시간 제한메모리 제한제출정답맞힌 사람정답 비율
2 초 256 MB118955358312173428.304%

문제

세로 $R$칸, 가로 $C$칸으로 된 표 모양의 보드가 있다. 보드의 각 칸에는 대문자 알파벳이 하나씩 적혀 있고, 좌측 상단 칸 ($1$행 $1$열) 에는 말이 놓여 있다.

말은 상하좌우로 인접한 네 칸 중의 한 칸으로 이동할 수 있는데, 새로 이동한 칸에 적혀 있는 알파벳은 지금까지 지나온 모든 칸에 적혀 있는 알파벳과는 달라야 한다. 즉, 같은 알파벳이 적힌 칸을 두 번 지날 수 없다.

좌측 상단에서 시작해서, 말이 최대한 몇 칸을 지날 수 있는지를 구하는 프로그램을 작성하시오. 말이 지나는 칸은 좌측 상단의 칸도 포함된다.

입력

첫째 줄에 $R$과 $C$가 빈칸을 사이에 두고 주어진다. ($1 ≤ R,C ≤ 20$) 둘째 줄부터 $R$개의 줄에 걸쳐서 보드에 적혀 있는 $C$개의 대문자 알파벳들이 빈칸 없이 주어진다.

출력

첫째 줄에 말이 지날 수 있는 최대의 칸 수를 출력한다.

예제 입력 1

2 4
CAAB
ADCB

예제 출력 1

3

예제 입력 2

3 6
HFDFFB
AJHGDH
DGAGEH

예제 출력 2

6

예제 입력 3

5 5
IEFCJ
FHFKC
FFALF
HFGCF
HMCHH

예제 출력 3

10
W3sicHJvYmxlbV9pZCI6IjE5ODciLCJwcm9ibGVtX2xhbmciOiIwIiwidGl0bGUiOiJcdWM1NGNcdWQzMGNcdWJjYjMiLCJkZXNjcmlwdGlvbiI6IjxwPlx1YzEzOFx1Yjg1YyAkUiRcdWNlNzgsIFx1YWMwMFx1Yjg1YyAkQyRcdWNlNzhcdWM3M2NcdWI4NWMgXHViNDFjIFx1ZDQ1YyBcdWJhYThcdWM1OTFcdWM3NTggXHViY2Y0XHViNGRjXHVhYzAwIFx1Yzc4OFx1YjJlNC4gXHViY2Y0XHViNGRjXHVjNzU4IFx1YWMwMSBcdWNlNzhcdWM1ZDBcdWIyOTQgXHViMzAwXHViYjM4XHVjNzkwIFx1YzU0Y1x1ZDMwY1x1YmNiM1x1Yzc3NCBcdWQ1NThcdWIwOThcdWM1MjkgXHVjODAxXHVkNjAwIFx1Yzc4OFx1YWNlMCwgXHVjODhjXHVjZTIxIFx1YzBjMVx1YjJlOCBcdWNlNzggKCQxJFx1ZDU4OSAkMSRcdWM1ZjQpIFx1YzVkMFx1YjI5NCBcdWI5ZDBcdWM3NzQgXHViMTkzXHVjNWVjIFx1Yzc4OFx1YjJlNC48XC9wPlxyXG5cclxuPHA+XHViOWQwXHVjNzQwIFx1YzBjMVx1ZDU1OFx1Yzg4Y1x1YzZiMFx1Yjg1YyBcdWM3NzhcdWM4MTFcdWQ1NWMgXHViMTI0IFx1Y2U3OCBcdWM5MTFcdWM3NTggXHVkNTVjIFx1Y2U3OFx1YzczY1x1Yjg1YyBcdWM3NzRcdWIzZDlcdWQ1NjAgXHVjMjE4IFx1Yzc4OFx1YjI5NFx1YjM3MCwgXHVjMGM4XHViODVjIFx1Yzc3NFx1YjNkOVx1ZDU1YyBcdWNlNzhcdWM1ZDAgXHVjODAxXHVkNjAwIFx1Yzc4OFx1YjI5NCBcdWM1NGNcdWQzMGNcdWJjYjNcdWM3NDAgXHVjOWMwXHVhZTA4XHVhZTRjXHVjOWMwIFx1YzljMFx1YjA5OFx1YzYyOCBcdWJhYThcdWI0ZTAgXHVjZTc4XHVjNWQwIFx1YzgwMVx1ZDYwMCBcdWM3ODhcdWIyOTQgXHVjNTRjXHVkMzBjXHViY2IzXHVhY2ZjXHViMjk0IFx1YjJlY1x1Yjc3Y1x1YzU3YyBcdWQ1NWNcdWIyZTQuIFx1Yzk4OSwgXHVhYzE5XHVjNzQwIFx1YzU0Y1x1ZDMwY1x1YmNiM1x1Yzc3NCBcdWM4MDFcdWQ3OGMgXHVjZTc4XHVjNzQ0IFx1YjQ1MCBcdWJjODggXHVjOWMwXHViMGEwIFx1YzIxOCBcdWM1YzZcdWIyZTQuPFwvcD5cclxuXHJcbjxwPlx1Yzg4Y1x1Y2UyMSBcdWMwYzFcdWIyZThcdWM1ZDBcdWMxMWMgXHVjMmRjXHVjNzkxXHVkNTc0XHVjMTFjLCBcdWI5ZDBcdWM3NzQgXHVjZDVjXHViMzAwXHVkNTVjIFx1YmE4NyBcdWNlNzhcdWM3NDQgXHVjOWMwXHViMGEwIFx1YzIxOCBcdWM3ODhcdWIyOTRcdWM5YzBcdWI5N2MgXHVhZDZjXHVkNTU4XHViMjk0IFx1ZDUwNFx1Yjg1Y1x1YWRmOFx1YjdhOFx1Yzc0NCBcdWM3OTFcdWMxMzFcdWQ1NThcdWMyZGNcdWM2MjQuIFx1YjlkMFx1Yzc3NCBcdWM5YzBcdWIwOThcdWIyOTQgXHVjZTc4XHVjNzQwIFx1Yzg4Y1x1Y2UyMSBcdWMwYzFcdWIyZThcdWM3NTggXHVjZTc4XHViM2M0IFx1ZDNlY1x1ZDU2OFx1YjQxY1x1YjJlNC48XC9wPlxyXG4iLCJpbnB1dCI6IjxwPlx1Y2NhYlx1YzlmOCBcdWM5MDRcdWM1ZDAgJFIkXHVhY2ZjICRDJFx1YWMwMCBcdWJlNDhcdWNlNzhcdWM3NDQgXHVjMGFjXHVjNzc0XHVjNWQwIFx1YjQ1MFx1YWNlMCBcdWM4ZmNcdWM1YjRcdWM5YzRcdWIyZTQuICgkMSAmbGU7IFIsQyAmbGU7IDIwJCkgXHViNDU4XHVjOWY4IFx1YzkwNFx1YmQ4MFx1ZDEzMCAkUiRcdWFjMWNcdWM3NTggXHVjOTA0XHVjNWQwIFx1YWM3OFx1Y2NkMFx1YzExYyBcdWJjZjRcdWI0ZGNcdWM1ZDAgXHVjODAxXHVkNjAwIFx1Yzc4OFx1YjI5NCAkQyRcdWFjMWNcdWM3NTggXHViMzAwXHViYjM4XHVjNzkwIFx1YzU0Y1x1ZDMwY1x1YmNiM1x1YjRlNFx1Yzc3NCBcdWJlNDhcdWNlNzggXHVjNWM2XHVjNzc0IFx1YzhmY1x1YzViNFx1YzljNFx1YjJlNC48XC9wPlxyXG4iLCJvdXRwdXQiOiI8cD5cdWNjYWJcdWM5ZjggXHVjOTA0XHVjNWQwIFx1YjlkMFx1Yzc3NCBcdWM5YzBcdWIwYTAgXHVjMjE4IFx1Yzc4OFx1YjI5NCBcdWNkNWNcdWIzMDBcdWM3NTggXHVjZTc4IFx1YzIxOFx1Yjk3YyBcdWNkOWNcdWI4MjVcdWQ1NWNcdWIyZTQuPFwvcD5cclxuIiwiaGludCI6IiIsIm9yaWdpbmFsIjoiMCIsImh0bWxfdGl0bGUiOiIwIiwicHJvYmxlbV9sYW5nX3Rjb2RlIjoiS29yZWFuIn0seyJwcm9ibGVtX2lkIjoiMTk4NyIsInByb2JsZW1fbGFuZyI6IjEiLCJ0aXRsZSI6IkxldHRlcnMiLCJkZXNjcmlwdGlvbiI6IjxwPkEgc2luZ2xlLXBsYXllciBnYW1lIGlzIHBsYXllZCBvbiBhIHJlY3Rhbmd1bGFyIGJvYXJkIGRpdmlkZWQgaW4gUiByb3dzIGFuZCBDIGNvbHVtbnMuIFRoZXJlIGlzIGEgc2luZ2xlIHVwcGVyY2FzZSBsZXR0ZXIgKEEtWikgd3JpdHRlbiBpbiBldmVyeSBwb3NpdGlvbiBpbiB0aGUgYm9hcmQuJm5ic3A7PFwvcD5cclxuXHJcbjxwPkJlZm9yZSB0aGUgYmVnZ2luZyBvZiB0aGUgZ2FtZSB0aGVyZSBpcyBhIGZpZ3VyZSBpbiB0aGUgdXBwZXItbGVmdCBjb3JuZXIgb2YgdGhlIGJvYXJkIChmaXJzdCByb3csIGZpcnN0IGNvbHVtbikuIEluIGV2ZXJ5IG1vdmUsIGEgcGxheWVyIGNhbiBtb3ZlIHRoZSBmaWd1cmUgdG8gdGhlIG9uZSBvZiB0aGUgYWRqYWNlbnQgcG9zaXRpb25zICh1cCwgZG93biwgbGVmdCBvciByaWdodCkuIE9ubHkgY29uc3RyYWludCBpcyB0aGF0IGEgZmlndXJlIGNhbm5vdCB2aXNpdCBhIHBvc2l0aW9uIG1hcmtlZCB3aXRoIHRoZSBzYW1lIGxldHRlciB0d2ljZS4gVGhlIGdvYWwgb2YgdGhlIGdhbWUgaXMgdG8gcGxheSBhcyBtYW55IG1vdmVzIGFzIHBvc3NpYmxlLiZuYnNwOzxcL3A+XHJcblxyXG48cD5Xcml0ZSBhIHByb2dyYW0gdGhhdCB3aWxsIGNhbGN1bGF0ZSB0aGUgbWF4aW1hbCBudW1iZXIgb2YgcG9zaXRpb25zIGluIHRoZSBib2FyZCB0aGUgZmlndXJlIGNhbiB2aXNpdCBpbiBhIHNpbmdsZSBnYW1lLiZuYnNwOzxcL3A+XHJcbiIsImlucHV0IjoiPHA+VGhlIGZpcnN0IGxpbmUgb2YgdGhlIGlucHV0IGZpbGUgY29udGFpbnMgdHdvIGludGVnZXJzIFIgYW5kIEMsIHNlcGFyYXRlZCBieSBhIHNpbmdsZSBibGFuayBjaGFyYWN0ZXIsIDEgJmxlOyBSLCBTICZsZTsgMjAuJm5ic3A7PFwvcD5cclxuXHJcbjxwPlRoZSBmb2xsb3dpbmcgUiBsaW5lcyBjb250YWluIFMgY2hhcmFjdGVycyBlYWNoLiBFYWNoIGxpbmUgcmVwcmVzZW50cyBvbmUgcm93IGluIHRoZSBib2FyZC4mbmJzcDs8XC9wPlxyXG4iLCJvdXRwdXQiOiI8cD5UaGUgZmlyc3QgYW5kIG9ubHkgbGluZSBvZiB0aGUgb3V0cHV0IGZpbGUgc2hvdWxkIGNvbnRhaW4gdGhlIG1heGltYWwgbnVtYmVyIG9mIHBvc2l0aW9uIGluIHRoZSBib2FyZCB0aGUgZmlndXJlIGNhbiB2aXNpdC4mbmJzcDs8XC9wPlxyXG4iLCJoaW50IjoiIiwib3JpZ2luYWwiOiIxIiwiaHRtbF90aXRsZSI6IjAiLCJwcm9ibGVtX2xhbmdfdGNvZGUiOiJFbmdsaXNoIn1d