$.....$.*.$.*.*.*...**$.....*...$$.$.....$$..*.*.......$*.....$$..$.....*..$.$.$..*....*$$$*..*...$....$$..$..*.$...
...$*........**$....*..*...**..$$*....*...$$*.*.*$**..........*.....$...$*..**$$$....$.*.$.$**..$*.$...........$.$$.*$.$....**.*$$...$.*...**.....$*$.*$..*$..$..$.....*.....*$**$$$..$.*$$...$$$.*$.$.*.*.......$**.$$..$.......$.*.*...$$$$*...*..$*..*$.$.$$..$*$.$$.$.$*$.$.$.....$*.$......*..**$*.*.***....$.$
*.$.*......*.$.....*..**....*.*.*$$....$..*$.$...$..*..$..$**$..$..$*...**.$....$....*.*.*$$..*......*............$..*.$...$....****.$.$$*.**$..$*$**..*.$*..*..*...$...$*.$*..$.....$.$$...$....$$*.$...*...$..*.*....*.*$$.......*...*..$*.$*.$...$.......**.*.*.$$.$..$......*..*.$*.....*.*.*$*...$*..*..*.....*
$.$*.......*$..*$...$...........*...*.....*$*...$*$$$.*$.**.*...**.$*...$...$**.$.......$.*..$$..$...*.....$.$..*.*.*$*.$.....$...$$$...........$..$.$*$**.*...$*.$$*.**....*$$.*...$..$.$..*$*....$.*.*$.*...$$.*...*..$*.$.$.$$....*$..*.......$**$$..**....$*.....**.$...$..*$**......*.$.$$....$...$...**.$.$...
....*.....**$..*...**..$..$.$.*.$*$....**...$...$$...$....$....*$.*..$.$*......*$......***...$...*...$.........$.$*.*.$....*.*...$$*..*...*..**$......*$....$.$$.$$.$**.$*...$**....$*.$.......$.......$$*..*....$.$.$$*..$..........$*..**.*..$...$..**$**.....*...$...$*...*.$..*....*..$.*$$**......*$...$*.$*...
.$$$....$$...$.$.$**..*..$.$*.*$.*$...*.*.*.$*...*$...***$.$.........*...*...*....*.$...*.$....$...**.$.....*.*.$*.$.$...*.*..$*.$$...$.$*.*$...*.*.*..$...$$*..*......$*..*$*.$.$*...$....*.....$.**$...*..$*.$*$*.$$...*.*$.....$*..*..*.$*.....$*$*$....*..*...**..$*.*.$.$...*....$$.$*$..$.*..*$....$*.$..$....
.*...$....*.$*..*$$.....*....$*..$...........$....$....*..**$*$*$**..**$**.$.*.......$.$*.$*.*$..*.$..***.*..$.$...$$.....$$$..$*$.$.$...........$...$..$.*..*$.$.....*..*.$$...$....**.*...*..$.*..*.*.*..$$.$$.*...$..*.*.*.*.*$$..$*.........$.$*$..$..$.$.$......*$..**.$...*.*...*..$****$...*.$..*.*$$.....$..
.*...$$..*.*..*....$*$$..**..*......$.$...$$*$.*.$.*.$...*..$..****$**..**.$..$.*.$$$$.$.*.*..*...**.**.....*...$$.$*...$..**..$....$.*......*$*$..$*.....$.$..*..*.$.....$...$..$..$*.....$....*....*$.....$.$......$.**...$$$.$$..$..***..*...*....$..$......$..$$.$..$.*$$*.$......$........$*.*.$..*$$...$.....*
*.*.$*....$....*..........*.*..$..$$**$**.$*$$*.$$.$.*.....$$$*.$.....$.*.***..$*.*...*....*$..*..*....$..$.....$.$.$.....*..*..*.*.....*.$.$..*$..$*...*..$.*..$**..$...$.....*.$.$.$*....*$$$.*$$$.*...$....*...**...*.*$*$..*$$.$...*.*$*............$.*.....*.$$*....$.$.$.*....$$...$*..$.*.*..*.....*$..*....*
.$.$..$*.*.*.$*..*...*...**$*..$$..*.*.$***$*....*.........*...$...$......$......**..**.$$$$.*..$$*.*.$....**..*..$$*$*.*..*.$..$$$.*$.....$..*..*.$..*.*.$$...*.*......*$....*.**$$$*.$$.$.$*$.*$..**.$.**$$.....$..$*....$......$$*...$..$$..$$.*..$.*.$....$*...$.$.$*$$$$...*..*.........*........$.*...*$.*$.$.
$$.*....*.$......*.$..$.*..$.*.$*...$..$...$.$.*$*......$..**.$$.*.**$*...$***.$..*...***$$.*.*....$...**..$.$.....$$.*.*.**.........*...$....$$$*...$.$$.........$.*......$..$....$.$.......$.$*...$.......*..$$...*.*...$.$.**......*$.....$.$.$.$..*.$.....*.$**...$$*....$***.**....$*.$$..$*..*.*.$..*.$.*$.*..
..*...$*.$.***..$$....**$..**...**.**..**..$...$.*..*$....$..$........$...$$$....*..$.$..........$*.*..$.*....*$.$.$*$..*.$.$*..$..$.*$.*$$..*..*.$.....*$....$...*..*$.*$.....**.$$..*$...$.$$**$..*......$.*....*...$.$*...*..*.*.$..**...$.$$.....*..$$.$.....$...$**..*....*$$.....$*.$........*....$$.....$$..$
.....$....*....*....$.$.$$....$..**.*.**$*.$...$.$....$*.........*..$$..$$.$$$.$.$.....*.......$.$.*.*$$$.****...*.*..$...*.$.$.*$*.$.$.*..**...*$..*..*$.$$****.$*..*$.....**.......*...*....*..**...$.*$$...*$.$$..$.....$..$.*....*$..*$.*..$*.**.*.*......$.$*.....*$.*......*****.....$$..***...$....**.*****..
............*..$.........$..$.$....*.$$...$.**.*..$..$.$.*.$.*.*...$..$.$..$$..$$.$*$$$..$.$.*..**.*.$*.$.$.$*......*..$.$.*.$**.....$*.$.$..$$$*$*.$*..*$..$...$...$..$$$$.*.*$$.....*$*$.....**.$*$.*...$..*...*......*.....$.$....*.*...$$$.*...*$.....$...$.$...$.$$.$$$.*$*...$..**..$.$....*.**........$......
$$.*.*$.$..$.*.*$.*.$...$.*...*..$....**.$..$..$.*.*...*.$*.**...$.$...*....$.*$.$...$...$$$*...*.*..$..$$$*..$..*.*..$...*..........**...*$*.$$......$.$..$...$..*...$......*..*.......*..$$...*....*.....$..**$....*......*.*.*...$.....*$$..*$.$$....$*.....$.$....$.$*.**.$..$$.......*$**......$....*...$.$*...
$.$*........*.$.**..**$.$$..$*.$$...$.*$.*.......$*$$$.*$$*......*$.$$....$...$$*......$**$..**.$*....*....$$.....*$....*.....*.**..$..$$$$...$.*.$..*..$.*****..*.$$....*.$.**.*$...*.$.$.$....*....$.*...$****.$$...$$......*$.$.*..*$...$.$$$$*.........*.*****.**.*..$*$..$..........***$$.$......**$.*$..*...*.
...*..$.*.*.*......*....*$.$....$$.**.*...$*.*$$$$....*..**.$....$....*..*$.*$$$*.*$....$..*...$$**.$*.$..*$.......*..*..*.*.*$.$.......*...*.$..*..*.*.$$..$..$...*..$...$...$.*.**...*$..*..$..*...$*...*.*.*..$..$...*..*$.$**....*$*.$*....$..*.$..***..*...$....*....$$$....*.**..$$.$$$...*....$$$....$*.*....
..*....$...$..*.*..*..$...*..*.*.......$*.*$.*..$.....$$......*...*......$.**.*.*..$..*$$...*$...$.*.**..*$*.$....$..$...*....*..*$..*......**.$*..$..$.$..$.$.*.*.$.....$*$*...$.**..$*$..*.$......*.$....*....$...$*...*$$.$*.*..$.$..*....**........$*.....**.$*.*.$**...**$.*....$.*$....$.....**.$*...*..**...$
.$.$..$......$.$*.*$*..**..$..$..*$......$*..*$...$$...$.*$...*..$*.$.*.......$.*..*...*$$.$$...**$.*..*.****..*.$..*..$.*$..$*.*$.*.**$*.....$*.....*$....*$*...$.......$.$$$$$*$.*$...*.*$*......$.*$$$.*...$.....$...*.*$$*$.$...$.$$$*.$$$.$$...$.**.*..$...*..........*.**.**$.*$.*.**...$..$....*..*$.*.......
.$*..$......*......*$.$.*.*..*......$..$$..*$....$*$.**.$.$..*.$..........*....$...*..*....*.*....*$$$$$$.$$...*...$*..*$*.....$..$*....*.*..*.$*.*.**.......$..*.*$$**...*.*.*.......*$..*.$...$..$**....**..$$$..$.$**.*.$..*.*.$..$$.....*.$..$.*.$$.$**..*.$...$*$.$..*.........*$...$.*.$.*.*.$.$....$*.$$$...*
..**$**...*$..$...*$.*.*.$$$*..*$..$.$.......$......*.$.$.$..$$....$...$*..$$*.$.*.....*.$*.**$.......*$*.*$*.$*.......$$....$....$..*..$.*.*.*...$...$$$..*.$........*..$$.....*$$$.*$..............$$.$.....*$$$$..$....$.$*...$......$*..$.**..*$.$.$..$.$....***..$.$$.*......*................***....$....$*..$
$.$$...$$...$*...*$.$.$.....$...$..$.*........*.$*$.$..*$....*..*..$.*.***$...*.*...$*.***....*.*.$...$..$.*...*$*$.$.$.$.......*..*$$..*..$.***.*$*$*.*..$*....**...*.....***..$*.$$.$.$.*...$*$*$.....$.*$......*..$.$.*..$.$*.****..*$.*...$*.**............$....$......$*$*.$.*....$.....$....*....$.*.$...$....
......**.*.....*$.$*.*.....$....$$$....$....$*....*...$$*.$...**$.$$.$**....*.....*$*$.$.$..$**...$.*.....*.$....*....$$$...*.$..**$...*.**...$**.$..$$**$..........*.*...**.$...*....*$..$*$.$...*......$....$........*..$....*.*..*..*..*$$..*..*....*.*$$.....$...*..*....*.$...*...$...$*$..*$.*.....$...*$*.*..
$.$$.**...$*$$...$.....$..*.......**...*...$.*$$.**.$.*...$.*.*..*...*.$$..$..*.$..$$*.*.*$*......$*.**..*....***..$..*$*.*.....*..$.*...$........$$..*......$*..*$..*.***.$*.$.......*.*$**.*$*$**.$..*$.$.*.$*$*$$......$.$.$..**$.*.$*$$.$.*..$$......*.*...*..$$.........*..$*.$..$..........*.$.$..*.**....$$*.
**..*$.$**$....$*.$.....*.........$$.$*....*$......*.*......$...*$*..$......$$*...$*$...$.$$..*...$$...$..**$.......$..*......$$$**$$.$*.$..**..*.*.....*$....$..*......$$.***....*..*...*.....*$*.$.$..$*.$*..*....*$..$*$*$*...$.*.$*$....$*$....*.$*$.....$$$$..*....*$.***$$$*.$......*...$*.**.$....$..*$..*$..
.......$.**$$....*$$...*........$.$$.$.**..$.$*..*$.$..$..$.$.$$$$....$..$..$$*.$.*$$$.*.....$...$$*.....*...$.$.$..$....$..*..$..*$.*..*.*.$.$$.....*...........$...*..$.*$.*$*..$.*...*............*...**....$*$$.*..$$...$..$...$.*$...*......**...*$.***..$..$.$$....$.$.$*.*...$$....*..$*$......*.*..$*.....**
$.*.$.$$......*..$.....$*...$$....*...*.$$$.$$.$*.....*$.$$...$*.$..$$*.*.......$.$...*.....$.*..$$.*..**$...$*...*.$..**....$$*$...$*$$.$...$$....*..$..*.$*.....***..*.$$...**...*.*..$.$$.$$....$...*.**.$.*..*.$$*$*$$.**...$$..***$$*$...$......$...*$..*..*...*.*......**$*..*.**...**..***$..*....*$$.*$.$$.$
..$$.*.$.**$.$...*....$*.$*$.$..$*.$*...$$$$....*$...$.*....$$*$.$$.*$.....*....*.*$*.*$.$..$.$..$$.......*...$.$*$.$..$*****.**$....*.$**.$$....*....*$$*$$*..$...*.$.**$..$$$.$....*$$*.$.*$$$....*$**$$.*.$..**.$...$*.*.$...$*.$....$.$....$.$*...$.....*....*.$.$.....$...*$.*.$.$...$...*.$.*$*.$$.$*..*$$.*..
.$....$.$.*$...*.*..$..$..$...*.$..*.*$**.$..*..*.....*..$....*$$..*..**......*...$*.*...*..$.$*..$.*.$.*.*...$$*.*.$..$.$.*.$$..$$..*...$*.$...$.$.....*..$..$.$$.**$.$$$..*.*$....*$.*..***......*..*.*........$$$*.......*.$$....*...$......*.*$*.......*$*$.........*.*$..........$.*.*........$..**.$..*.*.$*.$
....**$.$*...$.$.*.*.$.**....$....$.*.$..$...$.$$$.$.$.....*.*.$.*........$........$*.$.*......*...$*....$...$$.$.*...*...$$*$.*...*..*........*.*.$$..........**$.$*....$.*$$....$$.....$.$*...$***.*.....$**...*...**...**..$$.*$....$...$.*.$.....*..*...*......$..$$....*...*$...*..*..$..$*.*.$*.............*.
$...$$*$.$$.*$.*...$*..*..$....$.**..*...*...*.*......$..$$$.*$...***..$.*$$$$*.$.$**..$.*.*$**.*......$*.**..**$.........$*.......*...*.$.*.....**.*.$*$.$*.$....$...*.**.....$....**$**...*....$.*$$***.$.....$..**..*.....$**...$..$.$.*...$$..$..*$.......*......*$$....*...$.....*......*......*...*.$$*.*..$..
*....*.$...$$$...$.$..$.$..*..*.$...*..$..$*$.$.......$$*.....$$.....$$..*.....*$..**$.*.....*.....*$.$*$..**.....*.....$...*$$**..*..*..$*.*..*.*.*.....$*.$....$.*$*.*..*$*.$*..$$.$$...$....$*$*.$*...*$.$..*$.$.$.$.*....$$..$.$$....*$......$*$.*$$....$$......$..$.$...$...........$....$.$..*.$....*....$*.$*
*.$$..$.$$...*...**...**.$.....*......$.$.**.*.$.$$.....$*.***....*..*..**.....$*...$$$...*$*...$$.$......$*.**.$...*.$..*.$$.......*$.$..*$.*$*$.*$.**$*.*..***.$$..*.....*...*..*.*.$.*$$$..$.**.......$.$*$..*..$...*..$..$...$**$*.$$*.$.*$$..$..$.$*****$...*.*$$.*.....$$.......$.$..$*.$.......$$..*$$......*
....$......$$$...*..$$**...$....*.**$.*$.$..*...*.*...*....*.*.$....**..*$.....$$*.$..$$....$.....*$$*...$.$.**.*.$*.$**....**$$$....*..*.....*$$.$*$$**$..*.$.$**.....*$..*.*$...*$...$.$..**$$.*..*..$**.*.$..$$....*.$..$..*$*......*.....$*...*.**......$$**..$..**.....$$.$*.$....$.*...*$*.$.*.*..$.**.$....*.
*.$.$.*.....$$..$..$.......*$**..$..*.**...$...*$$$*****$....*....$*.$.*...$*.*.**..$*$$*$$$...$.$$*.$.$$$.$..............$$....*...$*..$..$.**$....**.*$....$*$*..*..*.$...*$$$$$..$$....*$$**......*.*....$......***$$.*.*........$.$.$.*.*.*$.....$.$.$*$...$..*$.$*.*$*.*$*....*$....$.$*.$.$.*$*$$......**$*.$.
......$$.$*$.$$......$*$.$.$...$*$.....*...$.$.$.......$*.*$....$...$.....*.*.*..$*...$.*..**$*$.*.*....$..*$$........$*$$..$.*.....$.$*$.*$$..*...*$.*..*....$.*$$$**$$$...$..*.$....*.$*.$*...*..$$$...*.....***.$.....$..*...**....$..$..*$$..*.$$*......*$**..$.**...*...$*.$*..$.....$*..*......*..*...*..**.*.
..$$$*.....***......**.*..$.*..*$$.$..**.......*....*..$....$$.*...*$...$.......$.......*...*..$$.$....$..$.*..$..$....*$..$.$**.$...$*.$*.$**$.*...**.*...$...$..*$$*$...$..$.*.$.$*$*.$$****$*....$$$.*.$..*$....$.*....*.$*$*$*...$.$.*$.**...*.*.........*.*.*$..$.$.*$..$.*$.......$$..$....**.$......$.$*$$$.$
..$.***.....*$$*$..$$....$.*.*....*.$$.*..*$...$.....*.*........**..*..$...**.$.....$..$..$*..$$.$.**..$*$$..$...*...*.$..*.....$.$......*....$$....*$$.$.$*$.*$.**..**.$.**$...$$.**$.$$........$$......$*......*$..$$..$$.$.***.*.*....*.$$*$*...**..$$.$...*..$**.......*$.*......$...$$.$$*..**...$..$.*..**.$*.
$..$.$.$.$..***...$$*..$.........$.........$.$..$*..**...$...$*..$....*$$.$......*..*.......*....*..$$.*...$$*..$*...*.$..*..$.$......$$.**$...*.$.*.$..$..$...$.$*$*....$*..*.$..$$$..$..**..$$*.*$.$...*...$..$**.$.*..*.$....$$*$..$*..*$..........*...*......*..*..$........$..$......*..**...*...****...*....*.
......$........*$*..***.*..$...$$**..$$$..$.....$*.$.*$$......$..$**.*...*.$*...$.$.*.*....*$.$...*..$$............**$*$*..$....*.*$.$*$$.*$*.$...*$......*$*$.$.*...$.....*..$.$.$*....$.$*........*$*.$*$$.$.*.*..*...*.$...$....*.$.$.$*$..$...*..$..*.$.....*.$.*.$.....$...........*.......$*$..*.$*....*.$...*
.**.$..*$.$$$*$.......$.*$..*.*.**.*$$..$.*..*.......*.....$..$...**$...$*.....$$*.$$..$..$.*..$..*...**$.$*..*.*......$$.*$*......$$$*...$$....**....$$..*$.$..*...$..*.........$*.*$*.*..$....*$$.$...*..$....$..$....$...*..$*.**.$....*$*.**.$.*$..$.....*.*$....$*.$...*......*....$*$....$$$$.$.$$.**$*.....$$
.$.$.......$...**..*.*.**........*$.......$*...$...*..**...$......*$.$.......*..*$...*.........$...$**$$....$**.$...*.*$....$....**$$...*.*..........**..$*......*..*$.$$.*..*..$...*..$*$**.$..*..$$....$**$.......$$$.*$*..*..*.*$...$*$.......*$$..***.$.*......$$.$.$..$...$$*...$*$..**..$...**.**.........***.
.$.*.*...$.$$....*$.*...*$$*..*.$.$..$...*$........$$***.$$....$.***..$.$$*.$..*..*$*...*.$$*$$*.$*.*.$....**....**$*.*....*..$...*...$***$$$$$.$..$..*.*$.$*.$.$$***...$....*.$*$$..*.....$$$*..$*$.*.***....*.$..$..**..$...**$$..$.*.$......*.$.***$.*...*..*$$.*.........*..$..*...$***....*.*$......$..*.**$*..
$.$.$$$$...*$.$..$..$$.$.$$.$.*$..**..*.....**....**..$*$...*$...***..*...$$$...$**..$...*$$...$.......**.......$.......$..$..$.$.$$$$..$*$$*$$.*.$.**.$...*.**$.$......*.*.$..$.$.$$$$.....*$.*.$..*.*$*......*....$..$*.*.....$...$*......$$.$**..$*$..$...*..*....$$...*........$..*.$**...$$..*.....$.$....$$...
**..$.*.....$$..$.***..$$.*$.*......$$.$..$...**.*$***.*.*..$.$*....$$..*........$....*$.$.$*$$...*$.*.$.*.*$$.*........$......*.*..$$..$.***$$$*...$$.$$.**.*.$*$..$$.*...$$$..$*..*.$$...$.*.$$.$.*.*..*$..$.$..$.$.......***...$.$**..*$.$.*.$...$$..$..*..*$....$..*.........$$$.*....$*.$*$.....$.*.**....$.$*.
.*.**$.$$....*.*..**..*........**.**.....*$...*$.*.$$*$..*.$..$......*..$...***...*.$.......*...*$.$........**$.*..*...$**.*......*$$*..$....*...$.$*$$....*.$.....$.........*..$$...$.*......$*.*...*.$$.*..*$$**..$**.*..$$..*......*.....$.*.$.*$...*..**......*$$..$..*....$.$$*......*.*........*.....*..*****.
....*$...*$$.$.$..$...$......*...$.$$$$..$.$*$**$..$.**.*....*.*..***..$..*$.$..*$...$$.*.$.$.$..$*.$*$.$..$...*..*.*.*..*$...$....**.*$...*.$....$$$$.$...$*...*$$..*$$$$$.*.**...*$..*$$....*...*.*.$$.****.$$.$...*.*...*.$$....$...$$.*$.$...**.**$....$.$.**$.........*....$.**...*$.*$.**........$$.**.$..$...
.......$...*...*....*.$*.....*$....*.*..*.**....$**.$*..$$*...$....$.***....*$.*$.$*$$*.*$$....*$....$...........$....$$.$$.$.*.*$..$...$**$...*.*.**$.*$*..**.*...$..***...$*.*...$.*$*$..*$*...$.*$.*....*.*....*...*....$..$*.$.$.*.....$*$...$*$.$..*.*..*..$..*....$*$...*..*$..**.$..$....*..$.....*.*.*...$.*
*.*.**$$.$*.$..*$..$$.$*...*.$*..$*.*$$*...*..*..**$$......$$.*$$..**...$*.$..$.$....*.$...$........$.*..$$.*.$$...$..$..$..**$.*..*$.$*.*.$**.......*.$$*$*$$$$$.......$*.$...$$..$.$.*.$*$.*$*....*..$.$.***..$.*$...$$....$$.......**$$..$..$.$.$$*$*....*$$.*...$$....*.$$$...*..$....*.....$.......$$$.$$......
......*.$..**$.$....*............*$*$$*...$.$$.**...*..$$$..*$...*..$.*.....$$$.*$$..$....*.$.$..*.*..$....$.*$...$....**..*.$.$......*..............$...*$$$**.....**.$..$.$*$..$.**$........*.*.......*..*$.$.*...$$.*$.$.*....*.*...*...*...$*.$.*.$.**.$...*....$......**.....$....*$***.***....*....*$$........
*$$.*..$**.......*..*$$.$$..$..$*..*.**..*...$$..*..*...*..*.*.$$..$$*.*.*.$.*.*....*.*.*$....*...$*.**.$*.$*....*$.....*.$....*..*..$...$.**.**.....*....*...*..*.$$.....$.*$.....$.....$...***.$...$.*.*.*$.*..$.$.$$$..$...*..**$*.....*.*.*........$..$$*...**...*..*.*....$*..$$.*...*$**..$*....*.*$.....$..*.
**..*..$..$.***..**$..$..$..**$.*$***....*..$...$.*$..*....*.*...$.$*.......$$*$....$**..$..*$...*.......$$....**.$.*.....$.$*..$.$$.$.*.$.$..*.**..$.*$...$.......*$$$...*$..$$..*..*$**.....$..$.....**..*.$..$..$$..$*....$.......*.$.....$$...*.*.*..$*..$**$$.$*....$*.*.....$*.$$.....$.$..*.....$.$.*...*$..*
........*.....$*$*...$*.$..***..**.$..$...$..$...$$..*........**..$.*...$.$$.$.*.$*.....$$.$*$*.*.........*...$...$.$..$.*$**......*.**..*..*.$.......*$.$...*$....$.*.$....*$..*.*.....$.$*...*....*......$.**........*$..**.$$..*..$....*.*$.*$..$.$...***....**.$.$.****$..***...**......*....$..$$....*$..**....
.***.$...$$*...$...$..$..****....$....*.**$....$....*$$..$*$..$.*$.****..$...$*$.*$.*...*$.*....$*.....**.$..$*.$.*......$$.*..**.*$.......$.....$$...$$$....$.$...*..$..$.**.$$.$.....*.*.*$........$.....*.**...$.*.........*.$....*..**.......$.....*.*........**.....*.*.$.......$.$.$$..$.$...*$..$....$*...$.$
....$.$*.*$.$$**.....*.$....$*.*........*....$..$*.*.$*..*$*..$.$**....*...*.$.$...*$$.$*$.$$*.$.**....*..$$.$.....*$..$**.*.$$*$..*.$$...**.$$*..*.$$**..*.$*.*..*..$..**..$.*.$*.$..$..$*..$*.**..*.*..$.$....$$.$*$$*$....$*$.*$..**.....*..*$.....$..*$.$..$.........$.$*$$**.$......$.$......*.$*$...$.....$.*.
.$.**$.*$.*.*...$.$$.*....**.$.$*..$$*....$...$.$...*$*$.*.....*..$.$.$*.**.*........**$.$........*.............$..$.............**.*.$$*$....$$.$.$$*.*$..*.$.........*$..*.$*.......*$....$.$**..*...$...$**$....$......*....$..*$.*.$..**..*$..*...$....**$.......*...*.$*$..$**..*.$*$**..*..*..**.*..*..$..**$*
..*....$..*..*...$..$...*$...$*..$.$$*.$..$..*..*..$$.*$$.**..*.$..$..***.$.*.*.$$.$$*..*...$..$.*$..$.*.$***$$..$........*.$..*..*.**..*....$*.*...$.*....$.......*$.......*.......*...*.$$*.$..$.$**$$$..*.*.*..$...*..**.$.$$....*......$$.......*.*..$*..*.$..*...*$......*............$....**.*.$$*..*.$......*
$....*.*......*.$.**...$.*.$..*$..$$.*$*$..$....$..$**.*..$$.***.....$.....$.$$*$*$....*..*..*.$...$..*...**$*$..........$.$..*..$.*$$$..$$.*$.$..$$.$.....$*.....*..$*...*..**...$...*.$*.*..$.*.*.*......*$*...*.$.*$*..*..*.$$..**....$.***.....**..$*......$$....*.$.$..**$*...$.$$.$*$...$.$.$*$..*$..*$.*..*$.
...$.*...........*..$$.***$****$....$...**$$.$$.*.*.*.$...$..$...**.$.*....*.$.$.*......*....**...$...*$.$.***.$..$.......*.*..$.*.*.*....*..*...*..*.**$..*.$$**$$$...*..*.$..$*.$....*..$..*$.*.....*.*$$..$$*...*.*.*......$$*$*.$..*.*..$......$..**.*$*..$$..$.**.$...*....$*$...$*...$.*..$.**.$..*.$...*...$*
....$..*.....$.*..$.*....*$...**..*..$*...$.*.*...$.....$...**$.....$........$.$....*..$.$$$$$*..***$.....*$......*.$..$**.$**..$$.*...$...*.$*.......*$*$..*$$..*$*.$*$**$$.....**.*.***.$*..$.*$*.*$.....*.*$$**$*..$..*.$$...*....$*.$.....*..$..$....$..*$..$*.$$.*$....$.$.**......$.*..*...*.*..***.*.**..*...
...****$..*......$.$....$$...*.*..**$..$..$$$..$*...*....$$*.$**......*...$$*$$...*......$*......**..$.....$$.*.$.*$.$.*.*..$***$.*$*.*..*.*..*..*.......$.*...**.$...$$..$*..$*.......$.$$*.....*..*$.$.$*.$$**$..$.$....*..$$.$....**..$*$.$..$*$...$..**....*$*..$..*..*.....*.....$..$..*...*....$.**..$$$**..$$
*...*.*......*.......$..$..*.$...$**$$..$*.*.$$$$*$.*..$..*..$$......$..$.$**.$...$.*.......$..$.....*....$.*$$.*$..*..*.*$..$*........$......*$.$$....$*$....**......*..*....$.$$***..*.......*...$*.$...$$.*.$....$....$.$..*......**.$..*$..$$...*$.$$$....**.*.*$**.$*.*$$.*....*$.**.*$.$$.$*....$**.$........$
*$.*.$*.$...*.$*...*.$$..**.....$..*.....$**........$.$...*.*.**....*$...$...*$.$$*.*$..*.*$..$$*.$$...$..*..$*...*...**.........$*$.$.$**...$.**..$..$$**.......**.$...*.$$..$.*.*$......*..**$..$*..*......$..*.*.......$**..$$..*.....$.***.....$.........*.*.$...*.$.$$$$...$.*..$$$**...$.*.***$.$.$.....$*$.*.
.$.$....$$.**.$....$*$.*.**.*.*$$$.$*.*.*....$.....$$.$$.*..*...$....$...**.........**..*..$$.$....$*..$$..***...$*.*.......*.*.***....*$..$...$.$..$..*$.*$.*..*$.*.***$.....$..*$.........*$$.$.**..$..$..$*$......$*..$*....*.*...*$**..*.........***.$.....*...$.*.....**$$...***$...$$$*..$.*..*$.*..$.......*.
*...$..**....*.*.$$.*$.....*.*...*.......*..$**..*.$*.*......*....**.*.....**..*.......*$$...$.$.*.*.$...$......$$$...*$$...*$..$..$.$.$....*..*......$...*.*...$.*..*.....$.......$.....$$....*.$.*..$*.....$**.*.**$...*..*..*.......$..$.*...$$...***$***.......$..$.$.$..*.$.*$...$..$...$$$*.****..$......*...*
$*..$.$....***.$..*$$..**.*..*..*.....$..*..$.$..$$$.$.$..$*.........*.*.*................*.*.$..*..$...$........$....$..$$..*.*...*...$.**.....*$.$$.$.$..*.$$...$$..*..*.$$$..*$...$....$*.*$.$...*..*....$*.$..$*$..**$*..$*$$...*...$.......$.........$.$...$*....*.$...*.**.*........**....*.*....*.*..*..$*.$*
$*..*$..*..*.........$.$*$...*....*.*$.*..*..$.*.*..$$.$*.....$....$...*$.*.$...***..$.*..$.$....*.$*.....*.*.$..*......$..$*..$$.$***$$..*$.*....*.$...**...$.$*.*$**..*..$$$$.*...$.$$..$**..**...*.$...*$.*.*$$.*.$.$.$$$.$$$.$..**$.$.**.*..$.*.$....*$..$$.$****.*..$*.$$$$$**...**.*.......*...*..$.*.*.$.....
..........**....*..*..$.*$.$...*.....*...$..*........$...*$...*.$..$......*$$.**...............$.**$**$**.$.$*...*.*$*..*.........$.....*.$..$*$...*...*$.$*....*$..*$....$...$$...$....*.*...*...*.........*.*.....*....*.*.$$....$.$$....$...$..$..*$*...$..*.$..$.*..$*.*...$$$...*..$.**..**$**$...**...**.*$$.*
.*...*.$*.$......$......$$$....*..**.$......*$.**...$$***.$.....$$**....$*...*........*.*$.$$*.....*.$...$*.**.$$.$.*$..$.**.$..*.$*......$......$...$..**.$$$.$$***...**.......$....$*.....*....*$.*.....**.*$.*..**.$*.*.*......*$*.*....*$*$.$..**$..*..$*$$.**....$.....$$..$.....*..$**.$.$$*$........**.*.$..$
.***.$.$.$..*..........$**....$$..*...*.$..*....$$$*.$$..*$*.*...*.*.......***.$..$$.$$....*.*.$*$$............$$*$....$...$..$$.*....*.$*.$$....$*..*.*.***$.$.$*.**$**$...*.*.$..$..$.*$..$$$*.*....$....*.*..$.$.$.....*..$**..$$.*.*...$*$.*..$*...*$.......*$*$......$.*.......*$...$.$....$...$**..$..$*......
.....*.$*.*.**..$..$..*$.*..**$..**....$.....$$*.$.......$...*....$*.$..$.$..$*.$....*....*.**.*.....*.*.*..$$**.$..*..*.....$$*.....$..$.*.....$$..*$*$*$.$$...$.$$*$.*..*...$.......*$..**.....*.$.$.*$...*..$..*...$***$.......$$*..*.$...*.......$.$*.*$..*.$**.*.*...*$**.....$***....*$$$.*..*..$.$...***...$$
$*..$.*.*......*$.**.*.$.$...**.*........*..$$**$.$*.......*.$....*.*.$$....*$...............$..$$*.$$....$..$.....$$.$..$..$$..*.*...*..*.*....*.*.....*..$$$.$**$$..*...*.$.$*.$**.$**..*.......$*..**...$.*$..*$*...**$....$.*$..*$....*..$*$$...*.$*...$...***$.$*$$..$...*.*.*$$.....*.$$.$.$..$.$....*....*$.*
..*$$.$*...*....*..*$$..*.*.$.$*$*.....**.$...*..*....$*....*...$$*$....$..$$..*...$*.$.....$*....$$..$.$$....$...$....*.*$$$$.....*..*.$.....*$..*******.....*....**.$**.$.....$.*.......$*$*$$*.$$*.....$.$.*.$*...$$........$$......$*$...$.$...$$**$**$.$$*.*.**...*....$$*$$.$$$.$$.$..$...$.$*..$....*..$$*...
....*$*.**$*...*.*$.$$$..$..$.$.$.....*.........**.*..*.*.....$.**.$...$.*.**$.*...$....*.......$......**.$...**$.$$.*....*$$.*$...*$......*.**$**.**.$...*$$*.*.*.*......*.*.$.......$....$...$.....*.*.*.*..*..*$....*$*....*.*.*.**...*.$.*$.$.*..*....**$...*......****.$*$....$.$.$...*...**$$*$.*...$*.*.$.*.$
.$....*..$*$.$*...*.......*..*.....$*.$.$..$$..$.$$$*..*..$.$.$...*....$$$$.$$.**$*....*.$$.*......*.$..$...$*...$..$$......*...*$...$**.....*.*$*.....$*..$**..*.*.......*.*..*$....$...$$.......*$*.*.**$.....$.*..*$.$**.$.$*$..****.*.....*$....$*...*$.$...$..**..*....*.*.$.$*..*$.$$..$$..$.$.....$..$$......
.........*.**.....$$.*$.$..$$*..$$..$.$..*.$..*.$......$.....$*$$.**.$.$.$*...$...*$........*..$.*$..$.$....$$.*$.**.*......$.$$..$$$....*.$$..$...$$.*$..*..$*$$*.$..$$.*...*$$*$...*.$....*$*....*$$$..*.....$.....*..**.*.$$*..*$...$.$*.*.*.*...*.**.*$...*$*$...*.*.*.....$**...*$.....$*......$*.$**......*..$
**.*.......$*$$...$$*...*...*.......$*.$****.*.$...***$....$$.$...**$*$.*.*..$...*....$....$.....*..$.*.*$$$..$..*....$..$...$$*.**..*.*..*...$.......$..$....$.**.**....*.*...***.$.....*$$$..*.*.$*.*.$..$.*..$.$$.$..$*$**$.$....$**...*.*.*..*$..*.$$.$...$*.$.......$$*.$...*...$......$.*.$...*..$*$.$.$.*..*.
....$.*....$...*..*...$.$*$$.*.$$*.*...*...$.*$.$*.....$.$$.$$..$$.$...$*.**..$$.....$$..$....$$$...$*..*..*$**.*...$*.*.....*....$$.$..*....$$....$......$$*...*....**.*.$..$......*$$..*.$.**.$.*$.*...$*.$..*.*.$$...$*..$**$....$.....$..........$.***.$*.....**$.**.$...$....*.$.*..*.$......*..*.**$.$*.....$$
...$.$.....*..*$***.$*..*$$$..*.*...*$*.....*$...$....$*...**.$..$..*...*.$****....$.$.......*.*....*..**$.$*...**....$..$*$.*.........*$...$.**.$***.......$.*.**.$.............**$$$.$*..***$...$$..*..$...$**.$.....$$...$..$..$.$.........$...$$.$.....$*.*.*..........$...***.....$$....***........$$$.*....**.
.$.$$..$...$$$..*$.$..*.*...*...*....*$.**...***.*$$........$...$...$.*.......*..*.**.*$.$*.*....*......*.*...$..$...**$...$....*....*..*.$*.*$...$.$$....$$.*...$...*$..$$$.........*..*..$..........$....*$.*$*...$$$.*....*.$..*...$..**$..$.*.*...$..*.**.*...$.$......***..*.....$.$..$.*.*.**$..*..*$*$.$..**.
$*.$$.$$$...*.....$........**$.$...**$.......$$...**.*$..**.$.*$$.$$.*..$*.$.$*.....$$***...*..$..$***...**....$.*...**.$$**$.*...$..*$*$*.$$.$**..$*.*....**.**$..**$...*...*...$$*..$$...*$*.....$....*......*..$$.***$$..$$*...*....*.$.$..***....*.........**.$..*$**..$$.*..$...*.*.*$...$.*....*$$$$$....$....
**.$........*......$*...$.**.$*....*..$*......*.*....*..*...*$..*...$.*......$.$*.$.$.$$..*....$$..*.$..$.$.*.*$..........*.*.*..*.$*......*...$*....$..*..$.*$..$.$.....$**.*....$$.*.$...$$..*...$*..$$....$*...$*.$$..$.*..*...$$.*......**...$*.$.$$.*.*$.$$*....$.*$$...$*..*$.*.*..*......*$$.*.*.$*$$.*....*$
.*.$.$$.**.*....$.$..$...$.*..$*...$.*..*$.............$......$...$$....*.*....*$......$$....*$*....*$*......**..$.*.*$.*$..*..*..*$*..*.*.$.*..$*$...*...*...$$*.*.*..$$**..$**..*$.........$..$*..$$.....$*$...$..$.*.$$$$.*$...*....**$...$*.......*...$*.......$*..*...$.$...$...*..$**..*...$..*$...*.*$.$.$$..
.$.*$*.$**$$...*.*$*$**...$....$....*....$....$.........*.$..$$$..$**..**...$.*..*.$.**.*..$*...$$$*...*..$*...*..*.....*..$...*...$....*..*$..$...**......*...*..$...$**.*...$.$.*...$...*...$$...$...$$..*.$$..*.*.*.$.*...***....$$......*...*.*$$*....$.$...**$.$$$.$$.$.*....$*....$.*..*.....$*.$..*...*....*.
...*$.$....**$$.$$*..$.$..$*$*$*.**..$.$...*.*.*$**.***..*.$*...$....*$$...$.*.*.$*$$...*...$$*$*$..$*...$$*$*.$........*....$*$..*.*$*.*..*.*.*..........*.$$.$.*.......$*$$$..*.**..$$$.*$..$..**$.....$.$.........*.$....*$..$*$.*.*$$..*...$$*..*.**$*$.$.*$$$.$*....**..$..$..*$.*..$..$....$*......*.$..*.....
*$...*.*.***$.$$..*.*$......*$*$*....**.*$..**....*.*.*...*$*...$.$$.*......*$..$*.*.$$.$..**....*.$..*.*.$$$.*.**.....$.$..**.$.*$.$.$*.*.......$$.....*$.*.$...*$.....$..$*..........*$.$.*$......*..****...*$*..$$.$..$$*$...........***..*..*$*..$**..$.**.$.$...*.$$*........***.....*$...$....$.....$.*.*..$.$
...$...*$...$.$..**....*..*..$..*$$.*$.....****...*....$..**.....$.$...$....*.*..*.....$***.*....$$.$.$.*.....$.*....**.*..$..$..$...*.$..$.**$....*..*.*...**.*..*..$.*$...*..$..$**..*.$.$$..*..*....**...$.....$...$.$***...$.$.....$*..$..*.$.......$$.*$.*$...*$**......**$*$*...*$$......*$...*.$.$..$$.*$...$
$.*.$.....$...*.**$**.*..$.*.*.$**$..$*...***$$*$$..*....$$.$....$$*..$$$...*..*$$*..$...*........$.$*..*....*...*.**..*..*.*......**.$..$$$$.*..$.$.....*.$**.$*$.*.*...**.$..*..*$.$$*..$..*$.....$......*.$$.*....$...*...$$..$.**.$*$.*..*..*..$*..$..$*....$$*..$*..$*...**$..**$...*....$$.$...*.$*....$$$..$.
..*$.$$.**..*...*.$..*.*$.$...$..*$$.........$.*$**..*....*$.*..*.....*$$**.*.$**...$$*$.$..$*......*......$$*.....$*$$.*....*.**$*.*.*..**...$*.$..$..$.**.*......*.*$..$.$..$...**..$.**$*..*....$*...$$....**.*...$.$$*..*..*...$$.$.$..*...$$$.....$..$.$.*...$$.$.......*..$$*.$$**$*$*..*.*.$.$..*$....$...$$.
...$.$.$*.**.*..*....$$...$.*....$...$.$..*$..*...$...$$*$*..*..$...$$.....*.....$..$..$$..*$....*.*$$...*..*$$.*$$.$$..*.....**......$.**.....*$...$$$.*$..$...*.$..**...*.$..*..*.$....$$*..$.*.$......*..*..$..$$$*..$.***.....*$.....$.***..*..*$..**$.*.$*$*..*.$*$$*...*$.*.$.$..***...$*...$............$*...
**$...$.....$*....**....$*$...**.*$...*$..$.$**..$.....$..**.$..*....$.*...$.$*$.$.$.....*$$.*.....*....$.*.$.$..$..*$...$*$...*.$......$...$$.....****$......***.*.***$$$..$$**..*.***$....*...*.*.$*$.......$...$.**..**$.$*.$..$...*..*........*.*..*$.$.$.$*$$****...$........*...*$**$.**......*.$$*..$*...**..
$.$.......*....$.....$..*.$*.........*..*.**$..*.*...$.$.......**.$.$......$.*.*$.*...$.$....$..$.*$*.*$....*..***...*..**$.$*..*...*.$..$.*...**$$*.$..$..*.$....$$.*..*..*...*.*.*.**$..*......*........$..$*.*$....*........*$.*.$$$$$$*..*.$..**.......$..$....**..*$.*..*..**.*.$.$..$......$..$*...*...$.$..*.
.*......$.$.$.$...*$$...*..*.....$...*..$.$*....$$....**.*.$$*.*.*.*..*..*.$.*...*$*.$**.....**.*.$.*.*..$*.....*.$$.*.**..$.$..$.$*..*........*$$$..$.**......*...*..*.$.***..*.....$.*..$...*.**..*$*****.*..$**..**....$$*..*.$.*$..$..$..***......$.$..$....*.*.*...*$**.**...**.....$.......$*$$$$$$.*.....*.*.
.......*...*..$$*........$.......$***.*....*$.*.*...*.**.**..$.*$.$.......$**.*.*$...*....*.***$*..*.........*.*$..*$$..$$..$*$.$*$.$*.$....$..*.$.$$..*...*..$....$$......$$..$$$.*$*..*.$..$$.*.*$*.*$.$**.*..*....*.$$**.$**.*.$.$.$....*$.$..**.*..**.$*...$.**.....**..$.*..****..$.*.$.*...$..*.....$.*$...**.
..**.......*.$.*...$.....$........*.*.*$$$*.****....$$.$...$......*..*.$..$*.*.*.$**.*....$$.$....$..*.*...$*..$.*..$...**.$...$.$...$*.$...*..$$.*$*.......$..**.**$*.*.**....*...........*$..*.........*$.$.*.*...$......*...$.$..$.$....*$.*..$..**$....$..$*$*.*..*$.......*....$..*...$$......$...*$.*.*..**.**
....*$*.**.$$*.*...*...$..$..*...**$.........$......**...$.....*$.$.*..*...$.$.**.$*$........*$*$.**..$*..$.....$.....$*....$..$...*$*.....*...*$*..*....$.....$.*..$.*...$.$$$*.$.....*.$$.......*..**$$.*....$...*.....*..*.$...*.*...*..$**..$.*.*.....$$...*.*...$$*****..*.**..*.$.$$$.$$..$$..........$*......
...*.*$.$*.*.**..$..*.............*.*..*...$.*...$**$.....$...*$*$$**...$$$*$*..$...*..$...$$.$.$...*..$$$*......*.*$..***$.$....*.**.**......*..$..$.$$$.*.$.....$..*$**$.*..*$*....*...***...$$..$....$.*.$.*......*.**.$.$.**.**..*.*....$...*.$*..*.*...$.$*...*$....*$*..*......$.$..*.**$.**....*$..*.$$*...*$
$.....$......$.*...$*$$$..*...$*$.$.$.$.*.*..**...*.*$........*.$$....$.$..$*$.**$....$.$..$.....*$.**.....**$..$..*.*.$.......$$$$$..*..**....*.$*.**...$*$....$$.$..*..$...$*.*...$$.*...$.*$...$....$..$*.$..*$*.*$$**$.....$*$$*...*$.$...$...$.*.....$....*....$...$$*.*$.*....*..*..*...$.****....*...*.$..$$*
.$......$$$..*..$....$.*$..*..$..**$..*.....$$.$*.*$........$..*...*.*$..$...*...$..$$*..$.*$.$$*.$....***$*...***........$.$$.$..**.....*......*$..$*$...$.*$$..*$...$$..*.*$...$*..$$.$.*....$*$$$..$.....*$..**.....$..$...$..$$............*.**...$.*$$.$.*....*...*..$.*.**.$$$$.**...*...*.*...$*...*$......*.
.$........*..$.$...$**.$$.*......*...$*.......$..*...*.$$..$.*.*..$$.*$...*$*...*.......*....$...$**..*.*..**$*.$....*..$$**...*....*.*.....$*..*......*...$.........*.*$...*...***.$.***.$$.....$...$*$.$$.$.......$$....$..*$.$..$.$*$*...*$....$.$.$$.$.$.*.$...$.*.$..*.$..$.$*$*..*$...$.$....*...$$.$**$...$.*
..*.$...*.$.$$$...$.$.$.$$.*.*.$*.$.*..$..$..*.$*.$...$$*....$.$.*.....$.$$..$.*.**..*......*...$*....$...$.$$**.*...$$....**.***.$......$..****$.$...$$$.*.......$..*.*.$$$$.**.*........$.....$.....**....$.$.......*$..*..$*.$.$...$..*.$....$$..*...*..*$..$...$*...*.........*....$...**.$$.......*$....$$.$*.$
....*.*.*.*...$..$...*.......*.**$...$.....$*.*..*..$...$.$.*.*$..$*.$.*.....*$..*.*$*$.*..*.$$....*.......$$.$..*..$.**$.**.*.....$.$..........$.....*$.$$.$.$..*$$*.*.*.**.$..*...*$.*$.$.....$$..*......$..*...$**....*.**...*...*$.$.*.*..*..$.........$....$$**..$*.**.$*..$......*....*..*..*......**..**..*..
..**...*..*$..$..*$..*...$.*.*.$$*.$.$$**.*$*....*..*......$*...$$.**.*$$....$*$....**.$.$..$*.*$$.*$**..*..*$$*..$*..$.$.....*.$.......*.$.$..$..$.*.*...**........**.........$$*..**..$........*.$..*..*.$..**.$.*$$$....$.$...*....**.$.*.**....**.*......$..........$..**$..$..*..$.$.*...$.$.....*.$*...$.$.$.*
..$...$.*......$..*.**$.*.*.$..$*...***.$...*....*$.*.$$$.*.$.$.....$*$*.*........$..$.**...*....$.$......$..*.*$.$..*.$$$..*$$.*.*$*..$.$.***.*.*..*$.$**..*.*.*..$.*.*$.$.$$...$....$...**$.*.$$..$..$..*$$.*$.*$$*.$..*.....*......*...*......$$.$..$..$..$$*.*.......$$*.....$....*.$*....$.**$...$$...*.$...$.*
$.*$$$..*$...$...$*.......$..*..*$$*........$....*....*$.$*..$..$.*.*....$*....*.$.$..$.*$*.*.**$.$....*..*$....$...*..*$.$..$*.$*...*..*$...*.....*.*...*....$$$*..*.$..***....**$.*$.........**...*...$........*.*$.$..........*..$.$.*$....$.........**..$.$$....*.$$...$*$.$..*.**..$....$..*$.**....***.$.*$*..
$..$$....*..*..*..$..$...$....$.....$*.$$..$..$.*.$..**.....**$*$.$**$$...*....*..*$.**..**$*$$.*$*$*$*..$*...*.........$*...$$*.......$..$...$$.....**$.*........*$.........$$.$$.*.$$....*.$*.....*.....*.....*...$.*..*..$...$.**....*..$*.$...$$.*..$$$.$*.*....$..*..$.*..*$.*...$.$.*......*$.............$$..
$$.*.....$.$....$$*..*.........*$...*.$.$*..*.*..*...............*$.$..**.$.*..*.$....*.$*..*$$....$...$.......$$.$..$.$..*.**...*.$..*.$..$.*.*..*..*......$.*.$$.*..*.*.$.**.*$*.$*.$..$.***.****....**...*..$...........*..$...$........*.*$*..$.*.**.$...$.$.$...$*.$....*.....$..$$..$....$..**..$$..*..*....$*
.$..$$....*.*$.....*............$..*$...*$...*.$.*$$..*.$.$.*..$$....**$....*..$...$*$..$...$$...$..$..*.*$...$..*$$$...$.**.$.*.$$.*$$*.*.....$$$.$...$$.$.*.....*.*.*.$..$....*.$*.$$$$....*$...*.*.*....*.**..$..........$.*.....**$.*.....$$...$*.*.$........**.$*.$.$$.....*...$...$..$..$$.*.$.....$*..*$...$*
.*...*.....$.*....*.***...*...$**$....*....*$*..*.$*...*$.*$**$.......$....$.$.$*.$...*.$****.*$......*..*.**$**.**..*...$.$*....$.*....$.$$.*$$.$.....*$*....$*...$.....**$$...$...$.$$.*.*.....*.$$.......$$*.*...*$$.$.$.....$..$....*$...$.$*...*..*...$....*..*.....$$..$.$$.$*.***$.*.....$.$....*.$....$.$***
.$.*.*.*...$..*....*.*...**.*..$......*..$.$..$*...*$$..*...*.$..*.$.$.*....$$$.*...$...*....*.*.$...$*.*.$.$$$$$..*$..**..$...$*.$..*.$$.**.....**....**$.*.**..*.....*$*......*..*...$..$.....*.$$...$*...$*..*$$..$$.$$.*.$..*....**.*.*..$.**$.$....$.*.*..*...*..*..$$.$.$..*.*.$*.**....$..$...*$...$*..*.$*.*
.....**.$..*...*.$..$..**...$$.*...***....$.*$*..*.$*$.*$*.$$$$$.$............$$*..*.*$..$.....*.**$..$$.*..**...$..$*$.$...$..*$..*............$.*...*...$$..*...$..$$$.$$*.$*.....$..*.$.$$$.$..*....$.$.$..$*...**....*..*.$..*$*.$$$.*$...$**.$...$$...*.*.$...*..$$*..**.$*$.*..**..*.$.$*$..$$$*...$$.*..$$...
*$..*..$$*$..*$$....*..**..*$$**.$.*.*...*$*.*$$$$.*....$.$$.**$....*$.$*....$$..*.$.$$$*..**.............**..$..$$.$.$$.....$.*...*...$..*.*.$*...**$.*............$..$.$**..$.$..*.$$.$.*.*$..*.$*.$.$$....*......$.....*...$**...*..*.**........***..........$*$*.....*.**.......*$..$*...*..*....$$...$*..$...$$
...$.$$$*.*$.*...**.$$.*$.*....$.$$..*.*..*..**.$*.....*.....**....$..*$.*.*$.*.*..*.....**$.$..$..$.*...$.$$..$*.$..*$$$...$$........*$****.$*$..$$....*..*.....*..$*$.$..$..$........*$..*..$.$....$*..*......**..$**$........*..$*$.$$..$..$.*.$$...$......$$$.*..$........$*$$*..**...*.......$.$*$$...$$..$$$*.
$.....*.*...*.......***.$.......*..*.$$$.*.*$$...*$**...**..$.*.$..***.*...$...*.$*.....*.$.$..****$*$...**.....*....*...$.......$$..*$$*..*.*$*.....*$.*....$...*$...$.$.*$$..$....$.*..**.$...*...............$*..$.*...$...*..*....$*$..$**.$..*..*.$.....*..*.$$.*..$..*$$.*..$...$$....$**..**.*.....$*$.$.....
.$**$$.$*..**....$.$$........$.*....*.$**...$*$....$**.$....**......*...$...$.*...*.*.$....$..$*.*$..........$.$$.......$........$.$**.$*.$.*.$....$..$$$*.$..$..$.*......*.$.$...$...*.....$....$...$*...*$**.*..$*.$......**$*...*.**$$..$$$....*.*$$...*.*.**....$**...$$*$.$..$$$...$..**$$.$.*$..*..$..$..$$$*.
.$$.$..*...$$....$$$...*.$*.$.**..$*.$....*.*$*$..*$*.**....$.$.$..$...**$*.*...*......*$$..$$...$.$......*.*.$..*....$.$*...$.$$$.....$.$*...$$*..*.$.$$*..$*.$$*...*.*...$.......$.......*$$.*...*.*$...*..*..*...*.*.*.....$$$.$.....$.*......*..$.*..*$***.$$.$....$...$...$...$.*.*..*......*..**.*.*.*.....*$.
....$$*....*..*.*....$*$....*.**....**...$.*.$*.*....$$.*.$*.$.$**$.$.**$.*$*$$...$$.*$*..$..$*...**.*.*....*$$.$.*.$..*$*$*$........$.*.$.$.$.$.......$.***....$....$.*.$**...$*$*$$....$...*$*...$.$.***.$.*$*.....*..$.$...$..$...*..$..$..*.***..*.**..*$*..$...$$***....***...*..*$.....*$$*$..**......**.**.$$
..*..$*.$.*.*$**$*..$..$..*.$.*$.$$.*.*..$**.....$.....$.*.*.*.*..*.$.*.$...**.........*..$..*$..$.*$$*$.$$**.*..***..*..$..$..$.$.*...*$*$....*.$$.**$.*..$.**..*.......*.....$.....$*.**.*.$$....$.*.*..$$.$..*..$$*.*.$*...*$..$*...*..$.**....$.$..*.$...*.$.$............*..$......$*..*.*.*..$....***.*...$$.*
*$$..$*......**.*..*....$**$$$..*...*$*$...*$...*.$.$..*.*..$.$.*.$.*...$*.$*...*$..*$$*.**...*$...$**.$$$..$$......**$$*.$.$$$.*......$...*$.*$$...*.$.*$...*.$.$......$..$...**$$...$..*....$**$*$..*.*.*$..**$.*..*$....$.....*$.........$..**..*.$.**$.$.......$..*.**...$**...$.$$$$.*...*$..*.$$......*.$....*
.$..*.....$**.$.*.....$.$*.$..$..*.$*.......*.............$.***.*$..$*$$$.$*....*$.$...*.*........*.*$...*.*..*$.*..$...$*.$..........$.*..*...*.........$*...$.*.$...$*...*.$*.$.*.**$....$$..$...$...$$.$.$$$**$...$...$$...*.*.$$..$....$*...$*......$$*..$..*.......****...$....$....*...$.$...$.*.....*....*...
*.$.....$.$...*...**....$$.*.$....*..*....$.$$.*$.$$*..*...$..*..*$.....$**.$....$....$...$***..$..$...**$....*....*....$...*.....$*$.*.$$$....$.*....*....$$..**..$$...*.*.*.$....$.*.*.$.$....*.*.*..**.$......$..$.$.....$........*..*......$*..*$....$*$....*$.......*$..$$..*$...............$........*..**...$
$...*.*.**.......$........*$.$...*.....$.........$*$**.*$.$$*.$$....$...*..$.*$**$$.....$.*.*..$..$.*..*........$..**$.....$...*.*...$..*...$**.$...*..**.$..*..$....*..**....*$.....*..*...$..*..*.$.*......$$*$*.$.*$**.....$$***..$...*$..*.*.*...**.*$*.$.*..$$$*..$...$*.*.*.....*....$.*.$*.*$.$..**.*$......$
.*$...*$.***...*$...*$$$$*..$**.*$*$***.$$..$**..$*$...*..$...$$..$$....$.$$.$.$..$.$*.**.$..*$.*...$$$*.......$..$.$...*$......$.....$$.*.$**.*.$.*$..$$..*$.$$.$....$*$$...*....$*.*.....*.$$**.*.....*.$*.*...*..*..*...*$$.$$*.......*$.*$.$..$*..**...$........*$....$...$...**....*$.*.******.*......**..*.$..
..***.$....$....$*..**.$.$*$....*.$.$..$$...*...*.*......*..........$$..$..$..$.$..*$$..$...$...*..**.$$*...*$$$.$.$.......$...$$*.$*.$.$*.$........*...$.....$**...*.$....$....*..$.*..*....**$.$$........$*.*.$$*$$..$.$*.$...$.......**..$$...$.$...*.**...$.*.*$..*..$.$.*....*.....*.*$.*...$*.*.....$...*$...$
..$.$$$.**$*..$.....$..$$........*.....$**.$*.$..$*..$.*..*..*$.*.$$*.$..$$.*.$..*$$....*$..$$.*...*$$$.......*.*.......$*...**.....*$***.***$.*$.*.*.*$..*...**$...$$......*..*.*$.***$$..*.*.....*...$*.**..$..*$......**...**$.$*..*.*.$$..$.$.......$.*$*..*...*.$$$*.....*..*.$.*$.****$$$....$*.*$$$..*...$..$
*....$$*.*$.*.**.$....*.*...$$.*....$$*.*....$....*....*.$$.$.......$.$***...*...........**...*....*...*..*...$$..***$..*...**.$..*.$$.$$*...*.$$$$.....$..*..**.$$.*$...$.*******$.$.$$.*....*..*.*$*$$.$**..$$..$$...*.$**.$......$$*.....**$.*$$.*...*...*$.***.$.$...*....$*$*$..*$*.$.$.$.$$..*$$*..*..$.....*.
......*$.....$*.*..*..*.*.**...$*...$....$$*$.$***...$*$..$$..*..*....*$$.*..$..$.*.*.$.$.$......*..$$....*.......*..*...........*...*....$$..*.$..*..$....*..$*.*$$.$.*..$..$.*$*.$*$..........$**.*.$.*..........$$..$*....*.*..$*$..$.$....$.*.$....$.$....**$***$..**$$.*...$$....$.$.$$*.$*..$**.*.....*.**$...
*.*.*.*.**..$.*.*.$...*...$$.*$$...*$...*......*...$$.*...$..*$.......*...***$...*.*.$.$..$.$*...$*.$.*$.*.....*.$*...$..$$*..*$.*$.......*..$**..$*....$*..*$...$$*.$$$..*......$....*$...*.$....$..*...$.$.*....*.$.**.$...$$$$.*.*$$.*....*.*$.....**.....*$..**..*$.....*...$.$*$...$$.$...$$*$$..*..*$......*..
...*$$.....$.*..$....$*.*..$.$*$*$.*..$$*.$*$*$.*$.$**.$.*...*$$.$$....$.*.**$.$......$$$......*..$.*.$.$.*....*.*$..*...$.$.*.$..$$..$***....*...$*..*...*$..$$$*$$$.$..*..*..$.$$$$.*...*$..**...*.***...$..*$.$$**$.$$.*$........**....*.*..***.$..$*..*...*..*..***.$$*.......*...$.$.$....$.$*.*..$$$$.$..$*$*.
..$$$.......*.*..$.*..$.$*.*...*$.*.$...$...$$..$$$$.....$$$.**..*.......$.....*...$*.*.**...$......$***..........**.......**..$$**$.$......*$..........*..$...$*...**$*.**$......$.......*.$*.$.*..*..$*.....$.*..$*.*....$.*.....*...$....$$.$.....*..**$*.**$**........*..$$...***$.$$.$*$....*..$.*.$..*....$$.*
$...$..$**...$$*..*.......*$*$...$...$**...*.$$$..$...$$...$.*$$.*.$..$$.**$..*.*.....*$*.*.$.$...$$$**..$..$$..*..*.**..*.......*$...**..**....$..$......$..$..$.**.$$..$..$$....$*.$.$$...*.....$*....*.....$....*..*.$.$.*$...**$.*...*.*......**.*..$*..*.$$***.$...*.....*..$$..$...$....$*..$...*$..*.*......*
*...$*.*.**.*$........*.*$*.$..$..*.....*.....*..$*.$*.**$..$$$.$.**.*$.....*$**...***....$.......*........**$$.$....***..$..$.$.*.*...*....**...$..$*.$$.$.*$.*$..$...$..*.$.$*...$...$$*..$...*$.*.$..*........*..$.....*.....$.....$$.*.....***..*$...$*......$$*$.*..*..$*$*..$.**..*..$..$$....*............*..
$..........$$..$.$*$...*...$.....$...**$..*$*...$$*...**...$$..*..*$.*......**..*.$.*.**..*.$.$*..$.$$.$.*...*..*.$$...$..$...$.*.$.*$...$****$$..$*.....$.*..*$$.**$.$....*.*.....$....*.$.....**.......$.....$...$.....*.$..**..$.....**$..$.$..*$.*$.$$.....$.$....$$$.......$.$*$*.*..$.........$...$**.$.*..**.
.....*$....$*.*$..$..$........$.$**.$..$$.$...*.$..*...*.*....$.*.$$*$..$.*$.$$*$$**.....$*$****.$..*..*.$....$$*$$**...*..$....*$*....$*..$..*.*...*$.$**.***..$**.....*$..$*$....*...$...*$..$.*..$$***...**.$...$.$*...$$.*$....*$..$..$$..$.***...**....**$..$.*$*...$...*......*.....*$...$$.*$$..**$..**.**..*
...$.$*...$....*...$.$*.*$....$.$...*..**..$..$$$.$*.........$$*.$..*...*.$*..$.*$**..*.*..*.$...$$....*.$...*..$.$...$.$.*...$.*.$$$...*$..$$..*....*$*.....$....$.$.*$.*...$**.$.$**........*$$........$..*$.$....$*..**.$$*$......*.*$.*....*$**$.$.$$$.$..$.$...**...*.$*....*.$..*.*..*...$...*$*..*.......$..$
.*...*...$....$*...*.*$.*.$*$.*....$$...$$$*$.*...**.*..**...*..$$.$*.$.*.$$.$**$..*..$$..$...**.$*.$$$....*$*.*....$......*..$..*$...*$.....*..$*....*.*...***$..*..*...*$$.*....*.*.$..$$$.*.*$$$*..$.....*......$.$$$..*$.$$$..$.*....$*.*...$...*.*.$$.*.***$..*..$*.$..$....*.$.*$...$.$..*..$$$...*......$$$.$
.$**$$$...$..*$..$.*$*$*....$..$$$....*.....****$$....*..*..*$....$.$................$**...$*$..$.*.$.*$.*.$.$$.....***.*.*....$.$$$$..*...*.$....**.$$.$.*.$**..**$....$*.*..$........$...*..*.*...$...*$...$.*...*$....*.**.$...*$.*.***$...$..*.*$$$*...$.*$$.$.$*...$.....$**$...*$..*$**...$...*....$$$.*..*$..
$...$.$.*...$$...**....*.$...*..$*.*.*...**$.*.....*..**$$*.$.....*$..........*..$$*.....**.......**....**..$.$$..$.$.*..**.*$...*.....*..*$..$.$**.$$.$**$..*$..$$.*..*$...$....$.....**$.$....$*$**$*$*$..*.$..*.*.$$..*$..**$...*$$**..$$$....$....***$.$.$.$.....*..$$$...$*.*.*...$..*...$*$..$*.$....*$..$.*..
*...*..*.*..$...$$**$...$..............$........*..*$..*...$.$*..$.....$$.....*..*..$$......$*.$$..$*........*....*$.$$$..$.$$...*.**..*$*..$**..**$...$.*$..$*..$.*.$.$.*.*$.$.$..$..*..$$.$$..*..$*$*...$**.$......*.....$.$.*.$.....*........*..$$.*.$.$...$.*.**$.............$.$....$*......$*.$.**..$.*.$$..**
...**..**.....$*$*$.*$$...***$..**.$....$$.$..$..$**$...*.$....$.*...$*.......**$.$..$.*.*$.....$$...*..*.*...$$.*.*.....$$..*$.$**.**..*....$.***.....*..*.$$..$*.**$.......*...*$*..$$$*...**...$..$.....$...**...$..$.*..*.$.**.$.......*.***..*.$.*.$*$.*$**$$$.$.....*$..$..*$......$....$..$.....$*...$.*.*...
.$*..$.....$.$...$$.*$..$.*$.$..$........***.*....$....$...**.......*.$...............*$$..$*...$.$$*.$.*.*..*.*$...*..$...$$*$.*..$.$*....*.*.$$*....$$*..$.**.$.*$.*.$$$*..$.*$$.*.$$...$$.*.**.*$$$.*...*.....$.*.$.$$$..*..**.....*...........$*.*.$*...$.$.$.........*..*..**.....***.$$*......$$.***$$.*......
.*..$.$.*$..*$......*$.*..*.$.$..$$.......$..$.$**..$*$$.$*.*...$*....$.*.....*.$..$$.$..*$$..*$..*..*.$.*..*.*$....$*$$......*...*.....$.$...*..$.$.......$....*$..$...*.$..*..$....$$........$...*..*..*.*..*.$....$..$..*..$*.**.$*..*......**.$...$*$..*.....*$*$*.....**....$$.**$........*$.$$$*......*.......
.$*..$..$..$**.$.......**.$*..*$.$.$...*.$*.*$.$$*.....*$*...$....$*..$*....*.....**...*...***.*.......$.$.**.*.*$.*........*.***$*.....***....*.*.$**..........$...$...*..*.*..***$*.*.*..$...*..$.$....$...*.$$***.*...*.$.$.$.*....$......*..$..$..*...$...$..$..*$..$....$........*$.....$..$...*.*....*$*$*.*.$
**$*....*........**..***....**.$.*....*..*$.$$....$*.....$$.$...*$.*$....*.$.......$$.*.$...*.$.$.$...$..$.**$.*...*..**....*.**.$..*$.*$.$*..$*....*.....$...*..$....**...*.**$$.$*..$.*$..$....*.........*..$...*$......*...*....$..$.*.$.*.*...*..$*.$.$$$*..*...*.$$.*.*.$*.*..$.*....$*.*.$...*$$......*.$..*.$
*..**..$..$....$...*..*..*.*...*..*.....$...$..$.*....****...*.*.*.*...**.$.*..*$$$..$..*...**.*..$$*.$.$....$$*.*...*..$*..**..*....*.*.......$..$.....$$.......$....$.*.*$*$.$...$.*$*.*$*.*.$*..*...$**$.$**.****...*$....*$*...*......*$$.*.*.$......*.*$.$*$....$$..$.*...**..*.$..$......$.*.$.*$.*.$$***.$**.
..............$$*...*$..$.****....*.....$......**..*$.*.*...**.......$***...**$.*..$.**..**$$......**$$.$.$..$.*.........*.$*$*.*...*$...$*$*$*$.....**.*.*$*$...*....$$....*.$$.*.*.$*.*.$*..$..$....$*.$.$....$*...$$.*..............*.....*..*..$*..$.$*...*......*...........*.....*.*..$...$....$.$..*$$.$.$*$*
..***..*..$$..$$...*.***.$..$.....*$*$.....$$.*.$.$*..$.....*..$......*....$.*$..*....*.*.$.$..*....*.$...........*.$.....*$**.$....$..$*$..$.....*.*...**$$$*....*$..$*.$.$.**...*$*.$**.$...*$$..$$$......*.$..*.$*$..*$.....$.*$....$.*..$$.....*.......*.$....*.$.$..$$*........*.*..*....$..$..$*.$$.......$.$.
......*$$*.....**..$.......*$..*..*...**.....***$*....$*......**$*.$***.$.....$$...*$...$...*$$*$...**$..$*......**...*..$$$.$.$.*.....$.$$*.$..$.*.*$.*.$*.$....$**....$....*...$*$...*....*..*$..$..*....*$...$.*$$.*..$.$$...*...*.*..$.*.......$.$$....*....$*..$$....$.$$..*...**.$..$*..*$....*..$$...*..$.$.$
....$....$...*..$.$.$.......*.*..*....*...$*.........$..$..*..$..*$*...$..*.*.$....*...*..*..*....*.**$...$$$...$.$..............*.....$..$.*....$*.$.*...$$$.$.$.$..*$**.$.*.$.....*$$...$**...*.$.$....*$..$$..$.........$...*$.$.*.............*.*$**.$........*..*****..$$....*.$.$...*$.*.$.**...$..$*.$*..*..*
.*.....*...$...*.$$$.$..$*..$..$.*.$.*..***$..$.......$..$$..$*.*.***.$.....$*..*..$$...$.$*.$*.*...$*$*.$..$*$..$...$$....*$.$...***.*$*.....$..$....*...$........*...**.......$*....*.*..*.$...$......$.*$.$..$.$$.....$.*..$..*.$....$...*$$..*.$...**.$*.$*.$.$.$....$.**.$..*..$.*..$.$.$....*.......$*$..$*..*
..*.*.......$....*..*$.....*.....**$*...$$$.*$....$$...$...*$$...$$**.*....*....$.............$....*.**.....*..*...$$....$..***.$.$$..*.**.......$*.$.$.$$**...*....*$............$....$...*..**.*....$.......*.$...*...*...$..*......$..$*.$*$$..$.....$..$$..*....$$..*.$.*...$...$....*.*$.**...*..**...*.$..$.*$
.......$*.$$*.*$*..**..$........$.*$...*$$.....$.*.$..$$..$..*....$$.....*.**....$$*....$..*.$........$*$.$$.*..$..$..$..$.$.$.*.***.$.**....$**.*$$...*$*....$$.....$...........*....*..*$.....$..............$..*...$$..$..$...$.*.*$....$....$....*....$$.....$...$...*.*$..$...$..$.**..$**..$......*...***.$**.
$$$*.**.....$*.$*.****$....*$.$$....$.$**$$*..$$...$...$...$..*.*.*.......$.**...*....$*..*$.*..$.*$..$$.**$.*...*$.$..*..*..$***$.*....$*$.$$$.**....$*..*...$.*$*.....$$*.....**$.$...$.*.$...*.$.............$..**$......*.$.....*.......$....$..$..$..$...*..*...**..*.*.*..**.$*$$.*..*...*$.....$.$..*$....**.
..*.$$**$..$..$$..........**$*$..$......*$...**..*.......*$$$.*.*.$$..$**...*..*.....*.*..$$$*.**...*..$....*$..*...$***$..$......*.*.***.....*.$**.....*..*.$**$...*..*..*.***.$$..$.....$.....$..$.......$$.*$*$$$.$**.*...*.$.....$$..$..$*..$..*..$.$$$....$*.$.$..*.*.*.*.$*..$..........****..*.....*$..$$....
$.*$*$..$*...$*..$....*..$*$....*.$.$.*..*.$*..*...*.*.......**$..*.*$.**..$$$...*.$.$.**..$....$*.*$...$$*.$..$.....$.$*$*.*.$...$..$$..*..$*.$$$*$..*..***$.*..*.**...**$$.$.$..**..$$..$...*$*....**$..$.**$..*...*.$.......$.*..*.....$*.*.$..$$.$..$$*...*.....*...$*...$*.*......$..**.$....**$.*$*..$**$..**$
..*$$...$..*....$.....*..*...*...$*.*....*$.$..*$$$..$.$$.*$*$.$$.**$$.$...**.*....$..$......*...$$$**$.$..$*$*..$*$.**$.$*$$$..$$..*$*....*.....$...$$...$.$..$.**.......$.$$$**$$*....$$.*..$....*.*$..*.*$*...*...$.$*.*...$......*......$..**...*..*......$...*.$....$.$$..**.$*..$*....*....**..$***$...$....**
.*...$$$..$..$*.*.*$..**.*....$*..*.$...$...$.$$.......*....$..**..*$$*.........$..*.....$$.$..***...*.*..$..*.....**$$.$$.*......**..*$.*..$..*.....*$$..$..$.**..*.**.*$.$....*$.$.*.$...$.....*....$$$*$*.*.....**...$**......$$.$**$*.$*.....*.*.$.$*..$...$.$.*.*$$$....*..$*.......*.....$*..*..*$.$*.$*......
.$...*..*.......$.*...*.*..$..$......$**$.$**..*.**.*......$.$$....**$....*..$*$.*...$....$.$.$....*..$**.$....***......$*.*.$.....$*.*.$.$.*.$.$*..$.*$$*$*.$...$*.$..$...$.$..*.**...*.*.$....$$.$*....$..$..$..$.....$..*.$$....*$.*.$**...*.$....*....*..*......$....*.$.......*.....*..***$$*...*.$....$$*.$..*
.$..*$.*....*......*.$****..$......*...*..$.*$*...................*......*$*$....$*.....**.....*$..$$.*..*.*.**....$*$...*$..$$..$*.$*...*.*$$$.$..*..$........*$.**$...**$...$$..$..*..$.$.$.$..**.....*$.*$...*.***.*$$.*.*$$.*....$.....*.......*....$*...$..$.$.*.$*....*...*.*..$$$*.$.*......$..$.*..$....*.$.
...*$...*.$*....$$...$$.**$$..$..*$.$..**.*.......$..*.......*...**.$.....$..$..*$...$..$*...$....$.$.**$.*$*$.$......**..$.**...$...**....**.$.*.*.$$...*..*$*.....$**..*$...*...**$$.*.$*...***$.$.***.*..*.*..*...*...$$**.*..**.$*..$*.$*...$..*$*.**$$.$.$.....$..*.*.$.$.*..$...$.....$.......*.....$....$...$
$$*..$*..$....*.$$..$$.*..$.**.**..*.....$**$..$*...*...*.**.$...*....*....**..*..$.$*$....$.**..*...*$$....*$..$.$.*.$......*$.....$.$.*.*$*$...*.....*....$.**..**....$$......*....$.$.*..*.$...*.*$..$........*$*...*...$.****...$$**..$......$*.**$$.$.$*.$.....$*..*$.*..$*....*.*..*.*$.*.$...$.*.$.....$...**
*$....$..$.$$$....$*....$..*.*.$.*.**..*.*..*$$$......$.....*.*....*$..*.$...$$.$**....*..$.$.$....$..*$...$....*..*..$....$.$....$$......$...$$$......**$..$$...*...$$.***.$$..$...*.*$.*...$.....*...$*.*.$.$*.....$.**$.....$*$*$.*...$.$*.$..*..$..$.*.*........*$.$....*..*$.....$..*....$$.....$$..**.*$.*.*.$
*$.*.*....*.....$..$.*.$....$.$.$.*.$**.$$.*...$.$......*.$$....*..$$.$.*....**$$$........$..*.**.$....$.$***$$$..*.....$..$......*..*.$.***$$$.*....$......*.$.*$.$.$.$*....****.$*..*...**.*$$$$*.*.$.$$$*$.....*.....*$*$.$*.$$......***$.......$$.$$*$$*.$$.*..*.$$**.$$*.$....$.*....$$$......$......$$...$$...
$...$.$...$...*.....*..*....$$..*...*.$.....$.$....*.$..$.$...$...***..*...$$$.*..*..*..$...$*..*$*.$*.*.*$*..$.*.....*......$.*...*...$..*$..*..$$.$.*......*$.$*..$..$$......$..*$..$*$*..*$*..$...$$$..$**....$...*.*..**.$*....*$$....*.......*.**.*.$*$.*....**...*$...*..*..$$..$$..*.*.**$.$.$*.....$..*.*...
..$$..**$..**$*.*.$$......**.......*..$*..*.....$.*.....*$.$*.$$.*.*$.$$*$.**...$...$...$.$.*$$***..*.*..*......$.......$..*$..*.$.*.*.****..**.$...*..*....*.....$.$***....**.*$.$*.*.*....*$..$.**$.*..$*..$$...$*.*.$..$.*...*.$.$...$..*.......$..*..$.*.....$...$.*..**...$*$.*$.$..*.$*.....$$....$$.*$.*..*$$
..$.*$*.$.$$.$........*$*...*$.*..$$.*$..$.....*.**.$.......*$......*....**....$*...$.*..***.*$$..**.$..$*....**..........*.**$*..$....$$..*$$...$*$..$*$..*........$.$.$.**...*.*.......*.$..$$*.$...$.$$......*.*$..**.*.....$$*.$$..*.$$..*.*.$*.$.$**$$..$$...$*$.*..*$$...*.$$.*..***$......$..*$*.*$..$.$*$..$
$.**....*.*.$..$.....$..*...$..*.$.......*.*......$*.......**$$.$*......*$*$*..$........$..$$$.*$...$*$$..*.$*....$.$..$...*...*..*$.*......$*..*$.....**$$.$..$.*....*$.*...*.*......**$...........*$*$.$....*.*.*.$**.$.*$.$*.*.$$.......$..*$*$....$..*$....$$.$$$*..$...$.*...$.$.*..**.$..*...*$...*$$$*..$.*$.
$....$*.....$*.$.**.$...*$...$**$.$......*$.$..$.$....$$*...*..$$......$.$.***.$$....**.*...**$...$......$$**.$$..*..$$.$*.......*....*..*..**..$...*..$$.....**.$....$...*...*..$.*....$$$.$$...$..$..$*.$...*.**$..*..*....$$.......*.*....$....$.*.****$.$$.*.$$$$**..*$*..$$$..$.$.....*.$...$...*.$.$..$$$*$.*.
.*...*......*$...$$...$.*..$.$..$.*$..$$.*$.$*....*......*.**$$$$*.$..*.*.*$.$....$..*.*..*..$**..*...$....$.$.*..*$...$$...$..$$...**...$....**$**..*$$..$....*....*$$.*$......*$...$.*.$.*.*..$*......$...*.$...*.$.****.*...*.......$.$*...$...$**.$....*..$*........*..*.$......**$..$.....*..***.*.$*$...$**...
**.......$...$*....*.*..$..*$*$..$$..**$*..**....$.*$..$.....$*$*$$.**.....**.*..**$.*.*$.$$....*$$...*.....$..$.*$...$$.*.$$*..$..*$$....$.$.*......*..$..*$$.$*...**.*.......$*....$.*$..$*..........$...$......*$*...$.*..$.$*.*$.....$$$$**$.$$**.$....$*....$$.*..*......*..**$....*....$.*....**.**..$...$...$
.*.....*...**.$.$.....*........**.*.***.$.....*..*..$..................**$....$*...*.$*$*.*..$$*...$..*......$..*..*..$......*..$$.*.....$..**....*.$...$....*.$$.*...$....*.$*.$$......*$..*.*.........*.....$.....*$*..$*.*....*..*....$...$.....$*.$$.....$...*.*.$.*.$*$.*..*..$..$$...$...$.*.$$..$.*.$........
.**.$..*$.*$*.*.$....*...$.....***..*..*$.$$...*...**.$..$...$*$.......$...$...*$...$*$....*$$.$.$.......$.*.....$.......*$....$*.......*...**.*....*..*$$..*...*.$...*$..$..$..*.$..*...*.....*$*..*.*..$$.*..$...**..$*.$$.......*.*..$........**..**..*...........*.$.*.$.*$$...$.....$$$.*.$.$..**..*.*..**.$*..
$......$*$..*.*..$..*.$..*...$$.*$**.*$..*..*.*....*$.*.....*..*.$.......*..$$$.$$$$..$....*..$$...*....$.$*$.*$$*...$.**.$*$....*.....$.**.$..$..$..**.......$.....**..*..*$.....$.....*$.$.$$..*.$..$*.$...*.....$...$.....$...*.........****.....*$...$.$*.......**.*.$..$.$.*$**.$....*$$$$...*.*.**.$..*....$..
*.*.*.$.*$*.$.**....*$....$..*.*.$.$*..$.*.*$.....*$...*.*..*...*..$*.....$...**$.$$$$..**....*$$.$...**.*$.*$.$.*.$$$.*..$..*.*...*..*.*...*..**..*$$..***$$.$*.....**.........$***.*.$.$.*...*........*.*$.$.$***.$*..$.$$..$..$*..$...$$.$**.....*....$*...$..*$.$.*.$$$$......$*.$$*$..$..$$$$$$$$***..$*.*....$
.$$.$.....$...*.**$$$..$**....*.*.*.$*.$...*$.*.$..*.$......*.*..$$......$...*$.......*.$..$.*$.........$..**...*.$...*.$**.****.$*...$.....$*..$...$.*$$$$*.....*.*.....*$$.$*$$.$......$..**.*.....**.$*........$....$*.....$.$*.$....$..*$..$.*.*$..*.....$$..$*.$....$.*......$*.$...*...$.*.$*..*...*..$..*..*.
....**....*$..*.*$.*$...*.*....*.*...*.$*$$..**.....$$..........*$$.*.*$....*$.$...........$.$...$$$.$.*.*..*.*$.*..$..**$...$.....$...........$..*..*.....$*..**$...**....$*.$.**.$..........*.$....*......*.$..$$.*.......$**$$*..$*$$.*$$..$$...*........$$.*....$*.$.$.*$*.$**.$*...$..*...$*....$....*.....**.$
...*$....$.*..........$...*.$....$*$.*$*..**$..$.$..**.*...$.*$.*.*.......*...***...$..*$...$*$*...$.......*..$....*.*.$$..*..$*........$.$$$.*$..$.......*$$...*.*..*.....$*....$.*........*.$*......$.....**.$.*.*$..**....*.$**...*$.$.$.$**......*.$*$*$$.$**...*$..*..*.$$.$.*..........$.$...*.*$*.$.$$$*.**.$
..*.**$*.$...*$***..*$.$..*..$$...*$$.$.$*..$.*.***.$.*...*$.$.$.$.*....$.*.**.....*.$....$*..*....$.$*..$$.*.$..*$.*$*..$.....$.$..**$*.*.......$$.$.*........$$.....*....*$$$.$..*$..$.$..$........$*.....**.*.*.$..$$....*.$.$..*$*......*.$.$.$...$....*.......*.**.$.$.*.*$*.*$......$..$$......$.$$.**.*.**.$.
*...$.**...$...*...*..*.$......**.....$.......$*$.....*....*****...*$...*$........$..$*...$$**$*$*.$...$.$$..$*$.*.$.....$$$.....*..*..*.$...*......$.*...$.*.**...**........*.$.*.$$**..*.***....$.*.....$$*.....$....*....*$$..*$$...$.**$....**.*.*$$..*.$$.......*..$*..*......$..$.*$..$$.$.*.$..*.*.*$$.$.*$..
......*$.*$....$...$*..**....**...*$.*.***$..**$.$.$..*$$$.$..$.$....$......$*$$*...*...$$*$$.$.*.*.....$..*...*.*..*...$....$..$.$**...$...*.$...$$.**.$..$..*.......*..$.......$..........$*$.........*....*..*.......*.*...*$...$*.*..*$.*.$.....$..*..$.*....$....**.**.$$....***.*$.....*.$.$**...*.*..*$.*$.$$
..$***.$*.**.....*$..$..$$.$*.*.*.***$...*..$*$$.$.***..**...***.$.*..*.*.....*$...$**..$$..*$$.*..**.***...*.**.$...*.$..$...*.$.**$$*$.*.$....$.$*.*.$.***$.$*.......$......$$*........*$..$*..*..*$*$$*$...$...$*.$$$$..$.**..*..$$$.$.$$.$$$.$$*$........$*$$.......**.*.*$*$$.....$*.***$$$..$.$..$..*.$...$.$.
$.$$*$....................$$.$$..*$...*$$..*..$**.*..$....*..*....*...$$.*..$......$........$$.$*$.*$***..*..*.$....$..*$..$*....*$.........*.*$.*.$..*.*..*..$..$....**.*......$**..$*..*.$$$.$........**$..$....$$.*..*..*$$*...$..*......*..$.*..$$.$....**.*...$...*.*...*......*..$..$.*$$$$...**.$.$$$..$.$...
$*$**.$...$...*....*..$*.*..$.....**...$.*..$*.$*....*.*..$.*$*$*$.$..*.*.*$....$.$..*.$$*.....$$**$.$$.....*.*$.*..*$*...**....$.$.***$..**.$..*.$.$$...$*$..........*...$.$*..*$..*.$.$..*.$..$*.............*.$.$.*.**....$$...$*.**..........***.....$*.*.$$*..$.*$.....$...$..**$..*.$...*$$**...*.$**$**...*.$
.....$*$..$$....*.$...$$...$....*....*$**$.*......*......*....$**$$.*.*..$*.....*$.$.........**...$*$...*.*.$.$$*$$.$.*...$.$$...$*$...***.*$*$..$.**.$.$..$.$$**.*..$......$$.$*$.$*..*.....*.$......$..$$$$.*..*...**..*.$.*.*.$$$.$$*$*.***..$......$.$$$$$$*$.$.$.$.*$....$...*.$.*..$.......$.$..*$$*...*$*.$$.
$$..***.$.$....$$...*$*$*...$$....$.$$..*.*....$......$.........$.$.$.*.*.*.*...*........*....$...$.....*..$$...*.....*....**..$*..$.*..........*.*..$.....$*...**.$..*........$$*.$$..$****.$..*........$...**.$$$..*.......**.$$$***...*..**$..$*...$...*.*..$$$.*.$...*....*..*......$.*..*.....*.$........$...$.
.*$*....**...*$**......*..$....*$.$$.*.*.....$.*$...*...$*****..*....$*..$..$*...*.*.....*..*.$.*.$.$.$.*..*...$...$...$*....$.*.............*$.....$.$..*..$.$.$$.$...$..$....**.*....$.*.*.$...$.$....**$...$.$...*......*.$*.$.*.*.$*$..*....*..*$.$$$.$.$.$.*.*$.$.*.$......$*.$.....$*.*...$..$.*$**.....$.....
*....*.$...$..$..*.$.*......*.$.**$..$*.$$..$*..*..*.*..$.........*..$$..$*.*.....$..*....**...$$*.**....$.*..*...$.$$..*.*....**..*.....**.$....$.*....$.$$....***.*....*.$*.*$$$*..$$..*.*..*.$.*..*$$...*.**..$.....$..$$...$.**....*.$...***...*.$.*..*$..**$..**$..**.**...$.*.******.$$$..*...*.$.$*...*......
...$.$*.$.*.**...*...*.$.$*.$..$.*.*.*.....$...$*..*...*$....**..*.*..$...$**..*....$...$$.$$*...*....*.......$..$.*.$..*.$..$$$.**...*...$...*$.$$$..*......*..**......$$$$*.$*.**.$...*.*.$.**.....$.$*..$*$...*....*.......*$..*...***........***.*....*.$.$.$$.*...$$.*.*$*.....*$.*.$*..$...**....$..*$....$...
$$$$......*......*......$.*$..**.$$...$.....*$.*..*.$*.*$$..**.$.*..$.**.*$$$*$***..$.*...$*.......$...**...*.$.......$....$$.*....$.***$.........$.$*.$.*.*.***...*...*.......$*$$.**.*.$..$$$.....*...*.**...$.*.*.*$$.*..*.*.$*..*....$**.....$..*..$*.$.**$.$*.*..$$..*..*.....*.*.$.**......$$.**..$$....**.*..
..*.*.$*.*$.....$.....*..$...*.......$...$*.$.$$...$.$..$.$$..$...$$$*$$.......**....$*$.$.*$***.*.**..........**..**..*...*..$.....**$.*.....*.*.**......$$*.*.$....*.....$.*...$$...*.$....*.*.$...........*.....$*.*$.....*$*.$.***$.......*...$$..$.*$...*...$**$*...*......$*$..*..*...$......$...*.*.$....$.**
*$....$$.*$*$*.....$...*...*...$........$...........$.*.*....*.....$**$...**..$...$*.****..*.$...$$*.*.**..*$$*....$.$.......$....*..*..*$$$$..$.**..*$...$.....$.$.*.*.$$.$..$$.*....*..$$.$*.......*.*.$....*$..$....$$.*$..***$..*$*..$$**...*.$$$$*.*.$$*$.....*$$$........*...*.$*...*$$*..**..*$.***..$.$..$..
*$.*..$....*....$......*$..$.$**.*..*.*$.$$.....*$*..$$...*$*.$.$....$...*...**$$.$$$....$.*.....**..$.....$.**.*....$.*$..$..**.$*.........**....$..$**......*.*$.*.$$**...*.*......$..$..$$**...$*.$..**.*.*.$...*..$*.*$.$$.*..$....$..$.........$......$.*...*.$$.*...**$.*$.$*$*.$*.*..*$.*$.$$.*..*...**...$..
*..........$$*$.$$.***.*.**....$*..$.**..$....********$$....*.....*$....*..$*$.*$$$.$..*$$....$.....*$$.*.$.*$*$*.....$.*...$.***.**......$.$$$.............$.....*..$..$.$*$$$*.*$...*...........*........$..*..*....*.**$$*$..$....$$*$$....*$...*....$$$.....*..$.*......$$..****...**$*..**....*.....$.*..$$*..*
...$.*$.*$......*...$$....**......*.*.$.$.....$$.$...$..$*.*.....*.$....$.$$.*....$$**.$**$*........$*..$**$......$...*......*.***..*$*.$.......$$$.$.$$.$..$.$.$...$...*$....*$$....$.*$*...............$***...$.$$$*$.....*............$..$*****.$....**..$$$$.**...**$$*...*....***$**.$.**.*...*.....$*..*.....*
**$*...$*...$.......**$*$....*.**....$$.$*$*$.$....*....*..*..*....*...$$...$$*...*..*..***.$......*...$$...$.....*$$.*..$*.*.**...$.$..$$......$.*$..$*.*$.$$.....$.......*$*.*..*.....*.$*$**.*$...*$$..*...*$.$.*$*.*..$$.$.*$....$.**..*..$*.*$.*..$*.$...*$$.**$$$....$..*..*....$$$*...$.*$.$*...**.$.*$.....$
*..**$.$*$**...$..*...***.$.$.*...$....$$..*$.*$..$...*.*$*....$*..$*.$.$.....$..$$*.....*...*$*..$...$*..$$....$$..**.......*...$....*.*...*.*$.*.$*$.....$.*.$.....***.*..*.....*$$....*.**..$...*.*.....$$*.*$....*...***..*$.*$.....$*.$*..*$...$....*...*.$.**$$.$$.**.$$*...$...$*.$.*.$$**...$.....$....$.$$*
$..$$.$.*.........*..$.****.$*.*....$*$...$$.**..$*$..*$$.........*.*.*$.*...*..$*.*$.$$.$...*...$.$*..$.**.$..*.......$..$$..*.$$*...$$.*..$$.*...*.*.........$...*..*..$..*......*...$$..$...*$*.$..*.**..$$**..$..**.*.$.***.*$....$.**...$.$.$*$.*.......$.......$.*...$*..*.$$$.*..$.*.**........*.....*.......
$.$***...$....*.$...$.......*.$..*.$*.*$..$.$$.*$.$........*......*$**..*...$.$.$..$.*..$.$*.$..*....*.*..$...$..**...$.*....*..$...*.**$$$$..*..$....*.***...**$.$....*....$.*.$*$..$...$....*.*.*$$.$..$..$*.$..$.**....***.......*$..$.$*****$*.*$..*..$...$.$*..*..*$..$.........**..$$$..$$*..$..$**..$.*.....*
....*..$....*..*.*$*...*..$.....$$.*.*.........*$*$$$$.$$......$$$...$*$......*..****.....$$*$.*$.*$.$.*....*..$*.$..$*.$.**$*.$$.*.$.*$..$..****$...$$*$.$.$...*..*.$.....*$....*...$$$*$.*$.$.$$.*...*...**$.*.....*..*..$...$..$.$$$$.$...**..*$**..*$.*........$..$*...$..$.$$..*..$*..$..$..***.$$.*..$........
..$*..$*$*.......$$.$........**.....$......$..$..*...*......*.........$.*$.$*.$.*....*.$....*.**.$...*.$.***.$....$*..**.....$......*....$...****$..$$......$$........*.......*..$...$$.*$..*.**..$$.*..........$.*..$.$.$**..$**.....*.........$..*.**.*...*.*.$..*$..$.$.*.$..$.$**....*...*..*.*..$*......*$$....
.$..*.*$.$$.$*..$..*...*.$*...$..$.*$$..*.....$.*....*.......$.*$*.*....$**.*..$*......*..**$*.*.$.*..*.$.$.....*..$..*.$..**.*..$$*$*...**....$..***..$.**.*..$.$.*...........*.....$$.$$*.**$.$.$*..$...*.$..$.......*...$......$.$.$..$.*.*$.$....$*.$*..*.*...............$..*$....$.$*......$....$......$**$..$
*.......*.**$$$.$*.....$$$.*..$.**....****.*$......$..*$*..$.$..*.**.$...*.$.$.$.*$....*.....$.$...*...**$....$....$$...*.*.$....****$.$$..$*$.*$..$.$***..*......$.$.$.*...*...****$*$$..$..*...$.*.....$.......$$..*....*...*...$.$$$$.$.*$$$.$....$..*$..*.*..*.*$$.*..*..$*$..*..$$$$.................$..**$*...
$.$.*$...$.$....$$$*.........$...$..$.*$....*.*..*$......$..*$.*..$$$..$$....$.*.......*$*.*....$$$......$.$.*.*..$.$..*...*...*...*...........$....$***...*.**..$$*.....$..$*..$.*.$..*..$....$...*.*...*......*.*$.*$..*.*.*...*.$.....*$..$...$*....*$$...............$.**$$$$*.$*....$.$*$.....*.$...$$$$....$..
*.*$**.*.*...**.*.**$..$*.$.$...$.....***.$.*...$..*.$$..$..*..$*.....*.**$*$.$...$$$$.....*...$$$.......$.**....*$..$..$$$...**....$*.*.$$....*$*$.....$$.$...$*$..*$$*$$*$.$..$......*.*.*.*..****..$.*..$*.$$*....$**$$.$.*$..**.$*.*..$*$...$$$...*..$...*....$.*.$.*$.$.*$*....***.$$.....$........$....$**.**.
.$...*.........$$$**.*..***$...*..*.....*..$.....$....$*..$*.*.........*.*$.........$$*...$$.*...*.....*..*....$.**$*...$.$*.$.........$.$*$.$$.......*.*.*.....*$..*$...*.*..*.*$.**..$..*$..*$.*......$$.....$$..$......*..$..$..*.$.$.$*$$.$*...$....$...$......$**.$....$$.$..*...$$***$*..*$..**.*..$.*$$.....*
.*..**.$$$.$.....$$**....*.$$$..***$***...$.$....*......$.....$.$$..$*$.*.....*..$.*$$...*.*......$.*.....**....$..$$...*$.$.$**..**.$.$$$......*.$...*..$$.*.$*$$............$..$$.**..$.$...$....*.*..*$.**..*$$..$.**....*..$..$..*....*...$*....*.**.*......$*.....$$.*...$.........*$*..**$*...$$..*.*$..$$...$
$.***.$$*.*....$...*$***$$...*..$.$.*.*$*$.$.$..$*.*.*.**$$.*$***...**$$.$..........*.$....*$......$.........$$...*.**$.$*$.............$*.*..$.*$..*.*.....*.$*...*.*.*...$$.*.$......*.*$.*$.....$$*..*$....*$....**.$.**.$$$$..*****.**.$*.$..$***$$**..$..$$..$.$.....$*$..*$....*$*.$.$...$..*...$*$.$$$..$*.*.
$$.*...$*$*.**$$.$*.*.....$...$$$$*..**$....$*..$*..*...**.$***........$........*.*...$.$*.$.*$*$*...$$*.$..*$.*..$*.$.$....$...$*.$...*.*.$*....*.*.....$.*$..*....**...$**..$$**$.**.*..$.....$.*.**..$*.$.*$......$**...$..**.*......$.*.$.$...*$$$.....*.$.*..$...**...*.*..***.$*.*..**$..$.*$.*..$**.*.....*.$
..*.....$....$.$*....$....$.$.$*.$....$..*.*...*...$..*$....*....$$*....$..$..*..$.$.$***...*.$.$*.$.*$...*....*....$.*...$*.*...*$*..$......**$.$..*...*......*.*.*.*.$..**.$...$...*.......*.$...$.....*..$$...$......*.$$$.$*.$.....$....$.........*..$..$$*.$..$.......*......*..*......*...*$*..$....$*.**$*..*
.*......$*$***...*..*.**$.$.......$*...*.$..$*.$.*$...$..*$*$....$.....$.*....*..........$....$*...*..*$*..$.*$$..$$**..*.**$.*..*...*.*..**.*..$....*$*$$*.$.$*$$$........$*..$*..*$.*...$..$*..*.$....**......*$...*.$$*$.*.$$$.$*.$..$$...$..$..$...*$.$.$*$.*$$....*..*$.....$$*...$...*.$*.$*....*.*.$.....*.*.
..........**.**.$.*.....*...$$.*..$.**.*..*..*.*.....$$$$.*.....*...$..*...*.*$$*.$..$*.....$.$*.*...*....$...$.....*$$*.**....$$.$.*$.*.$$..$....*.*$$$.$........*$.**.**$$$...$....*..**.$$.............$.$..$$*$*..**..*.$........$*....*..$.*.*.*.*.*.**....$$$*....$$..*...**...$..$*....$**$....*.$$*....*..$.
.$$$**..*.$...$*......*...*..$.*$....*.$.$.$.$.*.$..*.*....*...$..$$$.*..$..*.*..$...$.**$$**.$*....$.*.$$..$.*.$.$...*.*...*.$$$$...$.*.*.*$.$.............*$$*$$$*.*$.**$*..*$.*..*..$$...$.$*.$.$..*$....*$.*.*...$*$*..$$*$.*.$$.......*$.$.....*......*$*.*..$..*$.*.***$.*..*..*....$.*$...$.$.....$$.........
....*$*$.$....*..*.*...*.*...$...$...$*....*...$*$....***.*..$$$..$......$$.*.....$....$.$*.*...$$.***.$.*$........$.$$$**$*$.$$.$$$.*..$**....*...*.*..**..*.**..$.$..$**.$.$**$**.$.**.$$$..........$.*........$$..$...*.......*..**.**..*.*$...$.$*..**.*.$*..*.*$$..*...$....*......*...$.....**..$...**$*$$.$.*
...*$.*.*....$...*.$......$$....*$......*...$$*..$..$$........$..$**.$$.$*..*.*.....*.*****....$...*.......$.**.$*..$$.*....*..$....$$*....*.$..*$...*....$$.$$$....*..$$..$..**$...$$....$$$.$*.*.*$*.$.*.$.*..**$$.$...$$.$..$$...*.*..*.$...**$..*....*.....*...*.*....*.**$$...*...*.$....*.*....*..$..$.**.....
*...*$*........$$.....*.$..**$.*..*$$*.....$*.**.*...$.....$...$....*.*$$...$....$...*.*.*..........$...$.*.*...$.$.......***.*..$$**.*$*..*.........*.....$..*$..$..*....$$.$..*....$$$.**$$.$.*.*.$.**....$$..*....$$***.....**...$....*.$.$..$$*.*.$..$.$.....*..*$$.$*$.$**....$..$......$.*$.*..$$*.**.$$...*..
$..$*$.....$*.$...$$..$.$*...*$$.....$*$$*...$**.*..$$*......$**.$......$*.....*...$$...$....$*.*.....$$..*$$*....$.$$*.*.$...**..$$.$*$**...*.$..**...$.$..**..**$..$*....$....$*.*.$$$...$.*..$$.$$..*.....*$$..........$..**...*...*$.........*....$.*$..$*..$.$$...*.$..$...*$.$*............$..*..$..**$.*....*
$...****..$$.$.*......$.....$$.$..$**...$*........$.....$.$....*.$..*.$..*..........$$..**.$....***..**.*.$$$.$*.....*...***......$$.**..$$$.*..*$......*$*..*.$.$*....$.*...$$.....$..$**.$$..$$...$$*....*.$..$.$*$....$..**$..........$*$......$...$......***..**.$*...*$$$$**...$*$.$.**..*$$....*.*.*..$.*.*.$.
..$*..*$...$**...*.*..*.$...$.**.$.*.....***.....$.$$.$$.**..*..*.$*..$.*..$......*.*....$.$*.....**$.*....*$.......$$**.**....*.$*.$.***.$...$.*$.....*....*$.....$.$$..$.....$....$.*$*....$.$.*$.*..$$$*.*....*.....$$...$.$$..$*..$*...*$...*.$*$*..$*..*...$*$.**....$*$..$..$..$$..$$.......$...$.$*.$.*..*.**
.*$....$*..$....$$...*......*.....$*....*..*..**.$.......$.....*...$..**.$.*.*$.............$......$.......*..*.*..$.$*$.$.$$....$$*..$..$.....$*.*.$......$$.*..$.*.$..$.*...$..**.***...$.$*.......*$*$*....**..*...$*.$*...*....*..*.......$.*.$....*....***....*....$$....$.$...*..*.**....$.*..$$$.$.*$..*.$$..
......*.*.$$$$*.....*...$*$*$.*...*...$...$$$$.*$**.$.$*.*..*.$................$..$*..**.$$.....*..$.*$.....$.$*..$.....$.$.*.....*.**..**.....$...$**.*$$....$*$.$.*....$..$..*$.$..$...*...$$..$.***.$..*..$*.$....*$....$..*.*.$...........$...$$.*...*$..$.....*...*.....*.......$*......*...*$..$.$$......$....
.....$.*..$....*.....$$..*...*.$..$$..$*......*$*.*.*.$..$**..$.$$....****.*$*.......$*....*.........*...$.*.$...$.$*.*...$...*.$$.$......$....$..*..$.*...$...$..**.****..$$**..*.....$...$*.....*$*.$**..$........*..$$.*..**....**.*.......***....*.$...$$*.$$.$...*...$*..**..$..$.*$.$$..$$..$$..$....*.**$...$
...*.$.$*.......$.*.$..$**..$$*$..*.......*..$.....*...$.*.*....*.*..*.....*......*..*$$*...*...$......**..***.$$..*.*.$*$$.*$..$$..*.$.........$.$$*..*$..**.$*....$*..$.$..$.$*$.***..*$.....$.$**.*...*..*..**$$*..**..*$.*..$.$..*.$.$*$...*.......$.........$.*$....***....*$.$$$.$.*.$.....$....$.....*$.*$$..
.*..$.$.$.*.....$$**.*..$....$***$*.$....$$*.*...**$$.$$.*$.....$...*.$.*$$.$....*.$*.*.**.....$*.*..$.*.$.$......*........*..$**....**...$*...*...***.$...$.....*$...**......$.*.$...*....*..***........$..*...$*$$..$.$..$*.*.*.....$....*.$..*..*..$.*...$.*.......$.**$$.....$.$...$..*.*$.*..*$.......*$$.*...*
.$$.*..$*$$..*$**.$.$*****.***.....***..*..$**....*..$$........$**$.$...*......*$.........*.....$.$.$.*.$..*$.*.$..$.*..$*.$$...*..$.$.$........$..*.$...*...$..*...$..*$..**$.$.*.*...*.$..$..**...*.....$$.$........*.$$..$.*..$**...**.*...*..$..**.*.*.*$..*.*$*.....******$....*.....*..$*.$..$$.....****......
...*.$...$...*...$$.*.*$..*......*$.*$$.........*...$*$.*..*$.*$$.$$....$*.*..$.*...$.$..*$$.$$..$*.$$*...$..$......$$*.**.$..$....*$*.$.$...$...**....*.$......$$*.$...*$$*...*..*.$...*.*******.$.**..*$$.*..**..*.$$**...$**...$..**$...*$.$..$...*.....*$.**.*...*$*$*.*...*....$$.$***$..*..$...$..$..$........
.$..$*......*$$.**$.....$.$..*$.*.*.$*.....*.*$.*$....*....$*$*.*$...**.$..*.$....*$...*...$....$$$.....$..$*.$$.*.*.$..*..*..$$$$.$.$..$..$....*$$$$$.$$....$..*$.*..*$......$$*.$..$..$...$...$$.**.$...$...$$..*..*..***..$....**$.*$$*.*.$*$.*...*...*.*......*$$*.**$.$..*$$...*.$$$$....*.*..*$$*...*.*..$.$.$
**...$....$.***...*..*$.**$.*$....*.$*$$.$*..*..*..$$.$*$..$.$*..*..*.*$*.*.*......*.$.*$.$*$$$.$.*$..$...*.$.*..$*......*.$......*.....$.$..*.$$...*$..$$$....$$.$..*...$**..*...$*.$*.*...*.$.*.*...$*......$.*..**....**.*...$.$...$*....*..***$.**..$.$.*......*$........*$$*.$$....**$.........$*$$.$..$...*$..
..$.*...$.$$....*.*.****$$.*$..$$$.$$*...$.***...*.$.....*$.*.*.$..$....*....$$.$......$*.*$*.....*.$**$.$$.*.*.....*$..$.....*$..$**$*.*...*.*.$....$.*......$..*.***..$.*....*$..$*.*...**.*$*..$$$$.*..*.$$.*..$..$........$.....$....*$...*..**.....$.$*$$$...*.$$$*.$.*....$*....*..**.....***$.$.$.*...$$.$...
....**.$.$....**.*.....*$...$....$$.....$..*..$.*..$$..*.**...***$.*...$.**$$....*.$$*$$*.*.**$$......*.$....$...$.*....$*....*$..**..*..$...*...*...*$*.$.*$...$..$...***.......$.**$$***........$...$...*$.*..$...**..*..$..$...$*..*....***$*....*..**..$...*..*..*..$.*..$.*.$...$.**....*$$$.......*..$.*$$.**$
$..*..$.$..........$.$$.*.......***...*..*...*...$.$.$..........$$.......$*$.*$*$.*$..*....*..*$***..*.$*.*.*..$**.$...**...$.$..*.$...$.*...*..$$$.$..$$*$$...$..$.*$..*........$..*..$..*..**...*.*....$.........$.*........$.$***$.*..**.**$.$*.*..*$.....$.*$**$.$.*..*****....$$*.$...*$$...*.....$..*.*..*..$.
....**......$.$$*.**$.$....*.$$....$$.**.*.$...*..$...$*.*$$**$.$....$*$.$.$$.*.$$............**$.*$$...*.$*.$....$.**$$.$..*$$.*.*$*..$..$...$**..*.....$...**...$$**$**$$......$*...$.*....*$.**...*.$$.$.*$..**.......*$$$.....$..$*...*....*$$*...*.....$.$$.$.......*$....$$*.$$.$$.$..$.$...........*.$*......
$.$...$$...$$...$..........$$.*$......$..*$*......$$.*..*....*..*.$.$..***$$..$*..*$$.*.$...**....$....*..**$$*$.....*...*.....*.**......***..$*.....*...$$.*....$...*..........*..$..*$.*$*.*..*..*......$$.**$..$...*$..*..*..*...$*.$.......*$*....*.......*$.$...*.$...$$......$*.*$....**$.$$.$....$*.***.$$*$$
$$...$.$..$*..*..$$..*$..$$.$...$...$.$$$......$$...**..*.$.*..*.$$..................***.*.*.*....*$$$..*..*.$*.$$$.**.*..*.$$.**...*..*..........$.*...**......**.$*.*$........$*..*...$...*...........$..$....$.$*..$..*.*...***.$*.$.*..**.........$.*....**....$.......$****..*.$.**.*.$*.....**$.$...*.$$.....$
.$.*$$...$.*...$...$.**.....*.*$...$**.$...$..$*.*.$$.....$$$*$.*.$.$$.*$.$.$.....$*$....*....*......$**....$$$$.$..**$*.$*$..*$*.*...$$$*$..*.....*$$.$*.*...*..$*$..*.**.$.....*.*.**.****.......*$$..*..*.*..$$.$...$....$........$$$*....$.........$..$**..$..$*.*..$$..$$..*.$.........$*.*..$..$*$..$**.$..$$.
..*..**.*$.$.$.....$.*..*.....$....*...*..*$*$$$**$.*.....*$$..$...*...*..$$..*..***..$$$...*$..............$...*...$..$*.$..$*$*....$**.$.*$$....*.$*....$$$..*.....*$.....*.*$**.*.........$*.$.*$...$.*..*$......*$*.$.***........**.$**.*$*....*..$.$..$***......$*...*.$*..$...$..*.....*$......$$***$....*$*..
...$*..$.*.*..$**.*...$.$*..$.$....$..*.*.*.....*..*.*..$...$..****.**$...$.....*$....*.*.$.....*.*$...$*$...*.$...$....*....*.........$.........$....**.....$....*..*$*..$.....$*........$*.$.$$$.*.....$$.$**....*.*$.*.........$$.*...$$.....$*$.$.*..**....$.*..*..$*.*...*...$..$...$...$$$....$**....*$.**$...
$......*.$.*.*.*$$...$.*...$*.......**$$.....*.$.*..$....*$..*.$*...**....**.$..*..$.*..***.$.**$...$.$.*$$..$.$.*..*.$*...$.*$.......*$..*.........$$**........*.$*.......*.$..*$.**$.*$**.*$...*...$$*$...*.*.........$*$..$.$$......$.$...**$...*..**.*.*....*$*.$.....$$.*..*$.*..$$.*.*$...*.*..**..$.*.$.$*...
$..*.......$*.*.$..*$...$$.$..$*...*....$*$..$***.....*.**........$..***.$*.$.*..*...$..**$.$$*$.$..*..*..$.**..$$....$$$...$$$....$..........*.*.**..*.*.$..$$.$..$*..$*.$$...$.....$$*$.*.*.*..$.$..$$.*.*..**...$$.$.$.*..$*$$....*..$$.**...*$..*.$$....$...$..*.**.$**.....$...**$.....*.$..$$.......$$**......
$..*.....$$...*..$*..*.*........*.$$..$*..*..*..$...$...$..$...$.*..$.*.$$....$..$**$.*$.....*......*$...$$.$.$..*.*$$...$*$$*.$.*.........$$...$..$**$..*...$*.*.....*..$..*..**.$..$.*$$....$$.*.*..*.$*...**.$*..$...*.$$*$$..*$..$.****.......$.$*...$*...$$$*...*$.$...$.*..*..*$**..$*.*...*...$$$$.......*$*.
*.....$............*..$*$.**...**.*.**.*.....*.$$.*......$$...$.$$..*$..$...*.*.*.*$.........$...$$.....*....**.$...$*.*$.*....$**.*$$*$*....$..*...$....$........***$.$......*.....*$$*..........$.*.**.$*.....$...$.....$..$.*.*..*$.$......$$$.*$.*...*..**..*....*.***$*.*$$$.....**...*..*.$.*.$*.......$$..$..
*$.*.*....$**.........$*..*.....$.$.**......$*...$...*.....*.*$.$**$..$.**..*.*.....*..$.....*$..**..**.$...*$$..$$.$......$..*....$.$$$.*..$..*.$..$$$...*....*$...*.....$.*....*.$.$....**$..*......$$$.*$$.$.$...$*$...$...*.$..$.$*.*...$.$..$...*...*.*....$.*..$$*..$.$$*.$****.....*.**..*.....*$.*....*.$..*
..*$..$.*.....$$.***.*.*.*.**$*...$..*.*$*..*$.$.*..$....$.*..*......$****$.$..**...*.*..$.*.$$.*...$....*..$.$..$*$$*.*$....*....*..*.*..*.*$..*.*...$.**$.$.$....*$$....$........$.*.$$....$.$.$*..$...$.*..**$..$....$.**.**...............$$$**..$..*...$*$*........$.$..*..$..*...$.*......$$*$$$......**.$.*.*
.$..$...$$$$......*.*.*..*$*.$$.$.*.....$$.$...*..$$*.$$*$......$**.**.$.$.*..*$$*....*.....*$.....$.$*.**.........$.*....$.*$...*...$.***$***..$...$$..*$..*.$$.$...*......$..$..$.***.*..**.**..*$.$$$*..*.*****..*...**....$.$.*...$.*$...**.*..*$**.*...*$..**..$........*.$..**..*....*.*.....*$.$.$*....$...*.
.*.**.....*$$$...$.**.$$*..$*.*.$*.$$..$....*$$..*.*.*.....$.$.$.$.$.*...*.$.$$.$.*....$...$..$*...$**..*.*$$$.*$**$.$$.....$$*...*.*$.$.*.*.$......$.$.$.*..**...*********...$**...*.$...$..*$....$*.....*****.*$...$.$...$.........*..$**$.....$.*..........**.$.$$.*...**..$**..*.*$$*...*.*.$*.$.*.$$*..*......$
.......*....$.$*..$$...$....*$*$...$..$.*$.$.......*.....$*.$$***.......$*$..*...*..*....$....$.**$.*..$*$*$.*....*.*.....$*$*.....$...*.............*.....*.....$*..$$.*....**$...*.*$.**.*..*.*.$.$$..$...........*..*$.***.*.$..$.***...*$...$...$.*..*....**.*...$..**.*.$$.*..$..$......$..$$*...*.$.*.......**
....$$$..**...$..$.**..$.$.*...*$*$..$....$.$**..$..$$$$.$.*$.$............***..*........*$$*.$.*$**$.........$..$.*.*$*$...$$..$...$.$*$*..$.....*.$..$...$*....$*....*$.$*.*$*.*..$...*.$..$.*.$*....*...*$....$.*...**$$..*.**...........*...*..$.$.....$.*.$..*......$$*.*.$.....*..$..$$$*..**.$$**..$.$.*..$.$
..$......$..$.$$.*.$$$..**.*......**.*....$$*.......**$*....*.$..$*..$.$.$.$*$$.**$*..$.*....$$*$.$.$..*...*.$....*.**.$...$*.$.$.$$*$..**$..$$**$*.....$.$...$.......$....*.$.$...**$$$*.$$*$..*......$*.$*..*$.......**..*...*$.....$....*$*..*$...$$$..........$$.$.$$*$....$..***.$..$.*....*.*....*..$*.*$$**..
.$*.*$.*..$$.$$.*...$.*........*..$.........*.*$.....$.$....$..*.*$$..$$*..*..**..**$.$......$$*.$*.$.....$...$....*$.*.....*.$.$$.....$**...*$****.*......$$**.....$..$.....$.*.*..**$...*....***......$**.$...*.*.$*.*.*$*.....*.....***..*.$*$.*...*....*.*.$....$.....*..*..**$..$...**....**.$$..$*....*$*..**.
..*.......$..$$$*..*.*$*$*$$.*.....$.*.......$....$.$$...*..*............$......$$...$.*...**$.$.$*$....$$.*$*..$.$.$....$*$.........*..**$$$.$............**..$$..*.***.$*....$..$..$.$$.$.....$..$.*$$..*$.$.....$*...$..**...*.$......*$*...**.....$.*$..$.$...*.....$.$*.$.$$.$...$...*.*$.*.$.*....$$*.*..***..
..**.*$..$....**.*$*..**..*...*.*.*$.*$.$.*.....**$..$$.$.*.$$...$*.*.*..$$**$*...$$.*...**.$..*.*.*..$..*.$.$......$*.$...$.$...*.*.$$..**......*.$$...*..$..*.$....*..*..*.$.*.$...$.*..$*$.....$*$..*...*$..*$.$....*.....$.$....*....$..*.*......$$$.*$*...$*.$.$$.*$.....$.....$$*...*.$*..**.$...*.$$.$.......
.....*$**.....$*.$*......$.$*.............$..*.......**..*.*..*...*.$..$..$.*.*$$.*$$.$.*$*.$$.....$$.....$.$**...$...$..$.$*..*.$.$..*.....*........*$$*$$.$**......$..**.$$.$*$....$*..........$*.$$*.$*.*.*..$.*..*$**$..$...$*..$$$*..$..*.........$..*....*$*$.............*..*.....$$...$..*$*..*$$.*...$.....
.$..$......$....**..........*..**$.$.*..$*...*...**...$.$.....*$$.$*.$...$.$....$*.$.....*.*.*$*.$$.$...$.$**...$...$.*...$...........$..$*....**$*.*...$.*..*......*.....$*................*....$$$..*...*..$$.*..$*.$.*..*.*$..$.*........$$.$*..$*...**.*.***..*..$.....***..**$.....**...........$....$*.....*..
.*......$..$$.......*..*$*.*.......$$*.*.*$$..$.*..*.$..**...*.$..*...$$....$*$...$**$$.*$....$$*.$$*.***.$..........*$....$.*..$..$...*.*..$...*$*.......$.$.*.....*$....$*$***..$.*$.**$......*$*...**...$$.$.*.*.....*.....$....$*.*.$.$.$.......$.*...$..$*$$$$.$.$**$...*$.....**$.*.......*$$$.*.$..$......*..
..$.$$$**..*$.*.*$.....**..$$$........$..$....$..$.*..$..**.$**$$$*.*$.$**.*.$...$*..*$..$*$....$.*.*.*$..$$..**..*..$.$...$$.....$.*.....*.$.$.*...*..$.....**$.***.*...*.$*$......*.*$.$$*.*$*.*........$$..*.$.*..$.***...**...$*...*$..$.*.*$$......**..$***..*$........$*.........*$.$..$....$..*$..$.*.$..**.$
$.$........*....$.*.$..*...*..**.*...$....*.$.$.....$*...**.**.*$*..*.*.$.$.....$.$$*....$.*....*$*....$..*$.****$***...$...*....*...$...*..$..*.*...$..***..$.*..*$....$.*$$*$*.*....$.$.$....$...*..*$.$.......$*$..$.$..$*$.*...$........*$.$*$..*.*$....*.*.$....*..$$$..$..*..*$.*.*$..$....*.**$.$..*....$....
**....*$...$..$.......$.*$.$*....$.......*....$.$$...*$.....*.*..*.$$.......*...$$.$..*......$*.....$$.*..$$*$*..$.........*.**$$*....$$...$....$..$.......$....*....$.*..$*......$...$*.....$.....$.....**..****.*.*.*.$.$$*$*..***$...$.*.......$.*..*.$........*.*..$.$.*$..*.*.$*.$.......*$$$*..$....$$...$.$$$
*.*$.*.$.*.$*..$*$$.$..*..*......$*.*...**..*.$$..*$.$*.....$*..$........$..*......*.....$$..$...*.*..*$..$$$.....*.....$...$.*.$$.*..$.....$.......*.*$...*.*.$.$.......*.....*$*.$.$**$$$.*$......*.$.$*..*.$...$$..$*.*.$.*.**$....$.**$*.$..*$.$*$*.......*$**..*...**..$..$*.....**$...*$...*$.*..*.$$.*$..***.
..$.$$......*.**...$.**.*...$$......$*..$.*.$.*.....*.$..*.$$**.$.$.*.$.$..*.$....*.$.$..$.*..*$*$.$.*....***..$$$$..$*......$........*..*...*....$..$..*.*.$......$..*$.*$..*..*...$..**$...$.*$$.*$*$*.$$$.$.***$*.*.........*..$.$$*.$.$$.*..$..$.*$.*..*.$.*$$*..$*$.$.......$..*.$...$.$......*$$...*.$$*.$.$..
.....$..$$...$.$$..$.$$.....$...$$.**.$**...$..*.*.$$.......$.$*.*..$$*..*.....$....*..**..*.$$*$...*......*.*.....$*.......**....**.....$.*.$*....*...$.**..*$.**...*..$*..$.$*.$$.*..***.***....*$.**.......$$..$....*$*$$.$*....$$...$*.$...$..*...$*.$.....*.....**$..***..$..$....$*..$......$...*........*.$*.
**$..$..$*.....$.$..$*......*..........$....$$..*.**...$.$*.$..*$$***....$.$$.*.*..*.$$......$....*.$.$.*..**...$*..$..*.*.*.$.$**...*.$*...$.*.$$..$....$.*.$.*$$.$...*$....$.$*...*.....*.....*.*$*$....*.*.......*..$$...$*$....***..*$.$...*..$*...*...$..*.......$...$.**.......$..$.$*.$.*$*...$.$..*.........
$.....$.$....**.....**.....$......$.....*......*.$...**.$*....*.$$**....$*.......$$$**$...$$$*.$*....$$.....*.***...*.$.....$.****...$*..*$.......*.....$...*....*.$....*...$.$*$......$*.$*.*..$.*..*.*.*$..$.$..$$$...$$**...*....$**$*$.....**..**$$..*..***....$.....*$...**.....$**$.$$....*$*$$.*.$...*$**..$*
$..*...$..*..$.**.*....*$*........$*.$...$.*$....*........*.....*...$...$$.$.*...$$*.*...$*$$.$*$...$.....$..*$.*....**.$**.....$..$.*.$..$..*.$..*$**....$$.**.*....$...*.*.*...$..*$...***$$*.$*..$*$.$$....$.......$....*...*..$..*..$*.$*.*.*......*$.....*$.$*.*$$...*$.$...$.$.*..*..$...$.*.$*.$..*...*...$..
$..$.......*........*.*.....*$..*...*..*..**.*...**...$$$..*..*...$....*.***...$..$.**$$...*..$.$*$**$...*.*$........$.*..$*..$...*.$.*....$$*.*$....*....$*..**$$....$.$.*.....*$$$...$$*.$.$....$..$$$.*..**.....**...*..$$*.$....$$.$.$***...$*...$*$.$.*.$**...$***.....***.*.****...*....*.*.$*....$..*....$$*.
$$.**..*.$*$..*.$.*.*..*.*$...$..$*$..*..$.*...**...$$*.*$.$.*.$....**....*..***......$*$*.$.$.*...$*.........$*.$..$...***..$$*..$$$...*$.*.*.*.....$......$**$$**.$..$$.*..$$$.*.$**..*...$...*.*..***....$*$.*.$*..$*$$$...*$.*.$*..*$*$.*..*$*.**.$*....$...*$.*$*.$$$.$....**$.*....*$.*..$$...*.$...**..$*..*.
...*...$..$...**..*$.**.**.*..$..$.$**$..*$*$.*$$.*.**..$.$***..$..**...*.*$..$.$....*.$.....$*...$$*$.*.*.*.$.*.*..*.....$*..$$..$...$$.*.***..$*.*$.*$......*.**...$..*.....$..*$$****....$*.$..*.$.....$$....*$*...$*.$$.....$...*.**....$$$*.*...*....$.*.$*....*..$*$.$$....*.*..*.$$.**.$..*.$.$.*...$......*.
.$.$$...$.....*.$*.$...**....*.$.*......**..$.$..$.$...$.$$.$.$.$*.......*.*$$........*...***..*..*......*.$$**.*$$$$.$$...*..**.$.$.$...$*...$*.$$*.*..$..*...$$.$*.*...$...**..*$$.$*$.*..$.......*$...*...$.$...*......$$.*..*.$*..*........$....$$$$.$..***$**$*.$$*$..$..*...$...$**$....**.$$$......*...$...*.
*..**$$*..**$$**....*....*$.......$..*...*....$..*..*.**.*.$**...**...........*..$*...$......$...*.$....*.*......$.*.$*...**$..$.*..**.*..***$*$..*$$***...***.....$............$....*.*$.*...*.*.$..*...$**...$.*$.$.$.....*.........$*...$$$...*.*..$.**.*...*$$.........$.$...*$*$$...*.*$$.....$.*$......$.$....
..$..$**$$..........*.$*$*...$.*....*..*.**.**.........*..**..**...$...*$$$...*..*$....*....$....$$.*..*...........$...**$$......*$.......$......$.$*$....*.*$.....*.$....*.$$**.....$$...*.......$...*......*.*.....$$$..*$$*..$.$.*.$.$$..*...$$..$*$$.$$..**......*$..$**.........$...*..*.$..$......$..$*$.**..$
*.....**$..**$$..**$...**........$....**$.$$..$..**$..*$.*.$.*...$......*$.....$**...*....*.....$*....$..$.*...*....$*.*.****$$..*...$.*$.$*..........**......$$.*$$.$**.$.$...*$.$..*.$*$..*.***.....*$.**.*.....$$..*...*.*..$.*.......$.*.$...$..$$...$$.$..$*$*$...$.**$.*..*.*$..*$.$.*.*$...$.$...**$..*$*.$.$
*.$*$$...**....$.*..$.$..$$..**.*.$...$$$....$$..$..........*$..$.$$...$$...*..$.*.*.$..$..........*...$.*.$***$*.$.$.....*.$.*....$........*..****.$.*.$$..$$.*..$..$.*.......*$$........*...*.*$**.*$*..*...*$*.***.$.*.**....*$..$.*..*..$...**.$*...$..$**..$.....*..$...**.*..*$.$.....$..**...$$.*......$..$..
.$$..$.*....$$*.$$.$..$**....*...$$*.$**.....*.*....$..*.*$..$*...*..$.$.$.*.$**$..$$*...*......$..$...$*...$*....*.*..*..$.......*........$*.*.......**..*$$..$...*..$.**.$$$..$......$...$...*$$..$*$.*...*.$.$*$.$*...$.*.**.**.*.*...**$$....$..$.$........*..*....$*.$$..$*...*.*$.....*..*.....*.$...$...$...$
..$.....*.*...$$*$$.$.*.*.*.$*.$*..*.$.*..*......*.*....$..$*....$*.$....*$.*...*.$....*.$$$...*...*.$*$....$.....$...$.....$$$$...$*.....**.*..**.$.$$....$.$.$..*$.$..$..*....$...*.*.$..$**..*$......**.$.*$*..*.*..**.$$..$$$...*.$..*...*$.$$.*$.**.*........$..*...$..$*$..*.*.$*$**.$..*...$..$.$...*$*$.....
.***$*$.*..**....*..$*.....*..*.*..*..$...*.*..$.....$.....*..*...$**$..*...$*...$...$$......*..$$*.**..$*....**.$$..$....*..$$..*$...$..**......*..*......***$....*..$...$...*.$..*$*.............*.*..**..$$....$*$...*$$*...*.$.*$$$$...$..$$.*$.$......*$.$..$.*.*$.*...**..$*....*.$..$.$*.......*..*.$$*.*..$*
*$.$......*$$*.$.*$....$...*....*.....$.*$*...$..*$.*.$$.**$.......*.$$*..*..*.$....$...*..$...$....*$.$$*....*..**....*.$.....$$..$$$.*..........$**.$**$**..*..$.*$**.*..*.*..*.*......$.$.........$.*$.........$.$...$*..$....*....*$$*....*.$$....$*$**.$.*..*.$$*.**$$...$.*$*.$$$$.$..**$...**$...$....*......
.$.**.$...*.$$.***.$*$.*..$.$..*...$*$.$$*.....*....**$.*$..**.$..$...$.....*$.$......*..$*.*$........*.*$.$......*.........**.$$$..$.....*.*...*.*.$...$..$...$$..$*.**.*.*$.$....*$*.*$..$..$$$*..*$*...$$..$......$....*.*...$*$*.$$....$...*$*.$.....**$*.*.*$.$$.....$.*...$....*.......*.*$...**$$****.$$.$..$
*..$.$$*$..$*.....$..*$....$.*..*.*...*..$.*...*$$...$...$.$.$......*...$$.*.*...$$...*$.***....**..*$*..*$.....*..*...$$$$*..**$$*$..**..$$........*$..$$..$..$.**....$..$$.*$.*.$..**.$....$$.$...*.**..*..$**$.*.*..$..$..**.*.*...$*$.$$...$$*..**...*$*$$.*.**..**.$...$......*...$*.*.$...*$.$...$..$.*.*..*..
.$$*...$.$*$.$$*$$.*.$.*.*...$**$*.....$$...*.*.....**.....*$**$...$*.$$.$..*$..*..$...*..$$$.......$**.....$....*.....*$$.**....*$$...*.*$...*.$*$.$....*.*.*..*.*..$.*$.*.$**$...*.$$$*...$$*..*...$$$$*$$..........$.......**.$$..$.*.**..*.........$**...*$$*.$...*..*.*..$$*.....*$.$.....$.$**$......**...$...
....$..$$$.*..**.....$.....*...***$.$*.**..*.......*..$...*...*$.$.**......*..$.$$$.*.$.....*.*$*.$.*...*..*.*..*...*.*$*$.*.....$...$..$*.*.*..*.$......$.**.$...*..*...$....$*$$$.....*.$*..$....*....*.$.$.*...$$.$.$*..$.$...*$...$*....$$.........$......*....**$*.....$...*$.$.$.$...$$$...$.***....$.$..*..$.
$.**..$..*...$$$.*.$*....*$.........$.*$.*$*.$..*$$*.......$*$....*$....**$$...$.***.*.$*$$*$*......$.$..**$.....*..***..$.*$....$.....*$.*.*...........*$.......$$$.*..**....*.$$.*$...$.*$$.$...*$***.....$.....*$$.......*..*..$$.....*.*.*.....$.$.$$..*..*...$.*...$.$$...$.$*.$.$.**.**.$..$*$.$.......*..$*..
*..$*.......*$*$.*..$..$$*..$$$..$$.$$.$$..$*.*..*..$.*.*....$$..**.*.....$...*..*$.*.$....$..*.......$....*...*$...$.....$.*.$$*...$**$.*...*..$*.*..*.$*..*$*$..*$.$$....*....*.....*.....*.$.....$*$*...$$*.....$....$.$..$$.$.$$...*.*.*.**.$....*$$..$...$$..$.*$*.$*$..*$....$*.*.**$.$...$*$...$.$......*..$.
.*$..$$$....**..**$.....*.$.*$..*.$...*.*..$....*$**....$.***$.$*$**.....**......$$$..$.$$....*......$...**..........*..*.$*.$$*$*$..$.$$.***$..*$...*......*$.*..$....**$*.$........$..$..$.*$.$*.***$.*...$$**.**$.....$*.*...$$.........$*.$..$.$$*$.....*.$*...*.*..$*..*$.*$*.**.$$$.....$....$$.$...$$.*.$.*$.
$*..*$...$...*....$....*..***...$...$.*$$$.$$*........*$*....$..*.**..*.**.$....*...*$.....*.*$.****$$.$*.$$$.*..*.*.$..$.*....*..$.$...*$*..$...*...........*..*......*$.$...*$.$.**..$$...$$.....*....*.$$.*.$.*....$....*...$.**....$.$...$.$...$*.$***...*...$$.$.**..*$$....$......$...$*.$*.....*.***$.*.$..$.
**$.*$.*$.$....*$..$**$...$$.$.$.*...$.*$$*.*$*.$....**$...*$.*.*..***$**$..**$*....$..*...$$..$..$$$...*......$.$..$.....*$.*..$$..$**..$..*$...*.**......*$$......*.$...$$.....$*..**.*....*$*....*..*....$$*.*..*....$*$.$.......$*..$..*....$$*$.**$.$.$.$*.....*...$......$$.*.**.....*..$..$*..*$*...*..$*...*
..$..$.$..*.$...$..**...$....*.....*..$$*.$..$...$....**$..$..**$$....*....*..*.$..$.**.**$......*..**.*....*....$$.$$$.*..$.*.$.*.....*.*..*..$$$...$..*$*.*$$$$*..$...$...**.*.$$*.$..$.$$.$$...$*$$...*.$....$*$.$.*.....$$$.$*.$..$$..*...**....$.$.*.$..$.**$*...*...*..$*...*....*$$.$.$*$*.*..**$**.......***
$.*..$*.***$*$.*.*$..$...$.$...$..*.$**$$$.........$.$.**$..*..*...*.$..$*..*....$*.$$$$..$.*.*$......*..$*$.$.*.$.$...$...$$$.....$*..*$*$.*........$..$......*.$$.$$.$.*..$...$$$*$$.$$$*...$......*$.....*.....$$$...*..****...$....$$..*...$...$*...$..$...$.....$.....**..*...*...*$.....*..$....*...$...*....*
.....*..*.**...$.$$..*..$*.$..*.....$**..****.*$$$.*...$..*.$..*....*.*...$.$.$.*....$*..*$.*.*.$*....*.*.*.**..*$$.*..$*...*$..$..*....*.*.**$..$$$$$.$*.......$.$*$$.$.*........*..**.$$*..$$*$**.$.$*$.**$.$.$$*...$...$......$$.$$....*$$$..*.*.*$$*$$*.....*.*.*.........$.....$.$....$$.*$...**...*$$...$....$
.*..$.*..*$......*..*$$....$$.*.*.*.$*.$$...$...........*......*..$...$.*..*.**..*.$**$......*$$$****$.*..*.*.....$$.$.$$..**..*$$...$..............$$...$*..$.*..$.$....$..*..**....*$*$*....$*..*...$.$*$*.....****.*.***....$$....*..$.*.$...$*.........*$*.*..*$*..**...*$..*.$.....*$*...$......$...*.*.*..*.$.
$.$**...*.....*.$..$..$$.*.**..$...*.$..$..*.$$..$.$$.*...*$..$**...*.$.$*.*.$*$...**.$..$$...$*$$...*....$...*.....$...$..$$*.......$....*.$*...*.*$.*$...**$..$$..**..$*....$..$$.*.....*.$.......**$.$..$$*$...*$...$......*...*.$*...*..$$.$**$..$*..*...$.$.*......$.$..$..$.*.....*...*...$.$...$..*..$.*.....
*.**...$$$$.$$$*.**.*.*..*$*.$*.$*..*.*$$..$.$*.$......****.....*..*.*....*$..$.*....$....$*.$$..*$**$....*..*$.*$..*$$....*..*$*.$..***$*..**.......*$.*$...*$$$$..*$*..$$.$$*.*....*..*.*$$..........$..$..*..*$*.*.$*.$..*...*..**..$*.*$$.....$$*.*$*.*....***..$*$.**$....**.....*$.....*$.*...*.$*$$*.$.$..*$.
.*.$.....*..***...**$$*.$***......$.*...*$.$.$*..*.$.*..$..$$.$$...*$.$.**.$...$....*.$*..$.$*$*$$$*....$*$.....$.$.**..$**.*$$.$.....$....$$*...**$*$..*$.....*$..***....*......$...$*..$.$$*.**...$$**...**$$..*.*$*...$...$*...****....*.$..$.$**$..**..$......$*$*....*.*..*......$....$$.$*$..$$..**.$$....*$.*
$...$...*..$...*....*..*.$$.**....*.*.*....$..*.*****.*..***$.$$...$.*.$.*$.*$..$.$..$.$..$*.....$$.$.*......*.....$*$.*.$...*....*......*$$......$..$*...*...$$**.$...*$$*..**..$.........$*$.*...****..*.*....$................$.*..*........$..$.$...$*...*..$*$$$.........$*....**$..$$.**...$.....*..*...$...$$
.....$*.....$..*...*.$$...$....**$..$$....***.$$......*.*.$$$*$...*...$......*....*..*..$.$*.....*.$.$..$..$$..........$.$$.$$*....*.*..*$.....$..**.*.*..$.*.*...*$*......**..$.$...*.*.*$*.*$....$..**.$....$*....*.....$.$.$..$....*.*..*....*.$.*.$.$....$.....***$.*$$.$.*$.*.$*.....$.$....**..*.$...$.....*$.
..$*$.*$.$.....*$$..*$..$$.$..$...$$.$.$*...*..$..$*$$.......*..$...$.*.$$*$$*$$$$...*...$.*..$*..**.*.....$.$$.*$.$......*..$..**.$$.$$..*...$*.*..*$...*.*...$**..$......*...$*.*....*.$.*$$*.*....$......**..**.*....$....$.*.**.*$*$....$$.*$......$*..*$.......*$.....$....**$.$*..*$*$..*.***$$..**.*$.$.....*
.$..*$.$.*$....$$....$$.*$..**$...*...$.*..*......$.*......***..*$.....$..*$*..$*...$.....$..*...*.*....$*$.**....$$..$$.$....$*.....$*$$..$**........$*..$.*...$...*.*..***$...$*...$..*.*..$....*.$....*..*$**.$.*.....$.*.**$$$*....**.......*....$..$$...*$.***$..$.$.*.$..*$$$$.$.*.....*.*...$*$....$....*....
.**.$.$**.....$..****.*$*..*$..*..$*$.$.....$.*....*.*...**....*.....*.*.**$.$....$*......*..$$*....$......*....*..$**....*......**.*.$$...$*.*...$...$.$.....***$.*.*..*$...***$*.*..........*...*.$..$*.*.$$.$$....*.$.$...*......$$$...$...$$..$$$...$$...*.*$..$$*..$....$$$$$..$.....**.*..*.*.**.....*$..$.$..
$**$..*.*.$.*.**$.**.*...$$..$$.$*..*$....$..***.*.$..$*.$*.*.*.$$.$$......$.......*..$.*..***......*$*..**....$....$..*..*$..**....$$$*...$*..$**.*.$$$..$......**.*$.....$$........$*......*$......$*.**...$$...$$..$..**.$$.$.$.....$...$.*......*.....***.*$.$*........$.$*$...***$...$.*$.$....$$.$....$**.**.$
$*.*.....$...***$....$..$.*$..**..*....*...$$*..$..*.$.**$...$....*...**.....*.*..$*$*.$...*.$.*$....$..$.....$.$$..*$$..$*..$*.*$*$$.$..$$*........**.*..$..**.$..$*..$.$...$$$$*..**..$..*.$$.....$$...***...$*.....*..$.$..$.$$...$$*..$$*$.......*$$.*.......$.$$.*..*$***..$....$.*.***...........$**$$**.$....
...$.$..**.*...*.....*$.$*$*.*.$*..$$.$$$.*..*$*$*.$.*.*.$$*.$$$*.**$.......$...$...*......$...*.$.*$.**....**..*...$*$..$...*.$.*..*.*..*.*.*..$$*..$**.*$*.*...*...*..*.*.$$.**$.**$...*..$.*......$*.*..$.*.*$.*.*.*..$.*..$*.$..**.*..$$$*....*..**$****.$*....*..*........**....*$..$.*$.*$..$..$$$$.**$$.$..$.
...$**.......$....*...*$.**.*.....$$...**.$.*.*$.**.*$**$.$*$........$...........*.*..*.......**...*.......$*.*.*.$....*$$.$.*.$$..$.$$$...$....$.........$$......*....*$...$*.*$$$...*$.*.$$..**$$..$.....$*$...*.$$...*$.*$..$...$...$....$$...*$**...$*...*......*$$.......$..$*.$.....$.*$...*...*..$.$*....$$$$
...$.$*....$*$*$**$..**....*...*....$.....$....*.*.$$...*...*.$*.....*....$.....$...$.$.*$....*$*.*..*..........**..*..$***..*...$....*..$.....*.$...$...**$$..*$.*...*.....$$....$...$*$..*.....*$.....$$.*.......$.$..$*....*.$..$....$....**.$..$*.$...$..........$.*..**...*..*.*$*...*..*.$*.*.$*..*..$.$$...**
*.$*.$.***$*..$*.....*.$.$..*...$*....$.*$.*$....*...$$...*.**...$$$.*.**......$..$$.......***$$......$.$*..*.*.**..*.....$*.$.......*........$..$.$$*$.....*.$....*.**.$..**..$....*..$.....$$$....$..........*..$..**.*..*....$...*$..*.....$$.......$...*.....$.$..*$..$**$..$$..$..**..$.........$...$......$*..
$..***.$.....$..*$$..*.$.*$.$$.*....***..$*......*.$$*.*...*.**.*...*.....*.*.....$...*...*....*.$..........$*..$............*.$....$*.......*$..$..*..*.*$**.$$..*.*...**..$...$..*$.$..*.....$.$...$.........**....*$.$$*..$$..**..$.*$**.**....**....***.*.$$.*..*.....$.....*$*$.$$*.$$.$.*...$.$**$.$.$**$*$..*
..$***.*..*.$...*..$..***..*...$$..$.$*.***$$$........$$...$..$.*...*$$$.*.$$**.*.*.*.*...*.$$...$$$....$.*$.$.*$$.$.*..$..$$.$.$*.*...*....$.....$.$$....*.*$.$.*...*$..*..*...**..*$$.***....$.$.*$.*....*..$*..*...*$.*...$*...$...$.$.$..*.$.*..$*$*$***$.*..***$$*$$$..*$.....$.*...$...$..*$$.$.....$..***....
....*$*$..........$$......*..$$*$...*...*..$..$.$...$.....$.*.....$.$*..$..*.$*$..*..*.$...$.*$$$....*$$**..$.*.*.*..*.*.*..*$$.***.$.$....$*.****...$$.$$...*..*$.*...*....$$*$...*...$.$..*.$**$$...**...$.....$..*....$......*$..$.$.$.*.*...***$...*...*$**$...*..*$.*$*........$.....*..$...$..*..***.$$*..**$*
.*.**..*...*.*$......$$$.*..$..*.***.*...*$..*.....*......$$$.*.....$.$.*...**......$$.$*.$*.....*........*..$....$.....$.....*.$$**..*.............$**.....*$..$.....$..*$.*.....*..........**..**.*.$$.$*..$$...*$$..**.*.***.$.**.$$...$.*$*.*$....$...*...$.$$$*.$*.$......$*$..*..*..*...$...**....*......*....
..$$...*..*$*.*.......$*.*......$*.*.$..$$*........$..$$*$$*.*$..$*.$.*.*..$..*$*..*..$..$..$.$.*....$$..*.....*.$$.$..$$*..*..$$...*$$.**.....**$$.$$$.$.............$$*$.$*..*$*.*$....$....*....*..$......$*..$......$..$..$.......*..$...$...*..........$$.**.*.$.$.....*....*......*...*....*$.**.$$.$**..$...*
*$..$....$.**....*.$*...*.*.$...$..*.....**.*.$..*..*.*.$..*.$......*.......*..**....$.$.*...*.*..*............$*....$......$.$.$.....*..$..$.$......$..$.......$..*.*$.*..***...**.$.$.$...$....*$...*......$**$..*.$$**...*...........$...*..*...$.*.*$*.$.$...*$*$...**$.$**.*...***..*$.$*..*$...*...$...*..**..
***.$*$..*...$*.$..*...*..$*..$...*$$.*..*........$*$...*..*$.....*.$..*.$....$$...$$...**.$...*.....$.$...**$....$.$.**...*.......$.*..*..*..$*..$.*.*..**$.$..$..**..*...*.*....$.$....*...$$.....$*.*...*....*$*....$**$*.......$***$..$**$$$$.$........$...$$$.$..*..*...*..$..$$*$$.*...$*..*$...*.*..**..*...*
$**$.**...*..$*.*...*.*.$.*$...*...$$.$*.....*$*$*...*$*$.*.............$..$$....$$.*..*.......*.....*.$**.*..$...*......$*..**...$$..$.$.....$$.$.*$..$.$..$**....*..**.*$*..$...$....*...**.$**.$$........*.......*$..$.*........$.$.$...*..*..*..$.**....*.**.*.$.*$..$.*.....$*.$......$$*..........**....$.$..*
..$$$*..$$.....$....*....$.**..*......$.....$$$...$.*$.*.$*.$$.$$*.$*...$.....*...**...**.......*.*.$.*......$*$$.**.$*...*$*$........*$.*$..*.....**..*..**$*$...*$.*****....*..*...$..$.$..$...*..**.$..**$.$$.......*...*$$..$$*.*$$.*....*.*$.$**...........*.*$......$....$*....$$..$.......*....$$**$.$$.*..$.
$...$.*$**..*.$$.**.......$$$.....$..$.*..*$.*$*$.$......*$..*.*.*..*****..$$.$..$...........*.$.$$.$.$$**.*.$...*.*.....**..$..$$.**..*..........$..*$....$*$$...$**$....$.$*.$.....**...*.......$.$.$.$..$$...*..$$.$$.*$$........*$.$*....$*.....*$$...*$*.$..*.......$$.*...$.$.*.$.$...**$*..*......***$$$.$$$.
.......$.$.....*..*.*...**...$*...$......*$.*.**.*..*.$..*..$.*..$....*.$...*..$$$..$$**...$..*$*.*..$*$*$.*$*.*....*........**$$$....$.$*....$.$$....$...$.......$..........**..*$$..$*....$.$....$.*$..*.$*$.....$..$.*.................$$$.*.*..**...*$*$..$..$...$..*.$$$.....*...*$**.......$*$$.**..*.$.....*.
*..$$..*.....$*.....$.$*$.*...$.$.....*.*.*$.$.$$$.*...$...$.....*.$*...$..**..$..*..$$$....*...$.$..**.$....*..$*.*.*$$.*...$......*......$$.**...*.$.**....**$.***.$$$..$**...$$$..**.*$.$.*.$$*.*.$.$.....$..$...*.*....$.....$*...$$.*..$$*..*.$..*.$**.*.....$...**....$*$..$$$.**$..**..$....$....$$......$...
...$.$.**$*...*.$..$.......$..*..*..$$.......*...*....*.*.$*....*$.*...$..***..$.$..$$**..$$....$$$...**.....$$$**....*...*.*.$.....*....$.*.*$........*.*$$$..*.$*.*$*..*..*.$.....*.$.*$*$.**.*$*.*.*........$.$*......$$$.....*..$*...*.$*.*.*.$*.......$$.*..$*.*.*$.*..*.**.$...$$...*.**$.$..*.......$.*$*....
$....*$..$*.*.$...$.$..*...$$....*.***....$.....$..*....$..*................$..*......*.*..$...*......*.*.*.**.*$$.*$.....*....$..*...*...*.*.$..**.$$.*.*.*..**$.....$.*...$....**...$...$*.$*.$.$$...*.$$.**.$.$**$..*..$...$......*.$...*$.$*...$$*..*....$.$........*..$***..$.$*.**$*.*......*......$*.$...*..$
.$.$*$..**..$**$...*...$**.$.....$.$**$....$....$....$$.$.$.$.$**$..*..$...$.*....$..**.$..*.....*$....**.$.$...$...$..$.$.$..$*......***.*$.........*$$.....$....***......$*$.$$$$.$..$$$$..$......*.**......$*..$...*.....*.$..$...$$.$*$...*....*$$..*..$..*$$*..*$.$..*.*..$.*........$$$..**.**...*.*.*...**..$
.$..$.$..*.$$*$$*...*$$...$..*.$***..$.$..*..*$.*.$.$....*....$$..$*.$.*..*.$.*$.*.$*$$.$........$.*..$$$*..*$.$.*.**.....$.....**....*$*...*.$..$.$.$...*.$.....$*.$....*........$...$..*.$....$*.$*.........$*...$$$...$.....*$.....*$*..$....$*.*$**..$.$.$*........*$...$......$.....$.*.*$....$*...$....$.$$.$.
..**$.$..$$.$.$***$..$.....$........*.**.$$*$$**...$$.$...*..$$..$...***.$**$$.*....$$**$$..$*$.**...$.*.*....****.*$$..$.*.....$*...*.$....$*.......$.*$***...*..*$.$.*$$...$..$$.*.$..$$.*$*..$.$*$...$.*$*..$*.***..*..$$...........*.....*.$.*$*....$$.$...$....*...$.$.$*$.*....$..*..**..*........***...$..$..
....*...$.$..*......$..$..$*........*.$*..*.$.$$*.**.**.$$.*.*....$.**.$..*$.*...$....*$..*.$*.*.*.*...*.****....$.*.$*..**..*.$.$.$...*..$...**.$$$.$$.*..**.*$..$*$..$...*.$.$...$$..*.....$.**......**...*$*.$*..*.*$.......$..$.*.....*.$.....$.*..$$.*...*.$$.......$....$.$...*.$*...$....*..*.....*....$.$...
...$......$*.$$...*.$*$$....$...$$.****...$....$****$....***$.*$.$.$$$.$$.......*$.....$$..*..**...**$$.$.*$*....*$.$..$..*$.$.....$*..*..*$...$$**$.$...*.......$...*.*$..*.$.*...*$..*$**....$..$*.$..$*$.$.***......*..$$....*$...*..*...*..*....$..**.$..$*$$.$$.$$..$*.....*.$.$$......*.$........*..$......$..
.....*$*...*.$..$$$.$.....$...$.*...$.....*....*$...$...$..$..$....$...$.....$*..$$**...*.$....$*.$.$.*.$***..**..$$.*.$$..*.....**..*.*$.$.*....$*....**........*$..$...*..$.$*......*.$..$$$.$.......*..$***...$*$....*...*...$........*$*$...*.*.$.*..*$$..*.....**.$..$......****..*.$*$$.**.*.$*.......*..$....
.*.$.$*.*..*..*.$$.$$*....$*$*...*........$.$.*.*.$.$$*$....*..$.*.$*$.$$.....$..$.........*.....*.$*$.$...$*.*.$*.$...*....*...$$....*..**.*....*..$$..$**....**.$.....***....$*..$*.$....*.*....$*..$**.$.$..*..*$.$$*...*.$.*....*...$$$...$..*...*$..$......$....*.*.$.$.....$$*..$$$.$*$*.$.*..*.......$..$....
*...*.$$...*$.**.$$*.......$.$$..*.......$.*.....*..$$.......$.*...$....$..$..$.$..*.**$*$.$$.$.$..*.*.*..*.*..*$$..$****.$.*$......$..*.$.$..$..**...*......*..*.**.*$**.*.*$$$$*.$.*$*.$..$.....$.$$.....*..*$...$....*.*.*.*..*$$$$..***..*$.....**$*....**$..$$*..*$.$$*....$..*...*$...*.....$**..$....$....**$
$.*.....$$.*.$...*$.$.*.$*..$*..$**.*.....**$.$*****.*.....*.$*$$...$**.....$.*........**....$$$.*$*.....*.$*..........$...*.....**....*...$$.***..*.*$**..*.$$$.......*..*.******$...*.$*.$$.*...*.$..*....$...*.$$.....$..**.$.$*...*.$.*$..$.*$.*.*..*.$$$..........*..$..*.*...$.*$...$$.*..$.*....***$$$.$...$.
.$.*$$$.*..$$.*.*.*...$..$.$.*.$..*..$*..$$....$$*..***......*$......*.$.**...*$...$*.**..$.$..$*.*...$***..$.*$.**.$..$*.....*$...$........*.*$*$.**$.$.$**$$..$..........**$$$..$**.$.....$$..*$*....*.....$...$*....*...*.*....*.$...$..*.......$.*....*...**.*$.**.$..*.*$.*.$....*.$.*.$..$$$*..$$..$..........
..$*......*..$$.*$*$*.....*....*..$.....*.......$$..$**...$*...*.$.$.$$...*.*..$$.....$...$$*...*....$....$$*..$..*..$$*...*.$.$*.$..$...$$*$*$.*.$...$.$...*.$*$..$$..*$....*.....$..$.*......$...*.$.$$$......*$*...$.*$$.*$.$$$...$$......$*..*......$.$......$$.$..*.*....*....$*.....$$*....$......*$$..$*$..*.
*..$.$*.$$.*.......**.$$*..$*.*.....$..*..$..*$*.$**......$$..$**$..$...*$*.***..***....$..*.*$....$*..$..*$$.*....*......$*$....*.........$..*.........$...*..$*....*..*..$......$$......*.*$......*.***$.....*.*.....*$...$.***...$.*$..*$.....*.*...$..$.$....*.*....*$.**....*.*...*$*$$.....*.*$.$...*...$**..*
.....*$$.*$$$.....$...$.$.$$.*$..........$$$.*.$.*...$.....***...$*....$**..$...*.....$$...$.....$..$$.*.*..$....$.....$*$$*............*..$$...*$..**..$........$$..$*....$$..*$...$.$..*$.....*.**.*$...$..*......*...*.$$...*.....*..**$.*.$$**...**..*.*.....$..$.*$.*.*.*..$$$.**$$$$$.$..*$.$$......$.*$.$$..$
*.$.$$*.$..*...$..$*.....***...*.**.**..*....**......*..*..$...*....*.......$$*.$*$$.$.......$.....*....$..**.$$$....*..*.$.$$*.**$..*$.$...****$.$$..$..$*.....*$.*.$$.**..**$*..*..$$.*.*.*.**....$.*..*.*...*.....$...$.*..$..$*..$..**.*......$$*...*$.$..**.*.*..............*...$.$...*$.*....$..$.$.*.......$
..$**$***.....*..$....*$.$$*$$$...*....$.....$.**.***...*$...$*..*....$$.$$*.*.......*$...$$.$..**...**$.$...$$$.$..*.$.*.....$**..*..$..*.....*$$.......$*.$$*..$..*.$*$.**..$.*...$...*.*$**...$*..$..$*..**.$.$**..*$$...$.........$.$$...*...*$*$.....*.$.*$*.$.*$..$**.*...$$...$.$$.$.$*.$..*.$$$..*...*.*....
....$.$....$...***$$...*...*$$.$$$..*.......$**$.$.$...*$...$$....*.*.*...***.$..*.*..*.$.$*$$$...*.*....$*..$.$...$....$$..$$.........**.*..*$.$.$.$.$..$.**.$*$$.$$*..*....$*.*.*.*..*..$......$*.....*...$**.*..$.*$.*.$.**...*......*....$$$$$$.*..*.$*.**...**....$.$$..$**.*$$....$$.*....$**.*$$..*...*$$$$**
*...*$.....$..*......$..$..$...*.$.*..*.*..*.$$*..$$.$.$..*.$$.$*.$..$*$*...$.*........*..$$.$.*$*.$.$.....*.$.$.*.**$$....*$....*...*$*.*....$...$.**......$......***..$.*...*..*.*.*$..$.**.$.$.**...*$.**..****.$$.*$..*..*$..$*..*$.....*..*.$.$**.*.*..$$..*$*.$.$.*.**.$$.**.**...*.*.*...*....*$.$*..$$..*.$.
$..$...*$....*.$.*..$..$.$$.*.$*.....*.*$*$..*....*.$..$$..........**.*.$.$....$.$*$...$..$.*.....*$..*..$.*.*....$..$...*..$.$$..*...$$$...*.......$...*$.*.***.*.*.$.*.....*..*...$.$.$*...*....$....**$.$.*$......*..$**.$*..*.*...$**$...*$.**......$.$.$$.....$$*$.....$*$.*......$.$...$$...*$......$.*...$*.$
.$.........$..$*..*..$...$..$$..*$$$.......$$.$..*..$...*....$.**$***...$$**..$..***...$.*$.*..*..*..$...$..*.$**..$.$$$.*.$$...*.....**$..$...$.$.**.$$.$..$$.$$.$$..$$*....$.....*.*...*..$..$*.......**..*$...$.*...$*.*......$...........*.*$$*...$.*..$...*$*..*$$.*...$.....$$.$*.$..$..*....$....*..$**.**..*
$$$*.$.$..$$.*.*$...*....*.*..$..$....*$$*$...........*.$$*........*..$.*...$.$...$*$..*.$...$.$....$*.$.*$$.*$*.$*.....$......***$*.$$*...$.*..$*.**..$*$...$...**....$.***..$*$....$...*..........*$$...$.$.*.**$....$.....*....$**....*..*..$..$...$.$......*...**$.$$.......*.*$$..*.*...$$**...**.$.$$.......$.
...$.....$*.*.*$..$*.$.$$.*.$....$..$*.*..*$....$..$...*.....$*****.........**.*.***..$$.*.$.......*.**..$..$..........*$..$*...*.$*$$.....*.$*$..$.***$.*$.....*.$.$.$*.....*..$$......*$.*..$*...*.*.$$.$...**$..*$.*..*$.*..$.$.$$*.....$..*..$*....$..*$...*...*..*.$**.$.*.$.*.....*...$..$$..$.......$...*....
$.$.........$..$*.....$*.....*..$.$$$.**...*....$$.$$$$*.$$$*.*.$.*....$...**....$.*$$$.$$.$$...*.$.*$$.**$*$....*....*.*...$$..*.$$$.**.$$..*...*$.$......*$...$$...*...*.....**..*..$$.....*$$...$*.*.$*..*..$$..*$$****..$$*....$..$..$..*...**.$.....***..$...*$*..*..*..$.*....$.....*..$*.*$$.....$*.$..$$*..*
$.*..*.$....*....*..$..$..$*$$....$*...*..$..*..$*$**...$$$..**...*....**..*$..*.*$*..$..$*$**.$$$...*.$$*...*$$...**.$.*$*$**...$...$.***.**..$..*.$....$....*....*$.....$.....*..*.**..*.$.$$*...*$....$*..*.$$.*...*$$....*..$....*.*$*$.$..*......$.$..........*...$..*.*..$.*..*...$.....*$$..*$..*.$.$..*$....
**......$.*...*.$.**.$.*.**$*.$....$$.$.$$*...**.$.....$..*......$*..$.........*.$....$...$....*.....*$..$.$...$$..$.*.....$...$$$.$....$$*.*....*..$.*.......$..$..*......$$..$.*.....$*$*..$.**....*..$..$*....$.**$..***$$..****$.***.*.*..**....$$*$..$..*....*$**$*.*$*$.**.$..**.*.*$.....*....*..$$$*..$$$.$.
.*....$*.*..*.....$.**.$...$..*.$..$*$..*$.*.$$**...*.$.$.$..$..$.$***$....*.....$.*$*.*..*..*.*......$*...$.**......$*..*.$..*..$....*.$.$.$$......$..$.$.$$$...$..*.$....***$$..$......*..........$...*.........$...$.$.**.......**.$...*.*.**..*....$.$.$.$*....$*$.$.*..$*...$..$*.$*$$$$...*.$.$$*..$..*.$.**$.
..*.$*.$*.$...$.*....*.*$...$.$$...$...*.**.$$.$...**..*..**.*$.*.*.*.$$......*...*.*$.*..*.**....$..$*...*.$*$.*.*.**...$..$$.$*$.*....*......*$.$.$$*$....*$.....$$.$...*$.....*.$.......*.$.*$.$*.*.$.....*..$******..*.$*$*.....*....$*.........*...*$..$..*..$...*..**$......*..*...$....$$.*......*...........
$$$.$*...*..**......*..*......$.$.**.$...*..**.....**..$..$*..$*............$...$*.$...$*...*...**$...*.$$$.$$..$.$$.*..*..*.$..$*$.*.......*.*...*.$$.$..$.$.$*...$.*.**....$....$*.$**.$.*.........*$****..*......$....*....$$*.*.*$.*....$$$$.*......$.*.*..$*.......*$$.*..*..*.$..$..$**..*.........*.$$.$*$...
..*.$........*$.***.$.*..*..$..$.$......$$.$...$$.$$..$$..*..$.$$..*..*$....$.$...**.$.$..*.*.**........*.$..$*..***...$..$*.*....*$$.$....*.*$*...$...$.$.*$.$..$$.*$$....$.$.$.*..*.$.*$$*$$**.......*.**..........$*..*..*..$$...$.*....$$....*....$.*$..**$....$*.......*....*$...*.*$........*.*...*.$.........
***.**.***.*..$**$..$....$*$.*..**....**.$........*...*.*....*.$*..*.$........$....$..*.*.*....*..*.*$....$...*.$$*..*$$*.*$$$...*........$$*$.**$$*****.......$$..*$$..$.*.$*$.$$$..$...$$**$.**.......$$$..$...$*..*.$$$$*...**.$...$$.$.*.$.$*$*..$....$*......*....$.*...$....*...*$.*...*....*$..*$..$*$....**$
.....$*.$$.*.*$.*.......*$$.....$...$.$..$.....$......*$*$$..*...****....$..*...$$..*$....*$.*$$*$.$.$.**........$....$....$*..$..........$...*.*.$....*.$*.$.............*.$...*..*.$$...*.*$.*...**....**.....**.$$*..**.*.$......*$*....*$.$$...*..*.....*.$*$*....*.*.$...$...*.$..*...$***..$*.$*.*$.$.$$$.*...
..*$*..**$...$.*$***..$$$..$$**.....$$.*...$..*.**..$**......$$..$.**..$.$$..***..**.$*.**.*........$$..*......$....$$..$$*...*.....$..*$$..*........*$*...*.....$.*..**..*.**.***..**.$*.....*...**.****..**...*.$....$.*.....$...*$.$..$..*..$.*......$...*...*$$...........*$*..*..*...*$......*$$............**.
...$$$..$$.*....**$.....*...*.$$$**$$$**.****.*$.$....*...$..$..*....$*....$.....$....**.*.*$$.***....*...$*..*.$.*..$..*...$...$....*......*.$.$...*..***$..$$.....*.$..*...**....*.$.*.**.*.$$..*.....$$****..*..*..$***..*.*.$.*$*..*....$..$.$*.........**.$.$.$.$.*.*.*$..**..*$....$...*..$$..$*..$$*..$...*..
..**$.*...........$..$...*.*..*.*.$.*..*$*$.$$$$.**.$.$...$..$*....$...*..$$.$$..$.$$..**$$........$$..$.**..*$*..*.*...$....$.$**...*$..**$..$..*...*$$.**.....*......$*...$*...*..***$.*..*.......***.$.$$.***...*..*$.$...******$$$*...$.****........*...$.$$*.$.**.*$..*..$$*.*$$......*......*..$*$$...........
.$.$$.*..$.$*....$..*..$....*..**$$$...***.*....*.*$.*$$.......*.......*......**$...*.*..*.$..**$..*...$.*.$....$..$......$.....*..$.......*.*.$$$$..$.**.....*.*$..$.......$.$.$...$*.*....$...***...$.*.$*$.$*.**.*...$$$....*.*..****...$..$$.$.*.$.*.$*$.**..*$..*$.$..$.$$.$*.**.*....**..*$..*..$..$.*...*..$.
*...$..$$.$*..$$.*.$..$$.$.......$.......**...*$...*$...$..**$.$*.......$.....*.$*.$$*$$.*........*$..*..*.*..$*$.........$*......*.$$$$*...$.*...*...$.$...$**.$.$.**...*.**..*$...*.$..*.**...*$$.$...*$$$**.$*..*.*...$$*.*.$*.........**...*$*$........$$$.$.$..*..$.$..$...*$$....*$...*$.*..*$..**...$$$$*....
.$...$....*$...*..$$..**..$..*$..*.$.....*.$*..*..$..*.**....$.$....*$.$..$*.$.**.**..*...*...*.*............*...*$..*....$*$....*.*$...*.$..$$*$*$$..$......$.$$...$...*.*..*.$.$*$.$$$*.*.$.$*$*.*..**$....$.$$.*...$.*..*.....*..$$*$*.$*..*.$....*.$*...$...*.*.$$*...........****.*..*$$.$.......*$*.$.$*...$*$
$*...*.*$$*.*$***$*$$.*...$.$*.$..*.*..*.....$..*$.*...$..$....*..**$$..$..$....$...*.$.*....$.$.*......$..$....*..*.........$..$...*.$.$.*.....**.**...$..$..*.*.$..$.$*.....*...*...*.$*.$*.$..$.$$*....$.$.*$**.$......$.....$*..$..$..$........$*$*...*.*$....*$$$*...$$....*$......*.*.$*$$...$.$..$*$..$$*..$.
*.$$....**...*..*.$$***.*$$...$..*.**...$**.$....*...**.*.$*..$.$..$....$......*.$$.......$$*......$*......$.*.$..$..$.***.$.$....*$**..........*...$..*..$*...*$.$$.........$*.*.$$.$$.$..$..$..*$*.$*.*..$.......$....*$...*.*..$.$.$.$.*$.*..$.$.$*$$...*.*$.$.$.$......*..*$$...**.*..*....$.$..**..*$.......*.$
...*.*...*.$.$......$..$$.$*.....$....$***..*.*.......$*..*...$*.*....$...........$..*......$$.............***$$*$..$*$..$.$*.*.*.$.....$.*........$$.....*...$....$$....$..$$...$.$...$...$..$.*..$.$*$$.$....$$........$**$.$.*........$...**$$..*.$*.....$..$.$...$...$.$*$.$$..$$.$.....*.$$.$.$$$.*...*...*.$*$
$....*.........*.....*..$..$*$.....$..*.*$*$***.**.$.....**.*..*....*..$.*$$$.*.....$...*...$.$.....$*...*..*.*$........$.$..$$$*..$....$..*...*$.*$$.*.......$..*..$.**$.$*.*.$..*........*..........*$$..$*..*$..*.*....$.$....*$*.*...*.$.$$$...$..*.*.*.....$*..*..*..*...$.$......*....*.*.....$......$.**.$.$.
..$..*....$*.*$*$.$.*$......*...*.$.*.**.$.........$....$...$..$.....$..**.***.$.$..*.**..*.$.$*.**$.*..$$.$*..*.**...*.**...$...$.....*$.$.*.$..$$.**.*...**...*.....$.*.*....$$**..$$*$...$..*..$$.$...$....$.*$.$$$.**.*..*..*..***...*$$.$......$.$.$*$.*.....$.$...*....$*.....*..$.*.*...$$**.$....$..**$..*..
$*.*.$$***..$..$*.*.**.***...$$.$...*$.*$......***..$.$..$..$*.*.*$$.$....**....$..*..*..$..*$$*.........$$*.$.*...$...$...$$.$$$.$*...*.*...*$....*.....*.*.*....*..**.$.$........$..$*$..*.**.........*$...............$*.$...*...$....$**...$.*$$..$$$.$*.*$...$.....$...$....*$.$**.....*$$$*$........*..$.$$..$
$$..**..*$$*.*..*...$..$.**$..$.$...$*$$...*$.**.....*..$.$$*..*$...*.$....$*.....$..$...$.$.$$.*$..$.....$.....*..$...***......*..*.$......$**..$*..*......*.$......*..*..$*.$**..*.......*.....$....*.$..*..$*$..***$........*........*.**.$..$$.....$......$.*....*.$..$...$**$$...*.$$....*..$..**...$*$..$$$.$.
.**...*.$*...$$*.....*.$...$.*...................*.$.....*..*$$.$.$*.$.......****..$.........$.$..$*.**$$*...*...$.....$..$*..*..*..$*.$...**$$*......*$*.$.*$..**$.$..$.....$.*.*..*.$..*.*.*....*.$...$.$..*.$.$..$$$..$$$*........$*$$..........*..*$$$.*.$..$...*.**....*.*$*..$$$*.$$.$.$...*..*.*.............
.......**.*$$$..$...*..*.$$.$$*...*$..*..$$.**...$$*.*.$....$....$.$.$.*..*.*.$..***.*$...$*....*..*$.$*$*..*......$...$*.....$*$*..$.....$.*$..$.***$....*....$*.$*.$...$$....$$....*$$$**$..*.$.*.*.....*....*..*....*..$.$..*.*....$.$*..$.*.$$.*$.*...$.$$......$.*.$$$.**.$$..$..$.$.*..$.*..$$..*$.**$.*.$..*.
..$$.**$*...$.$.**..$.*$..$..$...$*$.$$......*$..*$...$*...$*.*$....*......*...**$.$$...*.....$.$...***...$..*..$..*.....$...*...$...*.....**$*.$....$.$*....$$.**$$.$.*...*$$...*.$$$..**...**..*$.....*..$**$$..$.*.*...*.$*.....$.$*$..*.*........$.*.......*.$.*.....$**$$.$.$...$$....$..$**$$....$.$*...$***$.
.....$**....$.*..$.$........**.$*.*...*$....*............$.$.*....$.$.....$*.....*$.***.....*$.*....$.*.*....***..$*.$.....*$.*....$$.....*..$*..$..*..*$....*$.*$...*.*.$.$.*.$$......$.*..$.$**..$*..$..$$..$$.$$....$$*...*...$.*..*..*.$*.$....$.$.$.$*$.$.$$$..$.$..*.*.$..*$..*..*..*$.$*.*..$..****$.*....*.*
.*$$$*....*..........*...$$..$$.*....$$...*....*..$..*$.*.$.$...$*.$....$*$$$...*$...$..........*..$$$..*$**$*....*....$*$...*...$**..*....$$.$$$$*.$$..*..*..**..$....$....*$*.*.$$..........$..**....**...*....$*$....$$$$$$.*......*$...$..$.$$..$.*.*.*$.*$.$.*..$...**..$.*...*$$.$.**....*...*.*....$.*..$....
$........*.*.....*$$..$*..*..*..**.*.*$$..*..$..*...*..*...$.*..*$....*.*..$*.*.*.......*.*$...*.*$...$.$...$**.$.*..*.$$........$*$...*....$....**......$$*.*..$$$.*.*...$$..**......$*.$..**$....*.......*...$*..$..$..$*..*$..*..***.*..***$..*.$...$$$.$$$$*....$*.*..$...$...$$$...$..*.......$$..$....$.*$.$*.
**......$..*.*.**.*..$.*.......**.$*..$..$**$...$.*$.$...$$$*$$.$....$*.*$$.**.$$...*.**..**...**.*....*$..$*..*.$.*.*.*$$.$*$$..$$.$.*$..**..*...**$.$..$*...*$$..*$$$.$*$.$.$.***.*......$.....$***$..$.*.*.....*.$..$.$....*....$.$.........*$...**.....$.....$*....*..$$......$..*...$..$$..$.$..$*..***..*$....
$.....$$..**$.$$*.$.*$$..$..**$*..$.......$*$$...*$...........$.....$*$...$..$$.*..$.$*$.**.*.$*$.$.$$.**..$..**.$...*.....$*$.....*.$*.**..$*....*..*$$.*$$..$.......*.$....*.$*.*$..$....$*$...$.$*.*......$*.$.$.....*.$$$$$........$.*$$.*.$*$$$.**$.......**...$.......$..*.$$..$$...*$$*.*$....$.*..*.$*.....*
.*$$$**$.$..$.*..**$.$$..*....$......$..**..........$..$.$$$*$..$..$.$$......*.$......$..$$$.$...$...*.$***$..**.*.$.*......$.....$..**...*.$*..$*$.$.*.*.........$.*.*...*$$$..*$$$.$$.$.***$..**.$.$..*.*$....**$.***.$..*...$**.$.....$..*.....$**.$.......$..*.......$$$**$*...$..*$$..$$.*.*.$......*......$..$
..*..$...*........**$..$..*$.$...$*$.$.......$....*.$.$$*.$.$$*...*.*.....$..........$$.**.....$.**.$$...$*$..$.***$...*....$*$......*$*$...$$..$....$$*.**...$..*..*$.$*$..**..**.$**....$.$.*$$.$$$*..***..$..*.$....$$...$.**.$*.*....$.*$.*$.*..$*....*.$*$..$.***$...*..*...*$.$.**.$....$...$**.......*.**.*..
.**.$***$**.$...*$..*****$*.....*...*.*..$$....**....*$.**$$.**$.$$.$*.**$*.....$*..........*.$$..*.*..$..*$$*.$*.$.$.*..***$*..$.......*$....$..**$$*.$.*...**$$*$....$.....*.$.*...$*..*.$$...$.$..*$..*...**.$..$*..........*$.......*$$...$.$.*$$$$..*$..$.$*....$..$..$....$.*........*...*....$.*$..*$..$$..*.
.*.....*...$*.$.$.$..*.......$...*$...$**..$*$....$....$$$.....*$.*$..*....*...$$.*$.**...**..$*$***.*.....$.$..$..$$.*...**$$*.$*.*..$.*$.$....$*..$*..$*....*.$*$*.....$$$.*..$...$....*.$.**.....**.$.$.*$*.....*.$$$....*.$.**.*.*....$*..*....*$.$.$...$..*$.$$...*.*$*.$.$..**.$..*.....*....$***.$*.*....**..
$..*...*..*$$*..$..*.......*.*.$$*.....$..$**$...*.....$$.*.*.....$**$$$....**.*...*..$...$*....*.$..$.$..$$$**.*.*.......*...$*.*.$.$$*...$*..........$...$....$.*...*.$$$*..**..$..$$..$.$$**..*..$.......$..*.*$.$**$$.......*.$...$....*..**$$$*.*$.$.$.$..$.....*.*$.$.......$**$.**$..*..*.**.....$..*.....*.$
$*.$***..$.***...*$....*.*......$........*....$.*..*.**..$.$..*.$.*.*...$$$....*.*..$...$*.....$....*..$..*..**..$.*.**...**...**....*$.*.**..*....$*$*.*..$....$...$.$$.**..$$**.*$.$..*..$*.*.*....$*$$....**.........$$....$$..*....*..$.$...$..$*..*.*$..$.$..*.$$..*.*..**$*.$$$...*.*.$*......$.*...$**.*.*$*.
$..*$$.......*.$...*$...*.*.$..*..**$*....*.**.$....$.***$.*...*....$....$*.........$......*.......$..$*.....$.*$$*..$.$..$....*..**$$..$..*...$....$..*.$...*....$......$...$*$$.*.*.*...$...$.$...*.$.$$.$.$..$..$.*..*..*...**.*.$...*$*..*.*.*.$$....$.*.$$**....$$.$$.....**$**.*...**$.$.$.$**..$$$$*...$.$*$$
...$$$$..**.......**...$...$.$$..$..$$...**.***$.$*..***$.....$$*...*$$...$...$...*.$$..$$.*..*$$.*........*$.........**$.*.*.**$*.$*..$..*...*........**...$.$.$.$....$......*...*.$*..*$.$*..*$**.*$.*.$...$..$...$*..*$..*.$*....$*.$*..$...**.$**.*...$....*$.*$*.*$.**$**$$$.*....$.$***$...*$*$**..*.$$...*..$
$**...*.*.**$..$...*...**...*...*..*$$....*$.**$*$*...*$.*.$.*....$......$*..$*.$$.*.*.$$$$.$$.........*...$.........*..*..$.*$...*......*.*...*.$..$**....*$.$$.$*.$$........$.$*.*...*.*..*...$$.$...*...*$.**...$$.....*$.........$$...$$.*.*$*...*.$.$$*...**...$...$.*.**.*..*.$.......$.$*..*..$$**...$.*..$*$
.*$..$.$**$*..*...$...*....$.*$.....*.*...$....$..**...$.....$*...$*.$.*.........*......$$*$.$.*..$*.$..*.$.$........$*.*..*..*......*..*$..*...$...$*.*..*.$*.**.*.$$*...$$..*.......$*.$..$....$$..$.*...*.*.**.*$..**..*.$$..*.$*.$..*..*.$.....$.*.*..$..$..**$*..$.*.*.$...$$**$...$*$$.$.$.$*$..*....*.*.$...*
.$$$..$**...$.$....*..$...*.$.***.*....$$..$...*.$.......*.$.....$*.$..$*.$.$$.**$*$*.**....$$*.*..$...*..$.$..**$$*.$.$*......$$*$.$......*.*...**.*...*****....$*****....*.$....*.$..$$..*....*.......$**$$..$.$$......*......$.$....**$.$$....*..........*..**......$.*..$*.$$.$.*...$....$$..**....$$$**.*.$...$
.$...$..$.**.*...*.....*..*.$.*$$..*.$$...$.*..$...$..$..*........*.**..$*...$..*....*..$.*.$.$*...........*..$...$*..$$...*....$..**.$*.*........*.*..$*.*$*.......***..**...**..$**.*$$$.*$.....*$.$*$..*.**.....$.$$.$$....$....$...$..$.$.*....*......$.......$*..$...$*.*..$.$...*...$.*....*$$...***..*$.*....
$.*.....$.*.**$...*..$..*.*..$..$*..*.*..$**$$...$...*$.****$**..$*.$*...**..**....**.*.$.*$*..$*.***...*...$.$*$*$....*$....*.**.*$...**$.*..*.$..........*..*.$*$$...$...$$....$..$$..**$.***$$$..$.....*$$...*.**.$.....**.$$...$...*.$.*$*.*...$*.$*$.$.....$*$.*$.*..$*...*.$$$...*.$*..$.$$$.....$...$.*...$.$
$$......$..*.**.**........*.*$....$$**...$.*.*...$$..$.$.*..*.......$...$*$$*.*...$.$...*...........**$**.....$$.$.....**.*...$*.*...$.$..*....*.$**....*...$..*$..$..$.*$$$$*$$*...$*.*.$.$$....*...$...$***.*.$.**.$....$....**.**$.$$**$...**$.$....*.$..$*.$..$.$$$...*$$..$.$*$$..$...*.....$...*.*...$..$*.$.$
*.$***.$.$.$........*.$$.$$*.*$*$.*..$...$....$*.$$.$..$$....$......*.$**.$.$..*...*.$$**..$.*.$$.**....**$*...*....*$.*....$*..$$$**.*$**..**..$....$.**$$.$..*..$.**$$$.....*$...$.$.**.**.$.$..*.**....$$..*....*$.....*$....$$.$..**.*....$$..$...$......$......*.**$......*..$**..**.$.*.*$..$*$$..*.....$*$*.*
$...*...$$...****$.$..**$$.*.*..$...*..$*.*$*..*.$...$...*$..$..$*..$..$..*...*.$$..$.$$$$.$***...*$$**$.$....$*.*.*...$.$..$..*$.*..****$$**$....*..$..$$....***........**..*.....*..$.*...$..$$.*$..$*...$$.*....****.........$....$.**.....*..$*.*..*.*.*.$....**.*$....*.*$....$.$*......$..$..*....**......$...
**..$..$*..*....$$.$*..$*$...$.*$*..$..*$..**..*..**......*.$.**$*$..*.$..**..*.*$..$....$*$..*..*$.*..$..*..*........*..$..$...*..*.*..$....$..$..$*.$..$*.$*...*...*.*..$$***...$..*..**$.$...$....*.....*$......**.$$..*.......*.$.....$*.......$.....*..$$*$.$*.$$.$$.$*$.*..*.*.....$*...$....*$$*.**....*..$.*
..$....*$..**$.$$$..$*.*$$..$$.$.*....*..*....$*.......$.*...*$.*....$.*.....$$.$....*$.*$..$...*$..$$....*.$$..$*.*.*.....*..$$...$$..$$.$...$.*...*..$*...$.$*$***$.*$.*..*....$$$.....*.*..$...*.*$$*.....*.....*$*..*..*....$.$..$...*...$*..*$.*$...$*..$......*.$...*..$........$.*..$.......*$....$**$......$
..$$$......$*..$..$..*..$.*.$.***.....*.$.*$*..$.....*.....**.....$*.*....*.*.$..*.$..*$.*$.$....$.........*.$.*$..$$*.*$*...$*.................$*.*....$...*.$....$......$*..*..*.$....*.$..$$..*...**$....*..*..*.*........*.$**.*$..**..*..***.*....$*$.*...*.*$...*.$*.$...$..*...**..$......***......$.$...*...
.*.*...*.$.$.$.*..........*$*.......$*$.$...$....*..$..$$...$*..$$...*...$$..**.$.*..*$.....$....*.*..........*...*.$*......*$..$.........*...$$....*.....$....$.*...**.$....*..$..*.*.....$*.$***$......$$.*.*.....*$$...***.$.$***$$..*.*.$$$...*..$.$.*.$*$..$.*...**.$..$**..*$..*..$.....*.......$..$.*..$$.*$$
$.*...**.$..**...*..$..**.....*...$..$...$$.$$*...$*.$.*.....**..*.$$.**$..**$*.*.$.$.*.***.$.$.......$.......*...$.....**$*..$..$..$..$*.$.$*$...$.*.*$..*..$**....*.$$$.$.......$..$$.$..*$.$.$..$.$.**..*$$..*$..*$...*$*.....$..$.*$$$$.$......$*$*.*..$$.......*.....$**$...$$$*.....*...*$$$...*$*$$.....$**..
......$$$*..*...$.**..*..$...$*.....$$.*...$...*$**..*...*..$..*$*...$**.....$*...*$*$$..$...$.$.$..$.*$.$.$$*...*.**$.*....*..........*.*..$.$...$..*..$*.*.*$*$..*.*..$..*...*.$..**..$.*......$**$*...**..$$.*$$$$*.*.$.*...$....*.......*.$*$$...*....$...*$*...*$$$.....$*.$.....$$$*.*....$..$...$...$.*..*$*.
....*.......*.*....$....$$..***.$.$...$$....*..$*$..$..$..$**...***$**$.$.$..$..........$*.......*.*$.*..*.*.$$$*....*$..*.$.*.$....*$....*.**...$.*$.*.....$$$*$*.$*.$.$.$$$...$..$$..*.$....$.$..*$.$*......*.*...*...*.$.***.**......*$...*..*...*.*.*.*$......*...*.*..*.*$..$..*$.$.............*..$*..$.....$*
.*.$$..$.*$$$$...*$.............$*..*......$*...*...$.$$$...**....**..*..$.$...$...$**.*$*..*..$*...$..**..$.$***....*$*......$..*...$.$......$*$......*.*$....$..$*.***$.$.*$...*...$..$*..*..**...*.........$......*..$.$...*.*.......$...***$....$..**....*...$..*......**$......**$..$*.*.$..$..*$.$$$.....**..*
*......***..$*.$$$.$....*.......*..*..$..*..*....$.$.$....*..$*$..$.....*.$.$$*...*$...*...*....*.$*$$.$*....$*....*$..*$...$....*.....$..$.*.*.$*...$$..$$$.....$..$......$.*...*.*$..$....*.*$..$.*.$.....*.*.*.*..**$.$$..$$$**.$.$*..*$$$.$..$..$$$**$..*.....*..***$$.*.....*$**.$*..$...$.....*..$...*..$**...
...**.*........$..$*$$.*.$.$*.***$*.*.$..$..*..$.*.....$....*....*$$*.$...*$.$*..**.$.$.......$***..$*.$.***$*....$.$.........$$....$$**...*...*....*.......$..$.$...*$......$..*$...$$**$.**..$*.*.$.*.$$$$**...$$..*..*.*.*...$....$....$.*$$$$$....*$....*.$*$$..*.$$.*.$$**.$*$.....$...$.....$*...***..*$*..*..
$....*$..$.$$$...*.$.$.....*......*$*..$.....$.$.....*.*.....**.*.*..$.$...$..$...$.$*..$....$*..*..*.$.$**.*.....*....*.**..*.....$.$.$...............$..$*$....*.*....*$...$*...*..*$....***$**.*$........$$$$..*$...*.*.*......$.....$..$*.......$$......$...*.*..**....$...$.$..$$$*$..**.$.**$...$..$.....*...$
$..$*..........$.**....$.*.$*.*.$.*..$$..$..*....*..*.***..$..$....*.$*.....*......**..*$*.....$..$$*...**.*.$.*$....$.....*..$....*.*....*.$.$$.$*..**.$..**.*...$.$*.*..*$.....*.*..$..$.....$.$$$.*.$$..**.$*....*.....*..$..$.*........$.$$*.$...*$......$$...**.**.$......*.**.$....$$$*.$.**...$.$*..**..$.$$$
$*..***.$....**$*..$.***.**.$**..$$*.$*$.$$.$....*.$$...$.*...*.....**.*....*.$....*$*...***$.*...*..*.***.$$.*..$$*$.$..$..$...$*.$..$*$$*$***.**$.$.$*...$*..*.*$..**$*$$....$*..$$*$..$$.**$$..***.**.*....$$..**$.*..$$......*..**$.*..*.**..*.....**...*$...$......$....*.*....**.*.$*.*$.*$.*$.$$..$$*$*.*....
$......**.$...$.$*.*...$$....*..*..*$$*$*$..**$......**$...$..*............$.$$.*....$...$..*......*...$*.$..$.$.$.$.*$...**..$$..*$*$$.*.$.$...*.*$*...$.$.*...*$*....$...*.*.*$.....*..$*..**..$..$$....*....**....$$...*....**...$...**........$$...*..............$..$.*...*.....$.**.$..$*...*.......$**$*..*$.
$.***....*$*$$**.*....*.$....*.....*$..$..*.$...*.$....$$.$..$$*..$...$$.*$.....$..$.*$.$...$......*.....*$$..****.*$..$$..*....$.....$...$.*.*.$...*$.*.$$.$*.**.*.....$*.**..$.$.*$.$....$.*.***$....*...*..$...$........*$.$*..$$............$....$..$...$..$....**.$........*$..*.....$.$...*.$*.$$.$$..........
***.$..*.$...*..*...**....$..***.$...*....*.$$$...**..*.**.*...$*.....$*$..*$.*$..$.$.$...$*..$......*...$.$*........$.*.$.....$..*....*.$.*..$*$........*$*...**$..***.....$.*...$.*$....*$..$..*.$.$.......$$$.......$*$$..**.$.*.$*...$.$...$$$...........*...$....$*.*$$*...$$.*****.*$$$...*$$.*$..$$.$**.*...$
$...$*.*...*....$...$.$....*.*$...*$...$$$*.$..**$....**.....*.$.$.$..*...*....$.$...$..*$.**.$...*.**..*$.$$......*.*.....*.....*..$.*$*.*..**...*....*$..$.$*$.*..$..$.*....**...*..$**$*$*......$.***$.....$...$.*..*.*$.*.**$..$$...*..*..**..*.*.$$..*$..$*$$...*..*$$.....*..$$$*$...*.$*$$$.**.$.$$$.*$.*...*
*..$$*$$..*$*$..$...$....*....**.*$.*$.$....*$....$$...$...*..$....$*$.*..*......*...$*....*....$.**$.......*..*.$.$*...*.$**..**.$..*......*.*...*...$.$.$*..**......*..$*...*$$...*.*.****$*.$..*.*$$..**$..*..*....$*.....$....$..$...$*.*....$.$$...*$.$$.....$.$*.**.$$*....$$........**.....*......$.$.*$.*.*.
..$..$.$*.*....*$$.**$.****$*$*...*$..*$...*$..*...*....$**...$..$.*$*.................$.$..*.$.$.$.*..$**..$.*.$$$.*..*.*.$..$.*$...*$.**$.*.$...*$*...$.$.*..$*.**$*$*$...*.$**.*.........*...$...$.*...*.*.$*..*...$$*.$..*....*$..*.*..$*.**.$.......$$....$....$$...$....$...$**..$*$$$*$...$...*....*...$...$.
......*$$$.*.*.$..$*$..$***...$**..*.$.....$.*...$.....$.$..*..$..*.....$.$$.$$.*..$...$.*$...$.*.*..$.$..*$..$.*.$$...*.$...**$.$..*..$.$.*..*.$..**.$**$..$.**.$.$..*..*.*...$..$$.....*.*$....*....$........$$..$*....*.$....$$$.$.$..*$..$**...$**$.$...$.*....$.....*.*...*....$.**.....***.$..$.........*.$.*.
.*.$.....$*.*.$*.$*.$..*.$$....$......$$.$..*$**$......*$$$*....$*....*......*.*....$.*.**$$*...*.*....*....**...*..$...$.*..**$$.$$$****...*...$.....$.....*$.$.*..*......$*..*$$..*..$.*.....*$..$.$.*$.*.$*.$$.**....$.$..$..**$.**$.$..$.*....$.....*..**...$*..*.$.......*...*.$...**$$...$.$....*$....$..$..**
.*...$.$*$.*$*...$.$....$*.*...*...*.$.*$...$..**$$$*....$$......*$$..$..$.$.$.*.*.*.*.....$..*....$....$....$.$...$...****..*.$.*$$**$*.*..*$....*$$*..........*$.*......$*.**..*.$.......$.$$*.$.$...**...$$*.*..$.$.$*..$.....$$....*$$$..*...$.**.**..$$.*$*.......$.*.*..*...$....*...$.$....*.*$.....$....*$.$
.$..$..$**..$*....$.*$$...*.*.$..*..*..*.*$$.....*$$....****$$.$.$*..$.....*$$.$......*$**...***..*.......$*.$*$.***..$.$.$*.*...$..$......*.*.....$.*.$....$**...**$...*..$......*........*..$*....$....$..***..$...**....*$.*.*...*....**..*..*..**..$.$..**$..$..**.**$***.**..$*.$...$$$*......$...*.$...**..$.$
.*....*.$.....*.....**..$..$...$......$.$.....*..*.$........$*.*.**.$*........$*........$.*$.$*...*.$....*$.$*.$$$*.**..*...$.**....*..$$$.*.$..$...$..$.$.....*$..**.*..*$..*..$*....*....$..$.$...$.$.$......*$*.$...$.*......$.$.$*.$...*...$.$....*.....$$$.$**.......$$...*.*.*.$.....$.$$$..*.*$..**...$..*...
....$*.$.*.*$$..$.....$.*.$...*....**.......*....$.*..*...*.....$...$.*...**$....**..$...*.$..*....*....$$$.*.$*..*$*$.*$$.....$$........*$**.*....$.....$..$$.$.$..$.$*$....$...$$*..*...$*..$.$..$*$.*$..$$*$$.$$$......**..........*.*.*..$*.$...**$.$$.$**....$*...**.........**...**.*....$.*..$*..$.$$*....$$$
......$...$..$**.*$**.*.*...$***..*..............**......*...**......*...$**...**...$$.*.$...$....*$$$$.*$*$$$.*..$*...$*....**......$*...$.....$.$.$...........$.$...$.$*.....$$.......$..$*...*$$....*....$.*.*$...*...$.$.....*.*$.$.*......*.$...**$$*.*........$......$$$..............*...$......*$$.$.$..$.*$
$*.$.*$....$*$....*..$*...........$*..*.*..*....$.$.$..$..$..$**....$..$$*.*$$..***$..*.$*......$*.$.$*.*.$$*$.$*..**.$$*...*$$*...*..*....$..***..$....$.$...$.*$*$.$.$...*..$.....*.*.*$..*.$**....$.**$...**$$$...$..$.*.$..$..*$...$*.*$$*.$*....*.**.$..$$...$...*......*.$*.*......$.*.*..*.$...$.*..$..$.....
*.$...*..*.$$*....$*$*...*$..$.*..$.$....$.*......$...$.....$.*.**$..*...$**$$*$*..$..$.*.....*.$.........*....$*...*.$$...$..***.......*....**.$$..$...*$**.......*....*...$**...$.$$$.$.**.$*$*$*$...$.*...*$.*..*....$$$...*$.....*.*.*.$*...$.$.*$*$*.*.*$$*.*.*.*.....*...........*..*...$.$.*...$$..*....$....
....***.**.$.....$$...*$....**....*......$*.$$......$.**..**.*..*.$.$$.*...$.....**.$.*...$$$$$*.$.$.$*..$..$.*.$$....*$**....**..*..*.*.*.$*$*..$..*.$*$$.*.*.$..$..$$$.$$.*...*....*.**$.$..*$..*.$...*....$....$.......$*..***$.$.$...$$.**.$...*.$*.......***..$**.....*..$$*$...*..*......$*....*.$.*......*.$.
*.*.*$$$$$..*.*$$...$$.$.***.......$.$..$.......$...$..*.*....$*.$.*.*...$$.....*$$...*.**.*.$**.....$*$....$....**$.$..***.*.....$..*$.*.*$.......**.$.........*$*$.*..*..**...*.$.*..$..*$*$$.*.$......$$...*$.*.**.**$...*....$*..$$...$.*.$$*.*...$.*$.**$.$..*.$$...$.$.$.....$$..........*..***$$.$.....*..$$$
.*$....$...*....$$...*.$$**....*..*..**$.*.$..**.*.$..$**.*......$....$....$.*$**.....$..$..$.$*$.**..$...*$$*$...*.$.$..*..$.....*...**.**$....*..$.*$.$..$*$...$.**.*.......*$...$$.*.$$**$.*....$....*.$*.......$$$.$..$......*$.$$..*.$...$...*$$*$..$.$.$*.*.$.*.*...*..........$$.....**.......$.*...$...**...
$....*.*.$....$$*...*......$$........$$$**..$..*.**$..*.*....$*.$*...*......$.**$.*$$.*..$$......$$.***.$*...*..*.*.*.$.***.$.*$.*.*..$.$.*......**.*..$.*..$..$...$..$...........$$.....$$..*..*.*.$$....*..*.**.*............$$*.......*.$.$$*.*$.$.*$*.*...*.*.*$.**.$$.......$....*.$.$..$$.$*....*.$..*..*$....
...$.*$..*$.$$..*$...*$.$.$..*...$..$......***.**.*$...*..*..$....**$.*$....**..*.**.$.*.......*.$.*....*$...$.....*..$...$.$*..$*$.*...*..*...$*.*.$.*$*..*..$...$..$.$**$$..$..$*....$*$$.$.$*.**...$*.*$*..*..$*...$...$*..$....*....$...$*.*..$$$.**......*......*.$**$.**.*.*...*..*....$.$$....*.$.$*...$...*.
.........*........$$...*..$*.....**.....$**.....$...*$*......*$$*.$....$**...$..$..$*$.*$$...*..$......*.*..$*.$..**.$.$$$$.*.*.$.$*.$*...$.*$.**.**...$.....$*...*..$.*.$...*.*.........**$*..*.$..$.*..*$$$$*..*$.*..*.$....$.*$.*.....*...**$..$*........$*$.*......$.*..*$.*..$.*....*.$*.$.*..*..$**..$.*.*..$.
.$.......*.****...*.*...$..**.$*.*..*..$.$*...*...*$.$*...$$**....*$....$*...*$.*$.*...*.....**$.***.....*...*.......***..$....$$**..$.*.***$.*.....$$$.**$..*$$.$..$**$..$$$$.$..$........*...$*....$.$$**.$...**....$*....*...$...*$.$...$$$$**....*..$$..$...$$..$.$..*..*$*$*.*$.....*$$.....$$...$*...$$.*$..$.
.***.........$...$*$$...**$**...***...*..*....*$.....$$.$$**.....$.....**...**.....$*..*.**...*.$...*..$$..$*....*....*.....$..*.*..**...$..*$...*.....$*......*.....*....**.......$$**.*$$.*......****.*$**.....$..*.*$*...$...$**.*$.....$.*..*.*....$.*$..$.$.$**..$$.**.*...$*.*$.....*$....***.*...$.....$*...$
$.$...$.$.$$$......**.$.*$*.$*..**..**..$....*$.*$..*.$*..$$.*..**.**..$$.*.$....$...$...*.$..$*$$..*..$.*..$*$..$.*.........*...**...*.....*........$.*.$*$*.*...*.$**.**$*$..**.$..*....*.$$......*.....$$$..$.*.$..$...*..$.....**.....*$.....*..$........$$$$.....$**....$..$...$.$..*.$$*.$....$..**.*...$*...*
...$$$.**..$.$.$..*.$...$...$..$...$...*$.*.....*...*.*...*$$$.$..*..***..$.$..$..*..*$*.$...$...*...*.**..$......*.$..$.**......*..*...$.*.....**...$$.$.*.....**.*.*..*.$....*...*..*.$..**.....$..$.$.$*$.**$..$*....$*.$....$*..**..$**.$.**$.$..*$$.$....$*.$$$*..**$.....*.*.$....$**..*$.....$.*.............
.*...**.**..*........***$..$$*.$**$.$...$..$.***$**..$$.$..*...*....*$........*$...$$$..*.*...*..*.......*.$.$.$..$....$...**.$$*$.**..*...*...*...$.....$$..$..$**.$$*.*.*$***...*$..$...........*.......$.*..$.****..*.**$.$.$*...*.*$$.*.$.*.$..*....*...$.......$*....*.*.........$**$$.$.$$.*..$......$.......$
.*$..$...*.......*......*.*.$.$..*$*..$.....**.*.$.*....*.....*.$$$........*$......$....*.*.*$.$.$**.$..$.$.......$$*........***.*...............*..*$.....*......*..*.*..$..$$.....**......$..$*..$.$.$$.*$...$*....$...$.*..**..$$.$..$.....$.$**.$$.......***$.$$.$....$..*$...*...*..*.***$$..*..*...$.$**..**.*
*.*.$$....$.*..$$.$.*$.....$..$**$*..$.......*.*.$**$.*..*......*..$.....$..*$...$*..$..*$...$*..**$*$..$*..$*.$.$*..$$.....$**..*.$$*$.*.$.$*..$.....****.$.$$*$.$$$.*$$.$.$$$.$.*..*.$...*..*.*.*..$...**.........$$..*...*....***$....**...$.$.$.*....$..$*$.*$.$...$....***$*.*..*......$.$*$*......**...$$.....
.....$*$..$**.**$...$.$...$$..*.$**.*.*......$...$....*$.*..*..*$.$*....**.*.*...*.....$.$..$$..*..$.**.$$$$..$.**$.$...*.**.*...*.**...*.*..*$...$..$*.*...*..*....$*.*.$....$.....*$.*$...........**$*...**.$$$..*.$*.$....$$.**....$*....$..*....*..$$.$*.$**$$...$.**.$....$...$..........$..**..$.*...*.*...$.*
..$.*..*.$.$*$*$*.$$.$$..*.....$$**$$.....$*$..$$.$.$*$*$$..$*$.*.*$*..**...*...*$*..*$..*....$$*.*$*.*.$.*.......*.$$.$.*$..*.$.$.**.*.*.$.$.$.*.*$.*....*$.**$$$*$.*.$.$.**..$$..$..**...$..*$$......$....*.$*..$....*.*..$.....$*.*...*..$$$.*.$*$$$$.*..$.$.$$.$$.$*$....*.$.....$$*....**....$*..***$....$$*.*.
$..$..$.*.....*$...*...$...*$....$$.$*...$...$*$$.$...$.*..*.......**..$$*$*$.$$$...$*$$*.*$..*...$.*...*......*$$...**.*.*......$.*...**$..$.....$*$........$.........*$.*..$**....**.$...$.....*$$$..*$..*...$*.$.*.*....$$...$.$..$.*.*.*...***..$$*...*..*...*..$.$*$.*$$.$..$**.$$$....$$$.$$***$.$$..*......$.
....$.$**...*.......*$....$.*$.*..*..$$*.$.$$$.....$.$..**...$....**$.......$$$..*.*.$$.*$.*$$.*$..$**..*..$..$**..*........**.$*......$.*..***...*$...$..*$*$..*...$.....$...$.*...*....$**$*.....$.*..*.*$*$.$......$*.*..$....*$....*..**...$..$.**.*$...*.....$...$.$.$..**.*.$$.....$*$.$$....$.*..$$.....*....
.....$.*$...$...*.*..$$....*$$.*$$..*.$.*$.*...*..**...$...$.$.$**.$...$....$..$...*$..$$$..$...*.$...$....*....*.$$..*$.*...*..$..*.......*.$..$..*.*.$*$*..$$*....$.$..*....$$.**$..**.*..$.$.....**...$.$$.*****$*.....*..***..$.....*$*..$...$....$$...*..$***....$.$.....$..$.$...$$.$$..$$$$$$*.....$$........
.*$.*$.$*...$..*.$..$.$**$..$.*.....*.*..*.....**.**$$$*..$.$.$*$.*..*$...*.$...**$.....**.$.$...$....*.......*.........$.$....*$*$.....$....*$....*...$$.$**...$..*$.*..$*..**....$*$.$.*....$....*.*$..*$*...$..*..$$*..**..**$*$.........***$***..*.$...$*....*....*.*..$.......$$...$$..*...*..*.$..$.*....*....
..........$*..***.*$**.*.$.$*..$.$.*...$.$*.$$...*$$..$...$.*$...*..$$$$........$..$$*...$$..**.$*$.*..*....*$$..*.$.$*...$..*..$.$....$*.$.$..$*............$$..**..**.*.*...$*$.$$$.****.$*...*..$$..**$**$*...*....*..$..$......................*$***.*.*$$...$$..*$*.$*......*$.*$.**..**...$...$$.......*$**...
.**....$.$....*$..$..**.***$..$*..$.*$...$*$.**.$....$**.$...*.................*..*.*..$.$$.....$*........$....$.**.$.$**$$.$.$......$$.*...$$*.**..$$.*.**...$*..*.$*.$.$$.$*.$..$............**..*$.....$.**.$$*.*..$.$.......*..$......*$$.$...$*.....*$$....*.$..$$$...**$.$.....$.$*...$...*.......$..$..*..*..
*$$......*.$.$..*.*...*.$..*..*..$...*.*.***$......$..$.$.**..$$$..$..**$$*..*...*.$$.$..*..$*$.$**$.$....$......*$$..$......$....*$*$$$*......*......$.*.*.*.*.*........$*..$.*....$.$...*.*.*.*$...$*........$$.*$$*...$..*...$*$.*$.$.$..*.$..$*........*.$.$..**......$.$..*$.*.$.$$....*.*$...$..***.*$*$*$.$.$
$$.*...$.$*.*..$.*$...*..$...*....$......$.$$......$**.*$.$$..$..**.*..*...$$$$.*...**....**$$*..$...$.$*..*$...*......***.***$......*...$*.$**$$.*...**$..*.$*$.*$..$....*$**.$$.......$$...$.*.$*....$.*..*.$..*$...*.$...*.**....$$..$.*$..$$$.*$..*...****.$$...$....**$..$$..*...*....$*$*..*...**.$****..$$$$.
*..$....*..$$.$*****$*$*.....*$.**.***..$..$.***....$.*....*...*.$........*...$...*$.$$$$*....*...*$$.$..*$$....$.$$*.......$.............$$.......$...*..$.*.*$..*......$*$*$..*..*$**.$....$...$$..*.$$...*$.*$*..*$.$..**.$..$$.*$*.......$..$*.$.*$.*.*.$......*.$.*.$$$.........*$.*....*.*.*.......*......$$*$
...$*$.**$$$.***.$.*.$.***........**..$.*.$......**$......**....$**..*$$..*$*...*...*.*.$$.*...$.......*...*.*...*$.......*$***.$**..$$..*....$$**$.....$$$...$.....*.......$.$..$$........$.$..*....$.$...*$.*...$*..*$$..**......**.*...*.$........$*...**.**...$.$..*..........*$...$.**...$...$...**..***$$*..*.
.$.$$$.$*...*.$*....**.....$...$$*....*.*...**$...$..*$$...****.....$*.*$.$$$..$.$...*$...$*...$$....$....*$...***$*..*$.*.$.*.$*$...........$.*$*..$*...*..$..*....$..*..**..*....$*$..$.$*$...*....*..$$$*$....$.....$*.*.....*...$$.***..$.*...*$....*.*....$.*$.$$$..$....$$...$$..$.**...*.$$$.*..*$.....$$....
$........$*.$..$$$...*...*$$.*$$..$**....$*..*..*$*....*$$.$..$$.$......*$*.**..$**...$...$....*..$*.$$$.***..*.$...*$..$**.$.$.$..$*..$.**..$....$....*..*....*..*...$....*.....*$....$......$.$.....$.*.$**..$..$............*$**$$..*$.....$...$*.$**.*..$.........$.$*$..**.$*....*.$**..$$.*.*$*....$...$*..$*.
$$$..$.$....**.$*.*$.*$$*.$....$..*$.$..$..$..$****....*..$*..$$.$..**...$..$$...$..*..*...*.$......*.....$$..$..*...**..*..$$.$....$...*$..*$...*..$..*....*..*..**$....$..*..*.....$.$.*...*.$...$..*.*...$.*...**.........*..*$.*$..*$*$...*$.*..$....$*.$$$$*.*..$..$*$...$.....*.$...*.$$...*........$*$..$$..*
..$..$***...*$..**..*....$...$.$..$*..*....*...$$...*.....*..*.*.*.......$$..*.*.$$.......*.......$$$....$...$*$***.$..****$.$.$*$*..*.$........$**$*....*$.**$.*$......*....$...$...$..*..$$$*$...*..$.**...$...$$......$$....$*..*$$.$......$..*..*....*.*.....$...$$$.$.......$..*.*.$.$.*$*.$$..**...*..**...$.$
$.*...$*...*....$**$.$.$*$.$..*.....$.*$...*$$...$**$.**.*$*$.*.$..$**.....**.*.**..**$..$..$.$$..$*$..*$$$*..$....$*$$..*.*.*.*..*.$.....**$....*....*.*$$......$*.***.*....$..$$*..*.$*.*.......**..***..*.*.*.$.$*.$.**$...$..*.$*.....$...$*..*...$...**........*$..*.*.***.$...$$*$$.$$$.$.$$...$.*....*$..$.**
.$......*$..**.*.$.....*...*....**.$.$$$$$*.$..*.$$*.*$$..$*.....$*....*.*$.$..$*$..$....$$*$.$..$*$.*.*$$.$..........$....**...$.*....**....**....*.*$..$...*$....$..*.*..*..$*..*.*..*.....***..$...*....*.$...$$.$...*$....$*$..$*...$......$$$.*.....*.**..*$.*.$..$..$*.*..$$**.$*$...**.....$.$$.*$..*..*.*..$
.$..$.....*.$..$.$..*.$.$..**.$$.*....$.$.$*.*.$**..$.*.$.$.......*.*$.$$..*.*.*......$$$.$*$...$.$.....**...........$*..*..**...$*..$.**.....*.$........*$.....$*.*$..$.$...$.*.$..$.*...................$......$..$$..*....$**...*..*$......**...*.$$..$..$.$..$..................*.*..*...$.......***.$...*.$.**.
$.*.........*...*...$$.*$.$.*.$*..**$*.....*....*.$.*..*..$......***$.....$*......**.....*.$$*..$.....$.*..$*.......$$$**.....$*$*..$*.$.......$$....*.*..$.**.$.**.$$*..$*.$..$......**.*...$*.$..*..*$..*.*.$...$.*....*$.*........$$..$.**..$*$..$.....$$....$.$.*.$.$$.**$.$.*.$....$..$.....$$.**....$.$..$.$*$
...*.**$...$.*$...$**.*....$*.*...***..$....$$$.$*.*...$.$.$.$..$.*$$..$.....$....$$*$.**$$.$$.*.*......$$$..$..**....*$..*.....$.*..*$.***.$*..*...*.$$*..*.*$*$*.*.$.$....$..$*.*.*.$**.***....$.*.*.$$$.*...*.$..*.*.....$*.**..$...*.*.$.$..$$$.*.*....$*.**$......$**$...***.*...**...*.$$...*.$....*$.$$.$..*.
....*.*$.*$..........*........$..$......$**.........$........*$..$.$..$$$....*.$*.****$.*..$..$$.....$....*$..$..$.$$*$$$*$.$..*.*......**..$*.$..*.$...*.$..*..**.**...*.*$.*..$..$$.$.*.*$*.$...*.....$.**....$$.$$*.$..$$...$*.$*.......$$**......$*....$...$..**......$.*$$**.*.$$.$.......$*.$$.**.$..**..**...
.....*$.$*........$.$.......$..**.$*.....*.$....$.$..*.$.....*........$..$........*...$$.....*.*.$..$....$*...$.$..*$*..*.....*..$$$.$*...$..$.*...*.$$.$.*.$..*..*$.....$*.$.$*$$.*....$$$$...$.$.....**$$.*.$.*..........*...**$.$.*.$.$**...$$$$..$.*.$.$..****$..*...........*.$...$$$**.$*$...*.$..$...$.*.$...
.**.$..$$.*.*$*..$*...*..*...*...$..$$..*.$.$....$$$.$*..*..***.$.....$.$....*.......***$.$$$$...*.$.*..*.*..$.$..*....$$$....*....$.$.$.$..*$..........$....$*.**.....*$$**....$......**......**.$...*.$....*..$..*...$...*..*.........$...*.$...*$*.$.........$*.....$.*$*$.*..*...*$...$$..$*..$.$**...$.*$*$....
...*...*.$...$*$.*...$.*.*$$..*.$...*....**...*.....*.*****.*.*$.*.**..$***$$.*....*....$.$*$$....$.*..$$*...$$.$$$*$...*.*.$*..$.*$.....*.$..$..$*.*...$$$...*........*.*....$$.$*$.*....$....**...$.$..$$.*...**..*....$..$....*$.$...$.$..$........$$.**$*..$*$.*$*........$..*..$...$..$....*...$..*.**.$...$.*.
$.*.$*.$...$.$**$.*.**$.***.....*$.*$...$..$**$.......$......*.*$*..$.$$**..*..$*....*....*..*...*..*..$...$$$.*..$$$...*.$...$.*.**$*.**...*.$$$.....$**.*.***.$*.*...........*.$.$$.*.*$*.*..*.*$.*.$$*..$.....$$....$.*........$$**$*..*.*....$....$$**$....$......**......$....$.*..$*...*.$$....**..*.$$**.$..*
.$$...*..$.*...*...**$....$...**..**$......$*...**...$....$*..$.$.*.*..$..$...$..*....*$.**.$..*$***.$.*$**$.*..$...*...*$.$.*....*....*.$$.*.....$*$......$......*......$**$$..*..*.....$*.......*..$*......***.$*$*$***..**..$.*$........*..*.**........$*..$...$*.*..***...$.....$.***.$...$.*....*****.*.$...$..
.......**..*.$.$.*.$.$**..$.$*..$.$....$...$...*....*...*.$.$....$*.**$.$.......*.$.*.*...*.**..$$$$.$.*..$**.*.$*.*..$$$.$$*..$....*..........*.*...$...$.$*...$$.$..$$.***..*......*$......*$.**.....*$*.*$.........*$.*$*..$......*.$...$.$.......$....$..$*...$..*.$*...$$....$.*......*.$...*.*$$$*$..*$.*$$*..
..$$...$..$$.....$*...$..*.$..***......*....*....$*.$..$*..$$....*$*.**..*.*.*.$...*..*$...***.$$.*........*.$$*...*...$...*........*.*.$$$.*$*$.$$...*$*$*.$....$.......*.$......*..$..$.$..........*.$*$$.*$$..*$...*.$.***$*...*$..$.*....*..*.$*.......*.$.$$*..*...**$$*.*..$.**$$$...$$*$.**.*$*.*$.....$...$.
........*..*..$.....*...*.$*.....**.....$$..**.....*.....$.*.$$*.*.*$....$*...*.$*..$....*.$.$$$..$$..*$.$.$$**....*.....$.$.$...*...*.$.*$.*.*.$.$.$.*..$.*.$.*$.*...$.*......*.$*.*...*.*.*..$.$....**.$.$.**$*.**....*.$.*.*.*$....$......$.**..$........$$...$$.*....$$..$..$...$$$..$....*.*..$$.*.*...........
..*$.*.$...*....$....$..$..**$.......$....$...*.$*.**.*....$.........*...$.....*...$......$*...*.$.*.$$...$*.$.**..$$.**...$.$$.$...*.*.$$*.......$.....$*.*.*.*....$**.$....$..**.*..***...**$...$*..*.$**...*$*.*...*$.$$$$$*......*....*$*..$...$.$..*...**...$..*.$..*.$*.$*$$$..$..*.*$.$.**.....*..*..$*..$*..
..*$...$*$..*...$...*.$*.$$...$*..$..*...$....**$.$.....$.**....$.$$..*$.$*.*.....*.$.....*$$...**$$.*$*.*.........*$.*.....*.*$....*.$..*.....*.**..*..***........$.*.*..*$$..$....*.$.$.$$$$*..$.$......*.*.*...$.....$.......$*..*...$.$$*..*..*..*.$......$$....$$**$..*..$$...$$...*.....*.....$.............$.
..$....*.*....*..*$.......$.*..$$$*...*..$....*.$.$....$*...**..$*$...$.$.*...*...*$$...$.*$.$....*...$$*........*$..*..*.$$...*....*$$..*......*.*....$*..$...$$....*.**..$**..***.$.....$$$*..*.....$$.....*...*$.$.*.$..*.....$..*...*.$$.*.$.$*..$.$*.$.......$$$.*$$$*.*.$$*$...*$.***..$..$*.*$*.......$...*$.
.$.....*..*.*...*$*$$.**...$.$...$$..$.*.$.$$.$.....*$$....*$*.$....$$......$.......*$*$$...$*$$...**.**$.*.$....*..$...$.**....*....$.$....*.**.$.$..$*....**...*....$..$...*$***.$.$.*$...$...*.$$.$**.*.....$..*.*.**..*$....*..**.$.*$.**.*...$$*.*.....$.$..$*........**$.*..$$$.*$$...*...$..*..$$*$....$*.$.*
...$$*.*.$..*$.*........$....$.*..*.$$...$.$.*$.....*..$...***$.$...$..$.*.....$*..$.$*$.$......$.*.*$...*.....*.*$.$..$.**$.$..$.*$.*....$...**...*..$..$.*...$$$.*.**..$...$.....*....$......*.$*.....*....$.$.*..*.$*..*.$..$$$....$..*.$....$*$*.$**.........$$$$*$........*..**..*$...*..*..*$.....$.....*.$$..
...$.$$..$$*$***.*........*..*.$$...$$...$$*...*$*..*.*....$.$..$..$..*$$**$.*..$.$....$$$.$......$...........$..$..$..$...$*..*.$.*.**...$$.$..**..*.....$$....$**$...*.$.$....*.$*....$..$.*.*..*$....$.*.*.$...**...**.....$***.*...**....*$.$...$**$.*$$.....*..$*.$*.$.*...$...*..*.**..$*$$...$*...*....*$*..$
......*...$*..*.$*...*..$..$..$*..*...*$$.*$$$.$$.*.........**.$*.*$*$.....*$$*....*........$.$$...*.**$$$....$.$.*.**.....$*..*.....**..$$$.......$*..$*......$...$..**.$....$..$$....***.....$..$*.....$.$.*..$..$$..*.**.*.$.$.$.$.$*.....$...*$.*....*$..*.$..*......$.$...*...**$.............$.*..$$$..$*$.$..
$.....$..$$**..**..*....*..$$...$*...*..*.$$$$.*.....**.....*.*$.*..$$*..$....$..**..*$$$....$...$*$.*$*....$*..*$$...$...$.*.*.$.....$.*.$$$$.$*$..$*.$...*....*$..$**...*.....$....*.*...*...*..*$*.**........$$.*.*****..*...**.**.$*$*$....$.....**.$....$$......*$.*......*.*...*......*..*$$......*...**.$...$
$....**$$**......*.....$$....$...*$$.$$......$$*.$..$$.*..*...$$.*........*.$.*...*....$..*.*$.$.$$.$$*..*.*...$...*..*$$......*.$$........$.*.*$.......$...$..*..*.........*....$$.*.....*.$$....$...*......$*......*.$.....$.....$.*..*...**....$.*.$..*...*.....$....*..*...$$$.*.*........*..*...*..$$$$.....*.$
....*.....$*......$.....***$**$**.$**......$.*.*....$..$**....*$$...*..$*.$.$....*...$.*...$$$*$...$........***..$......$$*.$$*..*$..$$..$..*.$..$.*$....*..$$...$*$*$.$.$$$..*$...$..$.$*....$.$..$...$.*....**$...$...$*$.*...*..$*$$.......*..$.........*...*..$.*....*.*$..**....$....*....$.......**$*.$*.**...
$*.$*...$.$.*...$$$.*..$.....*$.......*.......*..*...**..$.$.***$...*.....*.....$...$*......$...$$.*.*...*.$..*...$*.*..*.$..*$***...*$....**...$.$$$....$........$....$$.*$*.*$**.......$.*..*.......$...$...*.....$$**$...*.$$..$...$$*..$.....*$.....**...**..**..$**..***.$...$$*........*$$.*$$.$*.*.$$*.$....$
$*..*.*..*.$.*.$$.$.$...$....$.**...$.*.**....*.*.......$....*..****....$...*.....$...*.....$.***.*.....*..*$..*.$$..*.*...*..$$...$$..*..****$$$$*.$*.*$...*...*.*..*...$$..*$$$...$*.....**..*...*.$......$..$$..$*..*.*....$....$.$..$....$$$*.$.$*.......*.*..*$**.*...*.....*.*...$$**$.*.$$.**.**.*.*.$.$*$...
...$.*$.$..$.**$.*..$.*....$.........*$.*.$....$...$....$$*.$$$*$...*.$....*.......*...$.$*..$**.**$$*..*....$..***$*......$..*.*..$.....*.$...*.*..$......*$*$*..*......*.*$.*.***....*......$...$$...**.....*....*.$$*$$*..*....*$.$.*.$.$.*..........**....**.*$$$$.*....$.*$*$*$$.**.$$.$..$..***.**$$$*..$.$...
*..*$.$...*..$....$$.......$..*.$.**.*.*....$..*...$.*.*.*$$*...*.*.$*.$...........$$...*.....$*....*....$...**...$$.$.$$..$$.$*.*$*..$*.$..$..$.......$....$*$...$$*...*$$.**.*..$*.....$.*.$.$.$...$*$...**...*.*.$..*....$$..*$*$.$..*$$.*.*...$.*$.*.$**....**...$*...$.**......*....$*$....$...*.$*.$..$*$.$...
$.......$$$...$.*.$..$....$**$$..$$*.$..*.$$*......*..$*$$..$.*.*$..$$$..*.....$.*$$..$*$...$.$.$.........$.*.*.....*.........*$**.***.***.$*...*$...***.....*......$.**.*.**...$...*.$.*.$$..$.$..$.$..**.*.*..*$*......$*$$*.....$**........$....$...**.$$**....*.*.$.*..*$$..$...$*..$*$**..*....$$...$.....$$*..
...$.$$$.$.*........$$...$.*..*........$..*...........$$.*..**$....**.*.*$.$.*...........*$$..*.....$......$*$..**....**..$$..*$.$*..**$*$...$.$...*....$*.$$..$$.*.$*$...*.**.$$.*$........$......*.*.....*..**..$*...*$...$..$$*.*.$$$.$$.$.**$$*.**..*....*....*....*..$*$..$..$**.$.$....*...**....$.$*$$..***..
.$.$$........*.$*.$..*...$**$...***$.$....*$*.$$*..*....$.*.$.*......$*$..$.*.*.*$*......$.$$...***$*$$**.***...$.*..*...*.......*.........*.$..*$*..$.*$....*$$..$.*.$.*....$..$.......*.....$.$......$*.$$*$.$.....$.$$.........$.........*$.*.*....*$..*$...$$...$*...........*......$*..$..**.$*$.$.$....$......
..*.*.*.$........*.*....**..**..$..**$*..$.$........*...$*.....$*.$.$...............*..$$.*..*..***......$..*.$***....$..$..$**..$..*.$*..$...$..$.$......*$.$*..*$*.*..*$*$..*..**.*....$.$..*.*$*$....$$*$*$$.*..$*$$...*....$.$...$....$**..$$.**.$...$..$$....*.*..$.*.$...........*...*......*..$.*..$$.$......
.$$...$..*..$$...*.$.$$...*..*.$*$$...*$...$....*..*..$....*...**..$.$**.$.$$$..*$.$....*..***$.$..$...$.*.$.....$$$$..*.....$..$$*$.$*$..$.$$**.$$.**..$..**....*.$.........$$*.$..*...*...**......$.*..*.*..$.......$**$....$..$$*..**.$.$.$.$..........$.*.$....$.$....$..$.$$$.....*.$..........$.$*$*.....*....
.*....$*...*..$.$*....$.$..*......$*$...$$$...$**..*.*..*..$....*...$..$..$..*$.....**........*$.*...$....*...$.$*..*$...*...$....*.....*...*..$...$..$$.*..$...*..**$..**..*...$.**$..*...*.$$..*.$*..*$...$...*$..$$*....$$.*$...*.$.$$.......*..$..$....$$..$...$......*.$.$$$$..*......*.....$$..$...*$...*$$*..
..*.$**.$...$*.**..*.......$*.$..$....*.$..$.$.*.........$$...***...$..*...$*$**.$.*.$....$.........$$....**..*.....*..$*.$..$.....$*...*...$$...$...$..*$*.$...$..*....*.*..$.$.*.*$...$.$..*..**$$...$*........$..$$*.*$..$*.*$........$**..*...*..*.$$.*..**.$$..*$.*$*.........*.$*.....**...$.....$.*...$......
.$...$.$.*..*.$.......**$.*...*......*$.$....*.....$$$.*..$*.....$..$*$....*.....*.$.......*.*..$*...*.*$$...*.*$......$..$.$.......$$....*..$**.....$$...$$.*..$....**...*.*$*$...*..*..*.$.*....*$*...*$....$*....*..*....$*.$.$*..*.....*..*...$$.*$...*.$*...$..*$$.***$*.*$..**.*...$$$*.....$.$...*..*..$*....
$*.$..$..*$*.$$$.$*.$$.$$........*.*.$....$**..$.***......$...*.$$.*...**.$.$***..***..*...$.*.*...$..*.$.........$.$..$.*$*....$..$...**..*........$..$$$....$.....$*$.........$$**....$..*$*.$..$......*$*...$*$*..$$.*..*.***$....*$$......*.$..**....$$.*.$$***.$...*$.......*..*..$.......*..***$**.***$*$..*.$
.......*....$..*.*...$...*...$.$.....$$.*$**$.....*.$.$*........*.....$*.....$.$$*.$*....$.....*...*.$...$..$..*$*****.$$..$..*.$$...*$$.$.$*$..**.......***.............**........$$$$*$*.$....$*..*...*$*..*$*$**.$.$........*......*...$*.....$.....*..*.*.*..$.$.$*..$*$$*..$$$.$.*$.$$*.*..****..$..*.$..***.**
...$...$...*.*.$.$.$$....*....*.....*$$.*....**..*.....*...*$**....*.$*.........*..*....*.$.*.**$....$.*.*$$...$.....$....*..*......*..*....$.$*.$$.*$...*...*$.$$....$.*..$$..$..$$.*.*.$...$..$.....$**....$.*..*..$...**...*....$$$.$....$.$..*...$.$.$...**.....**$..*...$.....*.$.....$.$.$*......$......*$*...
.$$..*..$*..*.$....**..$....$..$*$$.*.***.$......$.*..*.$$*.$$.$..*.$$$..$$.$$$.*.$$*.$.**.$*..**.$$......*..$.$........$.$*....*.*.**..$$.*.*.....*.**....$...*..$*..........*..$$$.$$.$.*..*..$*$*....$.......**.*.....*$$..$.**..$..*...**$*.....*.$$..**.$.**$$$.***...*$$...*$..$........*...**...$...$$.$.$$.*
......$$..*$*......$.$$*.**..*..*..$*.**....*.*...$$.....$*.$$.*.....*$..$*...*.$...*.$*$**..*.*$.$.*$*...$*...***.$..**$*.$......*.....$..$.......$..........*.$$$.*$.$.*$$$...*$$**$.*.....*$*.$$.**$.......$.$*.**....$.*.*..$..***.$*.$..$.$.$.$.*..$...$.$....*..*.$*..$$....$.*.$..*$.......$.*...*..$..*$$*.*
*..*..$.**...$.$.*.......$**.*..**.......**...$.$..*.**.*.$..*.$......*$$.$$..$......$.$**$..$...*..$*.*....$$.*...$....$.....*.$...*.....*..**..*...*.$$$.....$......*$*..*$....$$**$*$........$*$$........*.$$$.*$.*..$$...*$..*..*.*....**$.$..$*..*$..*$..$$$.$.**..$..*..$$.$.$.$*.$$$$..*.$$$.....*.....$.$...
*.$.*$.$$$*...$....$$..$*....*..*$.$...*.$$$$....**...$..*.$**..**.*$..$..$...*$....*.*.*.$$*..*.*...*.$*.$$$**...*.*......*$.$......*.$..$....$....*..$....$.**.$..$.*$*..$*..$$**.$....*.$.*...$.$..$$..*...$....$.***..$$*$.$$...$*...*.**.$..$*..$..$..*.*...$...*.$.*.....$.**$.$.$*..*.$*$..*..*$$...*..$.....
.....*..$.**$.....$*.$**.*$..$*...$*$..*$...$.$.*..***$.....*........*.*....$.*...*.$$.......**.**$..$..*$...$..**..*$..*..*$.$*$.$$$.*$$.*...*...**....*........*$..$*$..$..$...*..........*....*$..*$....$.$.$..$*$.*$.$.*......$..*..$..$.*.$.*.*.$*$...**...*$.*.*.*.$*..$..$$$...*$$.$*...$..*.$$..**.$$...*..$
.*...$*.*....$.$....$$..*.........*.**..$........*..$*.**.*......*.**.*$.......*......*....$..*$.$*.*$$..$*...*.**.*$..$.$$..$.$.*.*$....*..*$..*...$.$$....*.........$...*$.$$$$.....**....$.....*..*...$$.....$.$....*$$....$.*..*...$*$......**.*$*..*$**$$*....$*..$...***...*..$...$....*$..*.....*..*.$*$.$..*
$$...*..$.**.*.$.$$....*.**$..**$.*$.*.*..$..*.$$....$.$...$*..$.*...$.$$.**.....*..$.*$$.......*$..$........*..*$.*.*.....*..*..*$.........$..*..**........*.*$$$*..*.$..*.$$$..$.$....*....*...$.....$..*...........$$*....$....$.**.$..$*$$..*.....$*$$*.$..*...$..*$$.*.$*.$..$**$.*.*..*.....$...$.....$.$.$...
..$..$.*.$*.$..$$...*$$..*$.......*.**.**..*$$.$$.$.....*..*$$..$...$*$...$..*...*..$....*...$..*........*****.....$...*$**$.$..$.$$.*...$*.**......$..$*......*$.$$...$....*...*......**..$**$.$..$$.*$....**.*.*.$.$..$*.....$.....*....*.......$....*$..$$**.*.$..*.**..$$.*.$*...*.$...**.....$...$.$....**..*.$
$.....**.$.*.*$.$$.*..$..*..*.*$$...$**..*.*.*.......*...*$.*..$$.*..$.......*$$...*......*..$....**...*..$.*$..***.$...*..**.$..*....$.*.$....*.*.*.....$.$*..*..$$$$..***........*....$....**.....$..*.$$*.$$.$....*.$..**.$$*..*...$$......*.**$.$....*.***.$.*..$.*.$$*...$*.$**.*.**$*.$*..$...$*.*$*$..**$$$*.
.$*$.....*.*.$............$.......$.*.....*..$..**$.*..$..$.$.$*.$..*...$......*.*$*.$.*.....$..**$.*....$$***$*.*.$.......*.*....$.$...*....*....$..$..*.***..*.....*..$..$....*....$$.*.$$...$$$*.*....$..$*.*$.*..$$....$$.$**..*....*$...$$.*$..$..*..**..*$.$.$.$.$*.**$..$*.$...$$$.$..$..$...........**$*$.$.
....$$$....$.$$..*...........*......*.$.$..*$$$.$.......*.$......$$......*.........$.$**.*..$..$....$.*..*.......*.....$...*........$..*$.$..**....$..$$..$..*..$..*.*...$...*...*..$$......*$..*$$*.*$.$*$..*...$$.......*...$.......*..*$$....*.$.$.*.*..$.*.$...*...$.....$....*..$$$$..$**.$...$.*$.....*.$.$*..
.**.$......$.....$*$.**.$..$*........$**..*..$$*$.$*....**.**.*.*.$*..**...*$$.$...**$$..*$.*.$.**....$..***..*..$*.$*$*...**$..*..$*........*......$..*..*....$$.*$.$*....*.*...*..$..$*$$.$..$.*........**....***.....$.$..$*.......$**..$.**..$*...$$$..$*.$..*$..$*$$..*......$*..........$..*.*..*$.*.......$.*
*...$$$**...*....*.*.....*.*......$....*$..*..$.***....$.*..$........$...$....*.$$..$.$.*..$.$$**......$*$....**$........*.....*....*.$$*.$*.$***....**$*....$$$....$..*...*.*..$...**..*$*.$.*.**..*.*....$*..*....$.$..*.*..*..$*.$.$**....*..*..*..$....$*....*$*.*......$$$$.*$..$*....$..***$..$*...$...$..$$.$
...*.*..*.*....$..*$*....$.$*.$.$.$.$*$$.$**..*..*.....$.$...*$$.**$.....*..*.$***$..*...*..$*$.*..*...$*....$*$$$..$..*$.*.$$...$*..*$.$$.**.$$.$....*$...$*..$......*.$.$...$..........$*.*.....*.**...$*.$**......$.*.*....*..*$....$*...$...$*.*..$**.$$.**$.*.$*...$**..$.*.$*.*.*.....$.$*....*$**.$.*...$.$..
$...*.*$..$..***.**..$*.$....*.*$$.....*......*..$.*..$...$.*.$....$..*.$.....*....$*...*.*$..$.*..$......$$$......$.....*.*$$.*.....*...*.$*.$....*$..$.*.....$.*....$.*$...$*..*....**.$......*...*.$.*.**.$**.$...*....$.$*..$$..$$.....*...*...$.......$....*..........*$*...$.$$$.**....*$$....$*.....*.*......
..*...**.$...*$$.$.**.$$.$.$$.*.$.*.$.$.$.$.$.$...$..$..**$.***$.**$$.**$*.....$.$..*.$..$.$..*...$.$*..$.....*$$....*.*.*$$*........$*.**..**.$.$..*....$...$.**....$.*..$.$.$.*.$*..*..*$*.$.$.*...$.$.*$$$.*......*$.*$*$*.$.$*.**....*...*$...$$..$***..$*....$.$.....*....*.*$$.*.*.*$...$$......*.*..$....$...
..*$.*..*..*$.*...$....$$.$....**....*.$.*...$....$$.$.......$...$$..$**.$..*.$.$...$*$$$...$$$.$....*$.$*.*.$.$..$........*$.....*.**$.*....**.*..$**$.*...*$*$........*$....*$..*..*.$.$.$.....*..*..*$.$.....***$*$.*.......*..*.$..$$..$.$.....*$**.....*..$..*..$..*...$*.$*.....*.$.$....*.*..*$..*.$$.*...$.*
$.**$...***..*..*..*$...$***..*.$*.....$.*...*.$*.$.**..**$.**..$$.$$....**......*....*...$**.$..*........***.**.**.$*.***$$..*...**$...*$$.$.*$..*.*$.*....$...*....$..**.*.$..*...*..$.$.$*..$*..*...$$*.*..**$*.$...$**..**$...$$*$...........*$...$.*.....$.....$.......**.$.*...*.**..$....*$.*....$*$$...*..$*
.......*.*....*...$*.*........$.*..$*..$.$....**.*$..$*$.*..$$....$$$.*$..$...$.$..$.$*$*.**......*....*$........*...*.*.$$.*.$..$*$*.*$...$.$...$.*...$.*..***$....*.......$..**.$$$*$..*$*..$$...$**..$*.....*.*..........*...$......*.**.....**.$..$*..$$...........$.*.*.....*.*$..*.*..$**$.$..$.$*$*..*...*$.$
....*.....**....$....$*.*$*.$.$$*$....*$...**..*........$.*...*.*$.$...*.*..$.$.$....$*.**..$..$*....$**.$..*$*..*.....$*..$....*$...$.*.$....$..$.*.$*.*$......$..$..$..$$.....$*$..$...$.*.$..$.....$.$$.$*...*$*.*$.**$.....$......*........*.....$.*$*.....*.....$....*..*..*$...$.....$$$.$.***...$..*.$..*.*..
......$.**..$..$*..*...$$**.$*...$*...*..*.$..$**$**$*.$..$.$.$.*...$$.*..*.$.$$.*$....$*$*.....$.***..*..*....*...$..$.....$*......$.*.**$...$..$..$$....*.$$.*$*...*.*..$.$.$***.**.....$*......$$.....$......**.....$.*....$.$.*.....$*......$$*........$.$*..*.....**$.$.$..........$.....***$.****......$...*..
*......**$*......*.*.$**.$..**..*...*$$.....$.**$$...$$$.$..*$.....$*$$....*...$.$.*..*$..$$*.*$.$..*........*..*$....$..$.......$.......*.....*.....*...$.$$.$.*$.$.*.*$..*.*.*$..$....$$$........*..*...$$**$..$.**$..**.....$$.*..**...*..$.*...$.$....$....*$.....*..$.....$$$.**$*$*.....$.**...**.......*.....
.*..$.$....$.*$..$..$.*.......$....$*...$*$**.*$*$....**.$$$.*$.*$*..$..$...$.*..*....*..$....*.$.....*$*...$*........*.....***$$..$.$$.$..*..*..*.*..$....$..$.$*..***$.$*$..*....*..$*..*$.*$...*..$..*..*.*.$...$.*...*..$..*.$$.**.**.$$.$*...$.$....*.*$**.......$$*..$....$$...*.$........$$..$....*.***.....*
..$$.*...*..*.*..*$.***.........***$.$.*......$.*.$..$$$*..$..****$*.......$.*$...**.*..*$$*$$....*..$..*...*.$$.$..$*..$$*.**........*.*$*$.$.$.$$.*$....*....$.....$.*$$.$..*$..$.$$......*$$$.*.*$......$$$*$**.*$.*..**.$$*..$*.$...*$..$$*.*..$..*..*....$..........*.**.**$..$....$$$*.*.**.$.$*$...$..$$...*.
$$$..*$$.$.$...*......*$*.*.$$..$.$...*...*...$.$$$****..$....*...$***$**.$...*..*..$.$*$.....$*$...*....$.*$*...$..$*..*.*......*.*..*$.$......$.*...*....*...$...$.$*$.*...$.$$.$.$..........$.$.$*.$*..*$...*.$$*$$.*$*....*.*...*..........*.*...*....*$**.*$.$.......$.$..*..**...*.$**.....$.$...*....$$*.$...
.....*.....*...$$....$...$.*....$****..*$.$*...$.$....*..*....$**..$$***...$*$*$..$$..*.*$...*..*..*...$.*.....$**.**.*....$*..$*...*...*$*.....$..*.$$.$....**.*..$.....$*..*.$$..$$.$.**...$..$..*.....**.*..$$***..**.$.$..*.***....$$.$..*.**$$..$...**$.**.**$.*...*$..........*...$$*.*.**.**.*...*...$$.***..
...*.......*..$.......**..$....*....$...$.......$**.$.****......$*.$$$*$...$..$..$.$*....*$.$$....$*.$*.*.*.$$.......$...**$.$.*.*$..$.*.**...$$..$$$..$**.*..*.*$*....$$*.$*$$..$...*......*$*.*.......*...$.$..$...............$..**.$.......**.$..*....*$......*.$..$$$$...*$.$.*...*...$..**.....$*..*$.*.$.$$*.
..*$..$.**$..*..*.*$...*...$$*.....$.$$.....$*...*.$.$..*..$$....*.*..$*.*$$.*.$....**$...$..*...*............*....*.*$..***.....*..$..*..*..$..$$...$...$$$....*.**.$*.***...**$.$$..$.....$..*.$**..$*.$.*....$*...**......$*.....$...*..$.*$......*...$.$$.*$..****$.......*......$...**...*...*$..*...$$$.$$.$*$
....*...$....$.*..*...*$.....$.*..*.$......$..**..$...*....$..$...*...*..$.$$.*....*...*.......$$..*$..*$.....*...*.....$$$*$.$..$.$$$*.$$.$.*..*..*.*$.....$.*.$...$$.*..........*.*...$..*$..$*.**....$...$$.....*.*$*$*....*..$.*..$.$.....$.**...$$..$....*$.***..*.$*.$.*.*$$.*..$.*....$....*...$.$$*$.$..*.*$
..$*$..$....$...$$*$.*...$.$*..........$$$$$....*.$.$.......$.*.*.$..$.*.*.$...$...$*$*.$..*.$.*.$.....$.$$$......$*..$...$.*......*..**.*$...$..*$.**.$$*..$...........$*..*..**..*.$*.....**$...*.***....*$..$.$.$....$$*$..$.$$.......*...*$$..*$**.*.$......*.$........*.$$.*...$.....$..****.**......*.*...$$..
.........*...*.**..*........*.....$........$.$....**..$..*$...$..$$*$.*..*..*..*$$..$$.*.$.......*.......*..............*$$..$.****...$...*...*$...*.*.*$....$.$*....*$*.$...**$..$*$.$...*..$.**...*..$.$.$..$..*..$..*..**$...***...$......*...*.*....$$*...$..........*****.$..$.$**....$.*.**.........*.$....$..
*...$..........**$.*...*.*......$$.$*.$.$.$..$..*.*.**...*.*$.$....*$*.$$.*.$......*.*..$*.....$$*$.$..*.....$...**.$*.*$.$.**.*$..$.....$*.*...$*$..$$...$..*..*...***$$.$.....$.*$..$$****$$$*.$.$.*.....$..$$$.*...$....*$....$**.$....$*.....$..$.*...*.**.....*..$....$....*$$.......$....*...$.*$$$.$...$..$..
.$$**......$...$.$.....$$....$.....$.*..*..$*$.*.***.*.*...$$*.*....**....*...*.$$$*..$.*.*.***...$.$...****.**....$*...*$...$*.*..$.$...*.$..*.*.*...*$..**...$..$.$.*....*..$$..*$$.$*$.$*.....$*.**..*....*.$....*.$......**..$*..$.....*$.........*...*...*.$.....*..**$.*.**$.*$...$........*..$*$*.*..*$$..$*$
..$*.$..$...**.$....$......*$......*.$.**.$$$.*$$.$.$.$...*$.*....$.$....**.....*..*..**.....*.$*$..$$*.$.**.$*$.$$$$.$*$...*.....*....**.*.$$$...$$**.$$**$.$$.*..*.$$$.$...$*......**.*..*$$.$........$.....$..$$$$....$...*...$..*..$.$*.$..*$....**....$....*.*.$*....*.$**$..$$..$*..$..$...$*$.$*.....**$.....
...**$*$.*...*.*$$.$$.$......*....$$....$......$.$........*....**.*.....$$**$..*.$....*...$.$$..$*.....**.*.$**....$..$*...*$$*$.$....*$..$.*.*......$...$.*$.*$.*$*..*...$...$.*........$*.....*..*......$.$**...$$$$**.*..*$$..*..*..$.....$....*$....$$.$.**.**.$..$.$...*.*..$$...$$$.$.*..*.*..$.....*$....$.$$
*...$**$.*.......*.....$*.$$.$..*.$..*..*..*.....*$**...**...$.***....$.*.*.......$..$..*$.*.....$...$$*...*..$$*.*.*.*$.**...**..*$*$.*$$.**....*$.$...**$$.$*.......*..*..**...*$....$*...*$.$...$.$....$..*.$.....*.......*$*$$.$...$*.*$.$$*.*.$.$.*...*...*.*..*.**$...*..*....$.*...$.$$...*.$$.*.$..*.*...$$.
.$.$..*.*....$*.$...*$.....$.....$.....**..*..*.*...........$...$.$$$..*........$.......$***.......*..$.**..$....$.$..*..$..*.$.$....**...*..*.*..*$.*....$$...*$.***..*.$.$.$...$..$$.$..*....**$*$$*..$***.**.**$*.$$.$.....*$....$$..........*..$*.*.$...$........$...$.*....$$...*.$.$..$.$$...$..**$.....*.$$..
****$...*.*.*.$..****$........$*$.$**.....*$*.$.**..$....**.$$...$.$$*...$...$......$..$...**..**$.*..$...*...*..$.*...*..***...$**$*..$**$$*.$.*.$*..*.*.*$...*.$$...**.......*$..$.....**$*..**$$$$....$**....$.*.$......*.$.**.$*.****.$*....$......$$.**...*..*.*.........$.$**.**......$..***..*....$.$...$..$$
****.$.$$...$..*...*.$...$......$.$*$*$..........$..$.$$.$*.$......*.$*.*...*.*$$..$.$..$*...$$**.****$.$**$..*$.*........$.$..$.$....**...*.$$.*..*.*.........$..$..$.*.....**$...*$.*..**$...*......$.$..$*...$*$.*...$.**.*......$..$..$$.....*....*.*.....*....*..*$$*.$.*.$........$...*..$$..*....$*..$..*$.$.
*.$...*.......$..*..*$..*.....*..*....*.*..*$***$*$$.$.$*.*.....$*...$*....*.$$$***..$.$$.$**.$......*...$....$*$*.$.$.$$.*......$.$$.*..*......$.$............**...**$.$........$**..$.$.....$..*.....$.$.**$...$$**.**.$..$$$$$$...$...........*..*..*...$..*....$.**$$....**.*...$*$$......$...$..$..$......*$...
..*..$.$$$.$.$...$***...**...*..$.*$....$....$$......$.......$.*.....$*.$*...*.$.$*...*.*$*..$...*$.*.....$.*$.....*$...$..$....$..*.$...*....$.*$**.$$.$..*$.....*$*$...*........*.*$.....$....$.*$....$....$.....$..$$.*......*.*..$..*.$.*$...*..$...$*$.$*.*.......$...$*....$$..$..*......$$.$$*$$.$..$$$.$....
$$$......$...$.*.*.........$.$.$*.*..*$.$.$$$$$.$........**$..*.*..$.*.$.*$$$.*..$*............$*$$...$..........*$.....$.*..$...*$.$$*...*.*$*..**$..*...**$$.$.$.$.....$*..$$..$*$$...............$...$$$$........$..**.*.....$...*.$..$..*..*.**$*.....**..*.$$$..$$.*.**$$...$*...*..$..$$*$....***.*.......$...
....*....$.....*.*.$.$..$..........$...*...*$.*..$*..*.....*$.*...*$*..*..$*....$*$.$..$*.$$*......*...*.$*...*....$*..*....$.$...$.$$$...$.$.**..$..*..*$...$.$*.......*..*.$.*.$*$$...*$*..$....$$.$$$.$$..*$.......*..**.$$$...$***..*...*$$.$....**....*..**.*.*...$**.*..$..*$..*.**$....$.$....$...$$$.*.$..$.
$$..$....$$.$$$$*...$*$.$...*$*..$$...$.$*.$.$.$....*..$...***..*$.$$..$..*.$*$...$..........$.....$$.*.....*..$..$...$....*......**...$.**$*.*.....*.$*.*...*$**......*.......$$***..*$.........*.$.....*$..$.$.*$.*...*$.$.*$$$...*.**....**...$..$$.$.$..*..$..*.*.....*...*.$.$$...$$....***......*.....$$*..$..
..$....*....*$....$$..*......**.*$.**...$..*$.$.$..*.$.*$.**...*.*..*..$*$..*.$$$.***...*..*..**$*$..$....*...*..$*.*$*...*$$.*$....*$$..$.*$...$$*$$**.*$$**.$..*...*$.$$..*...$$.**.$*........*..*$.*.....$...$.......***...**$.$**$$....$*.$.*.$.*$.*..$*....$..*..*..$.*..$.$$..*..$....$*.$...$....*$$...*.$$.*
.$$$..$.$$.*......*....$.$...$...*.*.$.*..*.**......$.*...$*....*...$...$...*.$...*.*$$.$$.....$$*$$$$...$.....$...$*....$.....**.*..*...*..$$$..*..*.*............$......*.$.*$...$.....$**$.*..$.....*..**....$*$*.$...***$....*..*$*.$.......$.*..$..$.$**.$...$*..*$*..........$*$$$.$.$**.*.*$*...$..*$..*$*..$
*$.*.*.*.**$.$*$*...$.*.$...*.**........*.*....*.$$.....*.....*$.*.*.$....*.**$.*..$..**..*...$..$....$.*..$*.*$.**$$............*$.......$**...$.$$.$..$*...$......$..$....$$.$*.$.*..*...$.......**$..*.$$...$.*.*$$..$$.$..*..***$...$..**......**..*.....$.$**..*.$.$......$$$.**.$..$$..$*.$..*..$.....$**....*
..$$*.*$.$.$.*.$$$*.....$.$.$.....*...$..*..*..*.*....****.*...*.......*$....*.*.*.$....**$.....*.$.*..$........$*..**.*...*.$*.$**...*...***..$.*$..*...**$$...*.$$*...*.*..*...*$.....$....$.**.$.$.***$.**...$.*..$..$$$*$...$*$..$..*.$*......*.*.$**.$......*...*.*.$....*...$.$.$...*...$$$..*$$$$**$....*....
..**.*.......*.***..***.***$.....$$*$...$$***$*..$.$...$.$...*......*..$.$..$..$...$.....$..*$$..$$.$..*.$.*.....*...$$..$....$.......$.$...$....$.*.**.$.$...**$$............*..*...*......**$....$...$.......$..$.$$***.*..**.*.$........$*.*.......$*..$.***..$.*.*$.$........$.*$*...$$$...........$.$.$*.*.$..$
..*...$..$....$..$$**$......*.$....*.........**..*.**..$.....$.*..$......*.*............**..*..$...*.....*.**..$.........$$*$*.*$.$.....$...*..**$....*.....*$..*.$.......$....$.$...$..........*$.$......$...$*$*...*.......*..****.*$..$..*..$.....$$..$.*.$....$*$$...$..........$$.$..$*.....*..*..****..***.**.
..**$*..$$.$*$..............*$....$$*$.$$..*.$*$..*.$.....$$.*$..........$....$.$.....***..*..*.*.*..*....*$..*.**.*.$......*.*$......*....*..$$$$$$..*.....****....$.*...$........*.......*.......$.*.....$$.*......*.......*.*$.......*..*..*........*$$.*..$**..*$*..*$...$$......*..*...*..*$.*..**.$$...*...$$.
..$*.**......*.*.*..$$$.**....**.$$$*.*...*...$.....$$*.*........*.$..$.**..$.*$..*.*$..*$$$.$.*.**.......**$..**$...*..$....*.$.$$........$*.$.$$.*$.$..*.$.$$...*$.$$..*.......$.$$$.*$....$.*$...$..$$$....$.$.*..*.$.*...$*.*.*.*.*$..$**..*.....**..$**$.$$..*.......$$.............*.$....*...*$*....**...*...
.$.*.....$**.$.$*..*....*...$.*$*...$..$.$.$...$.$........$*......$$$..*.........$...*$.....$*..**.$...*$...*....**.$*.....*.$$.*..$..*....$...*$*......*..*......$......*$.**..*$$.$.*.*...*..*.*...*.....$.$**.$..$$*...**.....*.*$..$*$*.*.*..*..*..*.......$$*....**..$...$$..*.........*.*.$....$...*$$.*.*..$$
..$...$..$$.***..$*......*....$$.***..*....$*$...$..$**.*...**..$....*.....**........$..*....$..**.*.*.$........$*.*.$.$$*..$.$$*....$$...$$.*$.....$*$..........$*$...*...$$*$.**...*****.$.......$.....*..*.$.*$$.*$...$..**$.$$$*$....*.$$....$..$..*.$*..*.*.*........*$.**$$.....****.$.*.*$*$.$...$*....**...$
.$.**$$.$..*.*.***$.......$*$.$.**.*..$...*.....*........$..$...$$$**$$.$....*.*..$..*$.......$*.....*...*....$.***...$.*...$..$$.*$.$..**$$$$....$.$.*.$*.$.***..*..$..$$.*....*$..$...$..$$.**$.$.$*.**.*.*..$*...*.$..$.*..$$....$..$..*$$...$*..**.*$*$.$****...$$.$*$...*$.*$.$$......$..$**....$*$.$.$..$**$..
*$.$...$.*$.$..$.$$$..$.$...*...$**$...$.........**.*.*.*..$..$$...$*.$.$.**$.$$........$...*$*.$*.*.$.$*.*$**.........*..$..$$***$*...$$*....$$*...$$*.$*...$.*...*.**.*$.*$*.**...$.......$.**..**.*.*$*.*..$*.....*.....$...$.**.*$*$$*.*....*...*.$..**.$..**.*..**...****..$$..*......*.*.*.*..*..*.$*.$..$.$..
$$$..*..$$...$*$$.$.$*..$$.....*..*..$.$.***.*.*...***.*..*.*.......*.***..*..$$.*.$.$.*$$.$$.**.$....*.$$....****...........*.$...**..*.....*$...$.$.*....*.......*.$*.....*$.*.*..*.$*..$.*.**$.*.$..$.*.$........$.*.......$$$$...$$**..*..$$.....$.*$..*.***.$$*..**$$...$.*..$..*.*..*$...**$......$.....$....*
.*..*.$...$......*.**.*.....*.$...$...........$...*.$...*...*$.$..$$..$............$.*.**...$*.**.*..*$$.*...$...**.*..$$...*.*.$*.*..**.$.*......*....$..*..$.$$$$.$....$*...*.$.....$$.$*.*.*.*..$$$*..**.*$$..*.$*..*$$...*..........*.$.**$....*..$..$.**.***...$.$**..$.$...$*$....$.$...*$..$*..***$*...*...$.
......*.......*....$.$*$*.$$**$$$.$....*.***.*.$*..**.$.*..*$...$***$$$**.*...$...$$..*..*$.**....**.......***.$$*....$.***..$**...*$$$**...$.$.*.$$.....$*.$.....**.$*..*$.$.....*..*$.*$.$..$..$*...*.*$.......$*...*.*.**$..$$.$....*...*.$.....*.*..$.*..*$..$.$.$*..*.$..$*$.....*$$*....*.*.*....*.....*.$$$..
....$.*.......$..*$..*..*...*..$..$..*$........*.$*..$.$...*.*.......$.....$.....*........$$....$.$..$.$$...*....*...$.*.$*.*$..*$$.*.$.$.*..$$..*$.$*$$$.*$.**.$*.*$.......$..$.$*.$$...*..*..$..$$**.**....*..$$.*$...$$.$.*$.*.$$....$$**..*.*.$..*.*..*..*...$$........$...$$.$.*.$..*...$*$$*$*$.......$.$$$...
.$*$**$.$..*$..*.$*.*..*....*...*$*.$*$$$..***..*..*.*$...$...*...$.*.*$*......*$.....$..*...$$**...*$............**.$$$.....$*$$...$$.....$***.....$*....*$..*.*.$**...$*.$.$.*$*.*$.......$$..*..$*.*.$.*....$....$......$*.$.*...*....*....*..$......**.....$..$.$**.*$$$**$**.$.$...$.....$$$.**..*...*....$....
..$....$.....*.*.*...$$.**.*...$*..$...$***.*.*...*.$$..$.*...*.....$*..*.*.$.$..$$$*.*....$..*.....*.$*.$.......$......*..****..**....**$....*.....*.$*....*...$$**....**$*.*$.**..$*..$$....*......$**$.*.*.$..*$....$*.**.*.**....$.$*..$...*$**$..$*$....$.....*$..$*$..*...**.$...*.*$.*....*......$.....*$*..$
*.$....*$$....*..$........*.**$*..$*$*............$$$.$.......*.*....*.*.$..$.*.$$$*......$.*.$*..*.*$*.*$..*.$.*.$...*$$....*..*$.*.$..*$....$...*..*..$..**...$.$*..*.*..$.$...$..$**.....$.....$*..*..$$..$.*..*...$$..$..$$.*.*.*.*.....$...*$$*.*..$$..**....$.$*..*$$$*..*$...*$..*..$.**...$.*.$*...*.....*..
.....*...$..*...*....**...**....*.....*.$......*.........*.*.$...*..**$*$*..$..$...**$.*..$.$$*..*..*...*.***..$.*.**$....$.*$..$...**.$........*$*$.$*...*..$....$*..**.$.....$*$...*...$...$.$.$.*.*.$*$$..$....$.$.$....*..*.*$..*$.***.*$$.*.*..$*..........*..$*....$...*..$*..*$.$$.$...$..$...*..*.**..$**...
.$$...$.$..$$....*...**..$.$.*.*$****..*.$$.***.**..$$...$$..$.*..$.$.$$..$.***..$$$...$**.*.*.......$...$..*$$.*$...*..*$*$.$*$$.$..$*....*.*...$.......$$$.....*....*..$.$*..*$.$*$.$.**..*$*$........**..$.$*$*...**..*.$..*.$*.**..*...*.*..$..$...***..$....$$$.$*.**...$.........$$.$...*$....**.*...$.....$..
$$...$..**$...*.........*....*..*...*.$$$.*$...$*......**..$..$$$$.$.$...****$$.$....*$$.*.*..$.$*.$.$..*....$...$*$.*$*.$..$...***.......*...$..$*.$.$**$...$..**$$..$$.$.*....$..$.$...*$.*.*$....*..*.$....*.$..$.$*.*..$*............$$..$.....$..$*.*..$.....*.....$....$..*...**......$$$.*$......*$*..$..$$**
*.$.......$*.*...$..$$*..*.**....*....*..**.**.$..$...$....$.*..*...$*.$*.*.*..$$*.$**...$*..$*.***..$......*$.*$...$*.......*...$$..$**.*..*$$.*.....*.....*......$$.$$*...$...$.*..**.*...$.....$..*....$...*.$.$$$.*$.**..**.*.$.$....$.$$*$.....$$..*.*$.$.......**.$.*$..$$..*$..$$...*.*$...$..*$$.....*..*$..
$$...$*$.**.$.*...........$.*..*$.*$$...*....$.**.$$..**..***....*..*.$.*$.*.$$$$$...$.$$....$..*.*.*....*.****.***.....$..$.$.*$....$...$$$$.$......$$*$$.$......*$..$$.....*....$..*.....$....*......$..$..*..*..$..$.$...*$....$$$***.$...*.$*.**..$.$...**..$*$.$$..*$$.$....$$.*$***.$$*.$$..$*......*$....$$$.
...$**$.*.......$*.$$....$..*...*...*.**..**.......*..*..*...$*.*$..*.*.*$$**$.$.$..*...$.$$..$...*$.$......**.*$$$....*..*$.$.*..*...*...*....$..*..*.*$..$$*.$.$.*...$*..*..*$...$**..$.....*..$.*$*...*...*$*...*...*$...$$.....*...$.$....$$$****.$*.$$.$.**.$$$..***...*...$*$....*.*....$$$*.$.*....$$*$.*...$
....*..$$$.....*.....$.*....$*.......**$.*......$$$$..$*..$*....$*.*..$*....**.*.......*...$.$.....$$.*...$...**.*......$**...$**.$....$..***$..**.....$..*..*.$.....$..$*.$**..$$$*.$......$*.$..*..$.*....*....$*$....$...$*....*.......*.*....*..$..*.$$$..*..***...$*.$$.**.$..*.*$....$.....**$.$....*.*$*.*.$.
.**....$$.$...$**$........$....*.$.*$......$.$........**.*.*..$$$....*...$.$*.*.*.$$.$.$.*$*.......$$.*..**.$$$...*.$..*....*$..*..*.$.$..*...$..$.$...$...*$.$$.$.**$*.$.$..........$$*.*..**.*$...*$.*...$....$.....$......$$**$..$........$*..*$.$..$.$*.*.***.$.$$.*...........$.*$.$*..*$.$$.$.$..$*.*.$$..*$*.
..*.*...*.$$**......*.$..***$$*....$...$.$..$.$$...*..*.$$.**........$.$..$....*..$**$*....$..$$$***.$*..*$*.$*$..*....$*.*.$..$......*....*..*$$*$**.*$.*.*$...$$*...$.*$$*$.$***..$..$.....$.$.$$.....$$.*..*.$**..*.***..$..$..$*.***.$*$$$*$.*....$...*...**.*...*.*.*...$.........$*$$.*...$...$....*......*...
$.*.*$.*.$...$...$*.$..........$..*....$.*.*.*...**..$**...*.......*..*.$...*.*..*.....$*..*..**.**...*..$*...*$.*..*...$**.$..$*.*$$$$.$.*.$*....*....**...**.*$$*...**..........*$$.......**.*$..**..*$............$.***..*$$...$**.*........$.$*...***$.$..$..*.$.....***...$.*.....$..$$*$.$$*.$*..*.**.*$*.....
$...*..$.*$*...$.$$.$......*$*$*.$..$**$.*$.*..$.$......*....*...$$....*.*...$***.$$..**.$$$$$**$.$.*.$.$......**$..$.*$$...$...$$$....$...$$..*.$.***$.$......$.$....$.$.*$$*..**$.$.$*.....$...*.**.*$$$$*.$$...$....$$....$.$*$.*$...*...$$.$....*$......**..*..*..$*.**.$..*.*.$......$.$*$..$.$....$$*..$$..**.
*.$...*$*.$$$..$*...**$$..$....*...*.**.*$..*$.$.$*.$***$.*$..*$*....*.*$$*.......*.$*$$$$*.$$..$*.*..$$....*..$*.*......*.$..*...****.$.$*$....*...**..$..$*..*$.$$$..**$.$.$*$....$$$*..*$.$...$*..***.*$$...$.$...$.$..*$..**$*......*$....**$...$*$*.$..$.....*..**.**.*..*....**.$**.$$...$..$$...*$.$.**....$*
....*$.*.$.......*.$.$...$.*.$....*..*.$.....*..$$.....*.*.$$$$*..$.$..$.$.$..*...*$$$....$.***....$*....***...*.*.....**.$.$.*...*$*....*.$..$*.*$.....**.$....$..$$...$..$.......*.*....$.$.$..*$.$..*..$...$**$**$*.$..$...$....$..$...$***..*.*$...**.$$.$...*$*..**...$$...$$$.....*$..$.*$....**$.$.......$.$.
..*.$..$..***.......*..$..*..*$.$...$$.....$.*$$$.....$..$$$..*...**.$...$.*.*...$*.......***..$$..*$.$......*$.$.*..$$$....$*$..*$**.**$...*..*..$$$......*$.....*$*.*........$*$..$**.*..$..*....$...**.$...*$...$.......*.*$..$.**$*.*$.*.*.$....$..*....$.***$......$..*$....$$$.*...**......$.......$...*.*.$..
*.......$.....$**.*..$.$...*$..$$***$....**.*$.....$.$...$$.*.$.$..*....*$$..*..*........$$...$....*$$$...$...*.$*$..$$.**.*.$$....**.$*.$*.$.........$.*...$*..**...*...$....$*$..***$$*.*$$..$$..$....$$..$..*.***..$....$.$....$.**$..**.$$.*..**.$..*.$.*....*.$$$*.*$....$*$.......$.....$$.$...**.....***...$$
...$$$$...**$.$*.$.**.$..........$...*...**$.....**..*....*..*$.*.*..*$.*....$*$$......*$$.$$..*$.*.$$...*...*..$$$..*$..$**..$........**$$.*.....*..$...*..$...*$$.**..$.$$*..$$.*.*...*.*..$*...$.....$*.**.*........$.*.$..**..$*.*$*$..$...*...$$**...*...*...*$*$$*$...*........$.*......*........*..$*$.$..**.
....$.$*.*..*...$...*$.*...$.$.*.*..$.*$$*..$.*..$*.....*..$.**...*...*..........*.*.*.....*........*...$............*.$.**$..$....*..*$*$$.$$.$...$..$..........$*...*.*$$..$......$..*$.....*...*$.$.*.$..$.$**.*...*..$*.*$...*.$.......$****.$...*$*.$.***.*$.....$....$....*..*$**.*$....*.*$....*$........*...
.$..$.*.*.......*...$..$.*..*......*.....$$.$$...**....$.$.*$***.$.*.$$$.*...$..$...$*..*.*$..*.*...*.....*.....$.*..$..$*.*.**..*..*....*$*.$...$.$...**.*..*$..$.*...*.$**.$.*.$$.*$$$**.*.$*.$*..*...$*..$..$$...$..$..*...$..$......*$.*...*.*.*.*....*..*....$$.*...****.$$$...$$.$*$.......$**$$...$.....*$...
**$..$...$$....*..$.*....*....$.*..*.............*.**.$.*...*.*...$..$.$$..$......$.*.**....*....*..$$$.$..$.$$.*...$*.*.*$.*.*...*..........*...$$*.....$.........$.....*.$*...*..***.$......*...**..*...*$........$....*.....*$.$*$...$$$.$$*.*.$.$*.$$.$..$.$...$.*.*..$$.$...*....*..$$..*...$$*...*$..*$...*...
*$.$...*.$.$.......$.$....$*..*..$...........*...$$.*.$.$$.....$$.**..$**.$$...**.*...*.*$*.*.$*.....*.$..*....*.***.*..*$...$....**.$*$..**.$..*$$..$.$..*$..*..*.$..*.*.....$....$.....*..**..*.$...$$*$$.....$.**.$*.*....*$...$...$*....*$$.**$.*.$....*....$.*$.......$...$...*.$.*.$.*$*..$...$.....*$$$$.*.*$
........$..$$*$.*.$.*.$....$$$.$..$...*....$..$..*$.$.*..**............$....*$.$$*...$***...*..*.$*....$...$.*......$$$..$.$..$..$.*$.*.**.$...*.....$...*.....$*.$.....$....$.**...$*...$..*$.....*.*..........*..*..*$$.*.$.*...*.$*...*.*...$...$.....**..$.$....$*.$.*$**.*$..*....**$.$.$*.$.....$..*$$....$.$.
....*.*....**...*.$......$........**$$$..*.$$$.**$$.$$*$....*..*...*........*.....****$$$$...**..*.**$*.$...*...*.$$.$.*.$**.$..$.*.$.$.**$$.*.*...**....*..$..*$**.....*...$......$.*......$.*$....$..*.$.*.$.$$.$**.**$...$**..*.*...$.*$....*..$$..........$.$$...$*.**$$.....*$.$....$*.$..$....$..*$..*..$$$..*
.*.**.......$..$.......***$$$.....*$..**.$*..*.**$.*.*.$$.....$.$*.......$$..*$.***...$...*..$.$$..$.$..$$$.*.$.*..**$*.$..$$*..*.*..*$...*.$*..$.$.*...*$.*.*......*.......$..**..*....*.$.*...*.......*..$.$*$*$..*.....$.*.$**$...$...*.**......$.**$$..$...*.*......$..$.*...$*$$$.*..$.*.$.**.**.*..*$.*.**..*.
**.**.*....*$...***.$..*...$$....**.*$$....$.$...*...*..***...*.$.**..*..$$.$*.........$...*$..*.*.$....$...$..**$$....$.***.$.*$$.$.*$.$..$..$...**$.*$*$*$.*....$..$.$.$*.$.**$....**......***..$*.$*$..*..$.$.$..**$...$*$...*.*..$.....*.**$.*..$**$..$$....$$$.*$.*...$*$.*............$..$..$*...*....*$$$.*..
$..*$*..***$**.*$***..$.*....$$$.*..$..*.*.......$......$$...$$*.*...**.*....*$...$*$*$...$.*....$....*...$......*$.*.$$...*.....$.$...*$.**...*.*...*.$$...*$.*...$.$.......*$.*$.*...*..**$....*.*.*..$$.*.**.*..$$.$.....*$*.*.*...$$*.....$.*$.$$.$..$$**.*.$$..$**$$.$.$....$..*.*.$*$*....$.....**...$........
**$*$.$$....*.*..$*..*.$..*$..$$.*..$...$..*.*...**$*....*..*$.$.*$..*..*.*.$...**.$........$.*..$...$$.*.*....$..*.....$$....*.*..*$*..*..*....$$..*$*.$.....*$.......$$..$*.$..$.$...$...*..***$*.$*..$............*$$.***...**.**.*$$..$$.....$..**.*$$.....$....*........$$*..$..$...$*$...*.$...*..*....***....
.$$$...$..*..*..$$.*.$*...**.$$.$.*$*....$..*..*..$...$.*$.*.....*$$.....$.$*......*.$.......$***$.*$*.*$.....$*...........*..$..*...$....$$..*$*......$..*.$$.*$.$..$..*....*.*..*$..**.*........*....$.**.....$***.*.**$.*$*$.*.$*.$....$....**........$..$..$.$$....$.*.*$..$*$..$*....$$*...*.$$$.$$.*.*...*.$.$
...$*.$....$.*.$...*.$..$*......*.*...*.*....**$**.$......*.*.....$.**........**.$$..*...*.....$.$....*.$**$.*.$..$...*$*.*....*$.$$.$.....*.**..$*.*.*$$..*$$...........$$**..*..**....$$.*.*..*.$**$$*.*$$.......$.$*....$.*..*..*...$..*..$.$....*..*$*.*.$*......$$*...$$$**....*..*$$$*..*.$.....$*$.....*$.$.$
$.$$.$$.*........*$.*.*.$..**.$..**.*$....*.$*..*..*...$..**$$.$*$$$$.*....$.......*.*...$*.*.*...$**....***...$...$.*$*.*.$$..*..$$**$...*...$.*.$*...$........$.$*.....$$...$*..$...*.$$.$...$*$.$*....$*....$....*...*$*......*.*.$$$..$$$.*$$.$..*.$.$..*.........$..*.$.*...$.$....*..$...*..*$..*..*$.$...*.*.
.......$.$*.$...$...*.*..**..$*.$.$.*...**..$...$.$.$.$.$..$...*.$$$...$.$.$...$..$.**...$...$...$....*........*$*$.....$.....**.*..*..**.$......**.$.*$..$...$..*...*..$....$..$.$.$$$..$...**...*..$.....**.....*$...$....$$$$$...$..$...$$*$*..*****..**....*$...$.$....**....$...$$....*$***.$*$$..$.....*.....$
*.$.$.*.*...$.**..$...$*.$.$$..$.........*...$$$*$.*.$$..$..$$*..*$.$$$..$*...$..$.*..$.....*$.$..*...*.*.....$.$...*....*.......$$..$.*$.*..$*.*$..$..$.....*..*..$*..*.*..*.$.$.....*$..*......*$.$*.$$......**..$$$**...*$$....***......$.*.$....$..$.*$*...$..$...*....$**...*.$$.$...$.*.**..*$.$......*.*...$.
*$.$.*.$$*.*.*.........$*...$$....**....**..$.*.*.......*..***$$*...$*..$$..$.$*.*.*...$.**$$..$....$....$.$$.*...*$...*$..*..*.**$*.$$*$...$.*$$.$**..........$*.*...*..$...*..*$$$$.*..*$$$.**..$......$.**.....$*..***...*..$.*.$..$...*$.$...*$$..$..$*$**...*......$.....$.*$.$*....*....**..$...$........*.*.*
$*...*...**$..$....*$.**$.$$...*..*$.........$.*.$**.$..*$.$*.$..........*.*..$..$.**.*.$**$$$.*...$.**$$..$*..*$*......*.*$*...$*.$.*$*..$..$$*..***.....$.$.$.*.........$.$*.*..*.*.$..**...*$*......*...*...*.*.$$...****....*.$*$*$...*$.$...*.$**.$*.$..***.$$.$$...*.$..$.....*.*$.$.....$..$..$$$.$*$***.$$.*
....*..$....$.$*.$*..*.......$..*.$.$..*.*.....*$......$$*$.....$...*......$$.*..$.*....$*.*$..*....*..$$.....$$*$**$..$..*$$..*.$...**..$.**.$*$*..*...$$...*.$..*.$*.......**.*.$.$..*.*.*...$$*.....*.*$.$.*...*..$$...*$.*.*..$....*..*..*....*.*...$..*.$.**.......*...*......$**$.*.*$*..$.$*.*$$*......*..$.$
$*$....*.*$.$*.*$..*.*.$*.*...$$$*....*.$......$$*...$.$........$.$$*$...**.....$....$*$.$..$....$$$.*...*.*.$..$$...$..$$*.*.*.*$..$.$$$.*$..*...*.$.......$.*...*..$.......$$*..$...*..*$..$..*...$...*.$.*$....$....*...*$.....**.*...*.**....$..*..*.$.$*...$..*.$$..$$....$.**$.*$.$.$$.$..*$$..$..*...*$.....*
$$***$$.......*...*.*.............$..$...$......$..*.$...$..**$*....$$..$...*.*....*...*..*...........$$$.......$$*...*..$.$*...........*..$..$.$*$.....$..$...**$$.$$....$*.$......*...$*....$.*.$....$...*...**.....$....$.$.*...*...*...$..$...$.*.$$*...*.*..**..*..$.**$.*.$......$.$**$$$...$...$..$.*..$.*$*.
.**..$$.*.$..$..*..$*..*$..$........$*.*.$*..*$.......*.**.$..*..**...$.**.$..$.....*.......$......*.*$*.*$.$......$$$*.......$...*.$.$.*......$.*.*.*$.$$.$.*.$....$*$...*.*....$.*.*.$*$$$...$$.....$..*......*$....*...$..**......$...$*...$.**.*...*.$*$...$...*......*...............*...$..*$..$....*.*..*.*$.
...$*...*....*.*..*$*...$..**...*..*$...$.$*.*$...*.*$*.......$$...$$$.*$*..**$...*.**...$.....$*.$....*..$..*$.....$.......$.......*$*$$.$$....$*$$..$*.$$.$.........*..*...*..$.*..$.$$.*.....*.*$...$*...$....*.....*...*$...*$...*.*....$.$.$$.......$.*$..$.*...$........*......$..........$$...$....*.*.*$.*$.
.....*..*....**.$.*..$..*....*...$.*.$$*..*.$..$.*.$$*$$.*$..*.**..*$........*.....$..$.$.$.$.....*.$$...*..*.$...$*$.*............$$..*.**.$...*..$..*.*$..**.$...$$$..*$$*.***.*$...*.$*..*....*.......*...*..$.*...*..*$$**.....*.....*.*$.*$*.......$$..*.$..**...$...$....*$........$...*....$.*$.*$$...*.$$...
.*......$...$..$*....$$$...*..$....$..$...$.$..*.$*...$...$*$.......$..**.*.$*$..$..*$.*.$..$*$$...$$......*.*$......$*.*$....****.$..*.**$...*$*......$.$.*.$..*..***$.**$*...**$****.*$..*....***..$$..$.*.$$*$$....*.*$...$..*$$.*..*.*...$*..*..*$$.$...$..*.$.**..*....*.....$.$$.$**..$.$$.$...*....$........*
*$.$$...*.*....*........*..*..$..**.*..$.*.$..*...*..$$$$$.*..$..*$**$$$$*...****..*..$$*..$.*$*............**....$.**...$$...$..$*...*..**...$$$.*...$$.$.*.....$$...**....$.*..*$*.........*$.....**..$....*.$....*.....$..$....*.....$......*..*..$....$*......**$*..$*$*..$$.*$.*.$$$*$....*$.$.$....$*...$...$$
....$$.***...$.......*....$*.$.$.$$*...*...$.$*..$..$$$.$..*..*.$*.*$*....**$.*...*$..$*....$$.$..*....*.*$.*$.**$.....$..$**....*......*$..**....*.*...$*.**$$.$..$....*..$..$..*.$$.*$$...$..***..*.*.**$..$*...$....*....$*..$...*....$..*.*.......*....**..$.**..**$....$$***...$*.....*$$$..*..$$$..*$*$*.**$..
$...*....*$$*..*$..$..$$..**.$*$*.....*$.*$..$*$.$*$$*......$$*....$$$..*...*........**.....$$.$.$$.$..$*.....*..$*....$..$$..$...*$.$.*.*$*$....$..*...*$*...$.$$...*.$......$.**.*$$.......*..*$$...$.$.*...*.$.$$.$.........$$.$.$..$..$$..$$.**......*$.......*$..*.**.*$.**....$.$....$.**.$..$..*..$..$..*....
...*........*......*.$.$.*.*.$.**...*...*.*.$..$**...$*$.....$.$.....$.........$*..*..***...**.$*..$.$.$$$*......*.*$*.**$...*.....$*....$....*.$*.....*.......$....*$...**.$.*.$....$.**....$.**.$.......$*..*.*...**.*...$.**..*$..$.**$..**.*...**...*....$*$.*.*..*.$$*....*.*...$$..........*..$$$...*...$*.*.*
.........$...$.*.$.......$$$$*......$.*.*.....$...$$.**.$$....$...$..**...$..*$**..***$$.$....*$...**$..*$$**....$.*....*...$..$.**..*..$...*....***.*..*...**$..**$*$...*$***$.......*..*.$..*.*...$..***.........$...$*...*.*$..$..$....*$.....$*$.*.....*.....$*$.*......$*.*.........$.$.$...$..*.$..$$*....*$$*
*..$..*.**..$...$*...$.......$***...........*.$.$.*$*..**.*..$..$..*$$.*.....$.$....*.$.**.$*..****.*.$..........*....$.*.......*..$..*..*..*..*...$..$.$....$$$.......*.$**.$..$.$..*......*.....$.....*.$.....$....*......****.$...*..$...**.*.*....*.*.$.$*.*..**$*..$*.*$...$.*.$*..$$.$....**$....*.*...*.$$...
*$...***..**$$.*.*...*$...$**.......*.*...*...$$.$...$**...$**.$..*......$...$*..**.**..$.**$..$*.*$.......$*.$$..$...$.**..***$....$$*$*.....$*.$.......*$.*.$$...$....$.**.$..*$$....$....*....$$..*.*.$..$..$$..$...*.$.$$.$*..*$..*...$*.$$..*.$.$$*$..*....$$*.*$..*...*...$*....*.*.$.....$*$$..$$$*..$*$..$$*
.$..$.$$$*$...$$*.....$.**.$..*..*$..$*$**$....**$..$.....$........*$$$*$*$.$.$$..$.*.*....$.........*****$..$.$...$$..*..$.....$..$..$$.*.*.*.*$.....*..$.$..$.*..$$.*$..*$...$.$$.....*.*.$$...***..$....$$.**$...*.$....*$...$.*....$...**..$...$*$.*.*$$.*....*....***.*.*..$$...$.$*$$.$..$$$$*$.*..*$.$.$....$
.$.....$.***$.$**$.$...$$..*..*.....*..**...$$$*..$.*$.$$$..*$.$.$..*...*...$.$...*.*$.***..*.$..$.$*..$**..*....*.**.*....$*.***$.$*.$.$$...$$.**....$$$$......****$$*....*.$*...$*..*...............*$$$.*.**...*.*$...$$.*$**....*$....$*.*....$....*..**...*.*.....*..$*$.$..$*...*..*$..*..*$.....*...*....$$$$
....*..$**......*$.*...**..$.*.$....*.*.$*.$$$$$*...*$$.*..*..**$.$...$*..$.$$..$.*.....$..*...$.......**..*.....*...$..*..*$.*$......**..$$$..*.$$..$..$....*...*.*.*$.*.$$....$.*..*.$$*.*..*.*......*$.*..**$.$..$**.*.*.**..**.$.**$.*.$$.*.*..$$..*$.*$..$..$*....$$.......*...*$*$.......*$..$..$...$..$....*$
..*.***....**.*..**....$.$$.......$.......$....$$....$$....$**.$$$.$.*.$*.*$..*$.$$.*...$....*..$.$.....$$*.$..*$......*..$.......*...*$*.*..**...$...$...$*$...$*...**.*.*......$...$....*.*...*..*.*.**.$*..*...*..*..$.$...$$*.$.*$..*.........*..*..*...*.....**.*.*..$.**...$..*.....$$$...$...**.*..$.....$.*.
..*.**.$*.*.$*.$.*..*$..*$.$*$.**$.*.$.*.....**.***$.$...*$.$*....***.****..*..$*....$.*...$....*$*.*.$..$...$......$$.$*..**.....*...$*$$.$*....$$$..*....$$.$*..$.$.**$$$..*$.*$...**...*.*....*$*..$....$.....**..$.*.$$...$.$**.$$$.$.$*$**.*$..*..$..*$$.$..*.....$$...$*...$..$......$*..*..*$...$*...$$.*...$
$...**$$.**$...*$.$.$$*....$.*...$*$.$...**...$....$......*$.*..*..$.**....$......$*....*...*.$$*$.$$.*.$$$.*$$*.*...**..$..***.$$....*..*$..........$$*....*...$$*......*$*..$.*$$.....$..$.*$.**$....$.$$.....$$$.....*..$..***...$$.$$$....*.......$$..*.$.*.....*.....*...*.*..*...$.....*..**.*$$$.....$...$**.
....*$*$.*...$....**....$$$*.....*.$*.*..*.$..$*$...**$...$..*.$...$..*$**...........$..*.*.$.*...*.....*$$.$$...$*...**..$..$.*...$**$.$$...$.....$*.*.**..**$....$..*......$...$$....$$$....*$$..*..$$...$..$$...***...$*...*....$$...$.*..$.$$$....*$*.$*$....$....*.**..**$.*.$....*$*.*$$$..*....$*...$*$.$.$$.
..*..*.*.*..$.$*...*..*..$$.$..*.**...$*..*$*.$$...$..$..$$.......$**$*.........*....$...***.*$.$...****..$..**.*$...*...*.........**.$......*..$$$..$....*...$$$***.**..$*.$$*$$$.*.*$*..*..*..$.....$..*..*......*...****.$......*...$$***..$.$...$*.$$*****..$$..*.....$*.....*$***.*$*.........$*..**.....***.*.
**.$$*$$$$.....$......*.$***........*$$..*..$.$.........$*..*..*..*.......*........$*.$$.*$.*....$*.$$*$.*.....**$*$..$.*.**...$$..*$.....*.*.$$...$*....$$*..$****...$*.**$..*.......$$$.*$*.*.*..*.*$.....*...**.$.$..$..$..$*$$$.$$$$*$*...*.*$....$..*.*.....*$.$**.$.*.$*$*.$.$$....*..$$..*......$.*.*.*.$...$
...$.$....*.***$..........$.$..*.$...$...$......$$......*$..$............*$.*...*$..*$$$$..$*.*$.*..*..$$$....$*$*$***$**.$.*..$$.$$$.*.*..$...*.*.$.$.$*..*..$*$*..*$..**.$.$$$.*...**$......**.*..$*...$$*$..*$.$.$.****$..$*....$$$$..$$..$.*..........$*.*$.***.$.*......*.*$.*.......$*....*.*...*$*$$...$*.$**
......*.$.......$.....*.$.*.$*..$...........$.*$$.$*$*...***$.*.......$.....$*$.$....$.*..*..*.**.$$...*.$*$.$.*$$.*.$....**..$....$...*..$$$.*$.$**.$..*...*$$*.**.**....*$...$*....*$..$*...*.......**......$.*.*.*.*.....$...*.$.*$$.**...$$.$**$...*.$.*$...$.....$...$.*$$........*$$.*.....*..$.*..*..*$..$.*$
.$.*...$*.............**.$*..*$..$*..*..*..$....$.....$..$.....*$....*...$*.**$...$...*..$*$.........$$...**.....$.*.*.....$***..*$...$..$$.*.*..$...$*.**$$*.*...$...*$$*...$.........*...*$...$...$.$..$*.....$...**........$....$.*.$.*..**...$.**..*...$*.$**$.*.*...*$...$........*....*$*....$*$..$*.......**.
***.$..*...$*.*..*$..$..*$..$..*.*.$.*$.$$$*..$..$**......*$....$$...**.*...$..**$..$....$$.$.$*.$$*$...*.....**.*$$..*.*.......*...$.......$*.*...$*.**..$.*.*.$$..$$.$...*$..**.......$*$.$...**.$*..$.....$..$...$...$**.$.$...*...........$.$.$*.*.....*...*$*..$..*$$$$.$.*$...$*......*$....$.$.$.$.....*..*$.
..*..*....*$.....*...*$$$....$$*..**.$......$*.*.*$$$.*.$.....$.*......*..*.*.*.*$*.*...$..$$..$*$*.$....***...**...*.$$..*.*.*$....$..***..*.$..$.$.*.*..*.....*.*......*.$..$.....$.....$*$..$....$**..$*.*..$..$*...$*$$...*........*....**$$*$...*..$$$*$**...*.$...$**...$$....*...$.$.$.$......*$**.$.*$$..$$*
.**....*.*..$...$$*$.$.*$$$$$..$..$..$.$**...............$*.$*...............$$..$..$$....*..**.$*...*$..$.$$.$*.*....$$.$*........*..*.....*...$..*.**$$.$..*$$..$*.$$...$.$...*$.....$...........*..$.....*$.$.**.*$*...$*.....$$.**..*$..*$.$...**..$$...$..$*$.*.*.*...$..$$.*..$...*....**.$$..*..$$..$**.*...$
..$*...*.*........$..$$...*..$$..*$*.*.....$..*$.$......*...$.....*...$.*....$.$.....$$..$.*.$**$...$$.$$....$.*$.*$.$......*...*$*..*.*.*.....*$$.**$.$$.***...*.$.**...*...**.*...$.....$..**.*$...$...*.*$*$..$...$.*.......$....$$..*$.$.*.....***$*.$$.$$..*..*......$.$$**.$.$..$...***..*.$...$$.....**.....$
*..$$.$$..*$....*....*...$..$*$$.$..........*..$.**.$..$..*...$..$...$*.....*.$...*$***..$$.$.$$..$...$...$.$..$..$...$.$.*.*.$......*........$$.......*$.*$.*.....*...$$.*..$**$..$...*...$..*.......*..$$.*.$...$*$.$.$$$*.........*..$.*....*.....*..***.**....*..*....*..$$.$..$$.*$$.$.**....$....*......$.....
..*..$..$..*.*$.$.*..*..$$...$..*..$*....*.$....*.$$$.*..*.*.$..**$$$**.......$$*.........*.*..$..$$$.....$.*...*.$..*.*..$$$....*$*$*.....*.$..**$.......**...$..*$$..*$$....$..*...$.......*$.$$.$.*.....*.$$....$*....$..*......*.......*.$.$...*$$........*.$..*$..$.$.............$$*.......*.............$.*..
*.**$.......$**$......$.$*......$......$*.*...*...$*.$.$$..**....*$*..$$.$....*....**$$**$.**....*....*$...$*..*.......****.*...*.*....$$.........$.*$...........$$.......$...*......$...$...$$..$*.*$*...$......$..***.....$..$...$$$$.....$.$.........*...$.$..*..*..$..*...$.......$****.$$*$..*$.....$**.$.$*.$*
..*.$....*.$$....*..$*........**$.........$*.$$...$..*...$*.*.....$........*.....$$**..$...**...$.$..$*...$...*.*.$*$*....$$.*$$**.....*..*.$.*.*.....*......*..$...*.....*..*.*..$.$.....$.***.....*....$....**$.....*..*.**.*.$*$..$$$..$..$.$.$$.*..$.$*$..**..$..***..$$..*...**$*.*....*..$*...$.*......$*.**.$
.....$..$...*..*.*..*$$$$.*.....$..$..$$*$.$.....*.*..**.............*...$....*$*..$.$..*$..$*....*.$$*$*.$**$.$..*..$*.$..**..$$..$*$.*....$*.$........*$.....*$*.........*$...$$.*...$$$..$..$**....*..*$$...$.$..**...$.*.$*..$$*...*...$...*.$*$$........$*..**....$$.$.*.$.**.$*..$.$$..$...*....$.*.*...$..$..
..*..**...$....$$....$.$$.*......*..$...*.*...$..*...*.......$..$.$$..$.$$..$...*....*..*....$*........*.$.$.$$$...$.$.*...*$*$*$.*.*........*.....***.$$..$$...$.$.*$..*.......$$....*.......$.$..**$$$$....$.$$..*.$$..***.*..*.$..*.$$.*.....*.$..$**...$*$.$..*...$$*..$..$*...*...$*.**....$...$$...*..$..$....
.........*$$...$*$**...$.*..$.*$.$..$.*.....$$$*$..$............$*...$*$...*.$......*.....***.**...$.$*...*.......*....*.$..**.**....$*$.........*$.*.**...*...*$*$......*...*$$*$.*...$*.$.*$*..*$.*...$.*$..$....*.*$$$$.$**....*$..*.*.....*....*..*..$..$$$.*.$.$..*.*..$..$.......$.$$..*.$....*.*..***.....**.
$...$...*...$.*..$.$...*.$$..$..$......$*$.$*.$.....$..***$.$*..$..$.$.$....$....$..*.$.$$..*..**$......$$*.**$..$.*.$.......*.*.$*...$.......*.**..$..$*.....*$....*.$$$**.$*.*...*...*....*.....$$.$*$*.$.$$........$*.*.$**$*..*$.*........*......*..*...$..*.....*$.**..........$...**..**.....$*..*....$..*$..*
...$.....$$**....$**$...$*$..$*..........$...$.........$..*....$.$...*..**.$$...*..*..*$$.*$*.*...$$$..$....*..*....$....*$...$...$$......$$*....$..$$...*....$.$$.**..*.$$.$$...*.*$.$.***.**....*..$..*....*...*.*$$**....*...*........$$...$.*.$$.*.......*...$$...$*...*...*..$..$....$.$.......*.$$.$..$*...$**
$.$..*.$....$...$$.**......*..*....*....$.*$.*....$*.*..*.$..*......$.$....$..........$.$$.$...*....$.***.$....*$..$*.**$*...$.$.*..*$..$..$....$.$..*.....**..$*..*..$..*...*..**.....$.....$.......*..$$..$$..$**$.....*...*.*...$*........**.*.$.$........$.$..**$*..$*....*.$.....*..*$.*$...*..*.*..$$..***..$*
$**.*$$...*$.$*$*..*..$..*.*......$..**.**..$$.........$.*......*.***$.$.*..$$....$..$......***....$.....$..*$.$..............$$..$.$$...**.$...**$$.....$.$*.$$.$....**..*...$...*...$.$**...*..*.$$.......***...$*.$$.$$.......$....$*.$..$..$.*.$..$**......$....*...$.$.*.$$*......*...$$$.*$....**$.....$..$...
$....$..*..*..*..$...**$......*.$$....***...$$*....*..*.**$.....$...*.*$*$$.......$***$..$$*$$$.$.*....*.$**............**.$*.$$..$***$...*$.*$..*.$.$.......*$.*$$.....$..*$..**$..$**$$*...*$$$$*..**.$.*.*.*..*.......*...*$**.$$...*...*......$$..$......*.$.....**$...$$.$$.$..$.........$$.$$*.$$$$..*.*.$..$.
*....*.$.$$*..*$$.$$....*....**.$..***.*$...**...$$.$.$..$..*...$$....$$$.$...$**$$$....*$*$...*.*....$..*...$........*...$.*..$..$$$**......$.***.**.....$*$$***.*$.$..*..........**....$...*..*...*.*$.***.*..*.*$.*.$.....$.*.**.*.***..$.....*$...*.$....$*....$*..$*$...$*.$....*$..$.$.........$**.*..*.$...*$
$....$$..$$..*......$*.$$*.*.$.*.$*....*$........$*...$.$$*$$.*$........$$$.**$...**.$.*.....$*.......$..*..$$*...*$..$.$..**.........*$.$$*...*$..$.$$.$$.*..*..$..$.......*.*$**..$.....$......*..$*.$.$.**$......*.$..$*..$...$........$*$*.$..*$.*$...*......$...$$.*....*.......*....$*.$$$.*..*...$....*$...$$
.$...$.*.......*..$*.***..$$$..*.$.*.*$$.....$..****.$..$$..*.*$...........$.$.*..$..$*.***.*$.$**.....$.*$..$.*...**.$....$*.$..*..........$*..**.$..$.$..$.*..*$$*...*.*$...$$*..**..**$$.*....*..*$...*..$$$*.*....*..**......***.$.**.*.*.*.......$$...*$...$.$....*.$.$$$**...$....$...*..*.*.$$*.$.*$....*...*
....*....$.*$$..$$...$.$$.$*..*.$..*$....*..$.......$..*....$......$..$*..*..**..*...*.**$...$*..*.*..$$.**...$.*$.$*$.$......$*.$*..$...$$..........$.............$$*.$$.$.*...$......$$.....*$......$**...*.*$.....$$....$..*$.....$.......**..**$........**..$..$...$$*$$..**.....$..*.$.*$*..$..$.*...*.$*$.*...
.$...*$.$.*.*..*.....**..*..*..*......*..*$$...*...$.$$.$*.*..*..$.....$$$*.$..*..$$*.***...$.*.**...$$..$...$$.*$*..*.....**$.........$**$..*......*..*...$...*..$.$**..*$.....$.$*.*..$$..*.*$$..$..*.*$$*.$.$...$....$*.$...*....$*..$.*$.$**.$$..$$*..**.*.*.$.*.$....*...**$.*.*.**.*$$*$$..**..$...$*.*$$.$...
**.......$*..$..$.........$*.......$..$*.*..$.*.$$..*.$$.$*.*..**........$**.$...$.*..**....*$.*..*$..$$*...*.$*..$...*.$.*.*......$.*...*$$$.$$$..*$.$.$..*$$...*..*.$.**......**$.*..$...$..*..$$.***$*........*.$$.....*$$.$*$..$.***....*.$..$$$.*$$.*.$.$*..$*$.$$...*...$......*..**.....*$$..*.$....*....$...
.$.....$.*$$**...*...*.......*.$........*$.*.$.***.*......$..$.*$...*....$..$.$$*$$**...$$.$.$*.*$.$$***..$$.......*..$$.$*.*$.$..$$.....*.$.***.*$$$..*$$.*.*..*.$.$.$*$$.....*...$.*$.$*.*..$..*........*$$$*...**$*...*..*.*.$.$$...*.$.......*...*$...$..$*.....*.$..$**$*.*$..*..........$.$$...*.....$..**....
.$**$$$...$..**...$$.$..*...*...$**.$...$.$*.......*.**$.$.*.$...$..*.*...*.$***..$.$.....$.$......*.......*.$.....*$$$***.**$.*..*$.*...**.*...*...$*..*...*......*....*.*...$.*.*.***..$$$....*.$.*...$$.....*.*.**.$......$...$.*......$$.....$...$$.**$$*..*$...*.**...*.$*.***.**$*...*...*..$..$*$.....$$.$...
$...*$.*$........$$.$$..*...$.*$.*...*.$$...$$$*...$$.**$....$$....*..**.*...$$*..*..*.$...$.*..$.....*...*$.......$****$........$....*$....***...*...$....*.......*.$.$*.*.*.$..*$.*$$$*$.$*$*.$*.*$.*..*.$..*...$..*.*$.$.*.$..$*..*..*...*..$*.$....$*.$..$....$...$*$..$$*.*$.*..*.$.....$$.......**$.$$....*.$.
.****.*...$...*...*$.$..**$...*...*..*...$.$*$...$.**.......$.***....*.$$$$*.*..$...$**$........*$$.*.......$..*.$*..$.*$*$.*$**.....*..$..*..$.***....*.....$..*.......$...$.$.**.$........$...*.$$.**$.....*....$$$....*.*$$$..*$*......$$..$...$..*.*.*.*...$..$**.$*...$*.$$$*..*.$*.*......$*.$$...$....$.$*$*.
*..$***..*.$.*...$.$.....*.$.$..*.*..*.$.*..*..**.$$.*..*....*...*....*.**..$.$$.$$...*.*..*...$$.*.*...$..*.$..*........$..*....*....$*.*..$*.*.*..$*.*.$*.*...$$.$$..*.$*.*..$*.....**.$.$$...*$.$*$.$.*...*.$.**...*......$..$$$...$$*$*$$........*.*$*$$.*....$$$..*.$.*.*....$$$***..$..*$.**....$$..$.*.**$$..
***..$.*..$.$....*.*.$$..*......*..$*..$$...$..*..*......*$*.$**.$*..*.*$.....$$.$....$**.*...*....*$.$$..$.......$.$*.**.$*..$.$..$*.....***..$....$.**..*...*...*.$...*.........$...*.*..*..**...**.*......$*$$*...***$*....$$.$$.*...*.*..$..$....$$....*$.*$$.....*.....*..$**$.*...***.$.$$*...$..*..$.$..$*.*.
.....*......*...**..$.....$*.....$..*$.$$....$..$$..*$.**.....**..*..$...*.$.$.***..$...$.$$$$.$.$......$$....*.$*..$**$...........$...$$$...*......**..*........*.**.*.$.$$.......*....*.*$$*...$*.$**...........$.....*$$$*$*.*$$...*$*......$*.*.........***$.$.....$*$$.*$..$$..*$....$.....*$$...........*..**.
......***.$..*$.**$..*...$**..**..*..*...$$**$$..$**.....$$..*.$*...$**.*.....**$.**..*$*.$.$....*.$$...$.*$....$....*$$.....$....*..$*$.$..*.$....**$$*..$.*.*.$..$*.*..$...*.**.$*..$*.....*....*$*.$*..$$.*..$.......**.$..$$.......**.*..$.*.$$*$....*$...**......$.*.$$.$.$....*.............$$*$$....$.$.....$
.$*..**.$*$..$.......*..**$*..*..$*.**.$$.....*$*.**...*...*.**...$*...*$..$*..$..$..**$.*.*.$......$*.$$.$...$........$..$.*.$*$*.$$.$.*..$$*$$*$...$.*.**...$..*.*$$*.$.*..*.........**.*......$....*.***..$$$*.*...*.*.*.......$**..$**$....*.*...*...$.**.$.$..*..$......**$..*.*......$$.....*$$*$.$*.*........
..*.$**.$$........****...$.*$$....$.....$.$.$...$..$$$*$$.$*.....$.$.$..$..$*..$..$....*.*$..$*$...$...*....*.$..*..*$..$**$.*..*.....$$*..$.$...*.....*$..*$...*.$**$..$$.*..*$*.**...*..*....*........$...*..$......$.**.*.*...*..$.....**.**.*..$....*$*...**$*.*...*.*...**.**..***$$$$...$....*.$.*.$.....**$..
...***.....$$....$.$..**.*.....$$.$.$.$*.....$$$....$..**..*..$$.$*$$$..$$.*.....**.$*.*.$$*..............$.*.$.*..*$...*...*$.$$.*.$..$.$.$$....**....*..$*$$....***.*..**.*$..$..*.*..$$.$.*.$.*...$.$*.*..**.*.$**.....$....$***..**$.*...$.*...*$.$......$.....*........$$....$....**...**.$.........*.*.*.$$...
$..$$......$.....$.$.......*$..$..*..*$*$*..$...*.*$*$*.$$...$.*$*..$.*$$.**...$*$.*.$.**.*$.$.$$*$..$$*....$..*...**$.$*..$..........$.....$$*...$.**.*.*....*$...$*.*$.*$..*..$.*.$...*.*...**.$*..$.$$*........*.$.*$$***..*..*..**....$$$$*$.*..*..**.**$..*......$$.$*$.*$$$*$*..*..$*$$$..*..*.*..$.$*.*$..$.$
$..$.*....$........$..$..$$$..**.*..*.$$$..*......$$......$.*.**...........****.$..$*.*.....$.$..$*.*..*.$..$..$.$*$*$.*.$..$.*.$.$.$...*$...$....$$*.$....*$.$.....*...*.*.*...........**..*.*$.....$$$..$.$......**$*..$$.*....*..*.$*.**..**$.*...*..$*.**..**.$..*$...$*..*..$.$$*.**.*.**$..$..$*.....$.$..*$..
$.**...$.$...*$....$***..*.*...$....*..$..*$$$.....*.*..$*.$.*..........*$$$*.$...***..$$**.$....$$*.*......$**.........$..*...$*$*..*.*.$.$..$.$..*.$.$..*.*.$*..*.$..*$*$$$*$*..$.*.$$..***...*.**.$*....$..$....**.$.*$$......$.....**.....$.....*....$..$*.*.*$..$***.$$.........*.**$*..$.**.$$*.$*.$*...$.....
.$$*..*......$$$$$.*..$*..*...*.**$***......*$.$*.$..**..$$..*...$.....*..*...**....$.$.*****$.*.*.$$..**..........$$$.$..**....*.*..$*$*$.....$...$.$..*.....*...$$.*$*$.$..*...*...$....*...$*$$.*..$...*.$**..........$..*$...**$*.$....$*...$.......*$$.*...$....**.*..*$$..$......*..*...........**....**....*.
....$..*.$$*....$...$.$.$...$$......**..$.......*$...$*...*$*$.$....$.$..$..$..*..*$.$.......*$$.**.$...*$.$$*...*$**$*.$...*...$....*..**.$$****$*.*$*.....**....$...$.*....*..**..$.$.*......*..*.$..***..$.***$$.$......$......*....$$.*$.$.*.$.$.....$..*..$**..$.**...$..$$.***$**.$...$*$$..$.$.*.$$$*$***...$
....*........$.*$..*.$**.*..*.***.$.$**....*.$*.*.*$....$$....$.$$..*...$..*.*$.$*$.........*..$..$.*.*..$...*$...*$...***$...*$....*....$$.$..$.$..*$.$.*$.*..$*.*.$.**...$.*$.$.$..$$$*.$****.*...*...*$.$.*....$...$.$*..*.$$*.$.*.$...*.$$...$**.....$$....*$.*.***$$$..***.$*$..$...$**$$*...*$*..$.*.$...*..$.
.$.*$..$..$.*...***.$.$$.*.$..$*$.*..$....$$..$...$*.$*..*.$.$..$.....$$....$$.*.......$...$....$....*...$$..$.*.$*.....*..***$*$*.*..$$$.*..*.*.***..$*....$.$$*.*.$$*.....*......*..$*...$***..$..$....$.*.$.*$$..*.....***.**...$.....*$*$$.*...*$$**$..$*.......*...$.$......$$$*.$.*.....$.....*.$.*.$.....$...
$$.$.$...*...*.$......***..*.*..$.*.*..$.$*...*$.....****.*...$.......**.......$*$*$.$$$.......$.$.$.$.....$*........*.$..*.*..$..*..$$..$*..$.**..$.*$.$...$..$...$$*$..*.......$.*$$$**.*$........$..$.$**...$*.$.$.*........*....$$...$....$*$*..***..*..****..*..$.......$...$$.*$..*..$....*$.....*$*$...$.$.*.
..$****...$$........*..*..$$$.*....*.*....**.*..*.$*..*.....*$......*$$$*$$.*.$*$*$..$$..*...$..$...*.$.....$*..*$....$$.$*..$...*.....**.....$.*..***..$$...$*...*.$.....*$.$..............$.*..*.**$.$.$$...$*..$........$....*...$..$*.*..*..**.*$..*...$.....$.*$.$$....*..*..$...$*.$$$...$$.*.$..*.$.$$$$$...$
$*$..*$.....**$....***..$...*..$....*...$.......$........*.$..*$*$*.*......**.....$....*.......**$.$**..*.**....*.$..*$$*........$$$...*..$$.$.*$.......$.*....$.$**................*.*.*..*$$*.$$..*.$$..$.$.*...*..*$.$..$*....*$.$.$......$....*.*.$..$$$$.......$.$$...$*.*.*.$...*...$$......$$**$.....$.$*...$
....$.$.$.$$.....$...**.*$.*.$..$*.......*....$*.*.$...$.*...$$$.*...$.**.**$$...$...*..*.$$.*$*.......*...$$*.$.*...*.$.$.$...*...$..$*.$..$..*..*.*.......$..$$..**$.$.$$.$..**..$.$*$.*$.....*.$$**$*..*...*.**.$..........$.*$$$*.*$.*.*.*$.......*....****$...**..$.****...$.**$.**.$.*$..*$......$$..*..*.*...