시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
5 초 128 MB 119 38 15 48.387%

문제

일본 정보올림피아드 위원회는 일본 정보올림피아드(JOI)를 홍보하기 위해서 JOI로고를 모티브로 한 깃발을 만들었다. 깃발은 "좋은 깃발" 이어야 한다. "좋은 깃발"은 알파벳 J, O, I중 하나의 문자를 M행 N열 사각형 형태로 배치한 것으로, 아래 그림과 같이 배치되어 있는 곳이 깃발에 적어도 한 곳 있는 깃발이다.

다음은 "좋은 깃발"의 예이다.

다음은 "좋은 깃발"이 아닌 예이다.

일부 위치에는 이미 그 칸을 채울 문자가 정해져 있다. 이때, M, N이 주어졌을 때, 좋은 깃발을 만들 수 있는 방법의 수를 구하는 프로그램을 작성하시오.

입력

첫째 줄에 깃발의 크기 M과 N이 주어진다. (2 ≤ M, N ≤ 20)

다음 M개 줄에는 깃발의 모양인 N개 문자가 주어진다. 각 문자는 J, O, I, ?중 하나이다. J, O, I인 경우에는 i행 j열 위치의 문자가 이미 그 문자로 정해져 있는 뜻이고, ?는 아직 정해져 있지 않다는 뜻이다.

출력

첫째 줄에 "좋은 깃발"을 만들 수 있는 방법의 수를 100000으로 나눈 나머지를 출력한다.

예제 입력 1

2 3
??O
IIJ

예제 출력 1

4

힌트

[{"problem_id":"5559","problem_lang":"0","title":"JOI \uae43\ubc1c","description":"<p>\uc77c\ubcf8 \uc815\ubcf4\uc62c\ub9bc\ud53c\uc544\ub4dc \uc704\uc6d0\ud68c\ub294 \uc77c\ubcf8 \uc815\ubcf4\uc62c\ub9bc\ud53c\uc544\ub4dc(JOI)\ub97c \ud64d\ubcf4\ud558\uae30 \uc704\ud574\uc11c JOI\ub85c\uace0\ub97c \ubaa8\ud2f0\ube0c\ub85c \ud55c \uae43\ubc1c\uc744 \ub9cc\ub4e4\uc5c8\ub2e4. \uae43\ubc1c\uc740 &quot;\uc88b\uc740 \uae43\ubc1c&quot; \uc774\uc5b4\uc57c \ud55c\ub2e4. &quot;\uc88b\uc740 \uae43\ubc1c&quot;\uc740 \uc54c\ud30c\ubcb3 J, O, I\uc911 \ud558\ub098\uc758 \ubb38\uc790\ub97c M\ud589 N\uc5f4 \uc0ac\uac01\ud615 \ud615\ud0dc\ub85c \ubc30\uce58\ud55c \uac83\uc73c\ub85c, \uc544\ub798 \uadf8\ub9bc\uacfc \uac19\uc774 \ubc30\uce58\ub418\uc5b4 \uc788\ub294 \uacf3\uc774 \uae43\ubc1c\uc5d0 \uc801\uc5b4\ub3c4 \ud55c \uacf3 \uc788\ub294 \uae43\ubc1c\uc774\ub2e4.<\/p>\r\n\r\n\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/joi1.png\" style=\"height:100px; width:100px\" \/><\/p>\r\n\r\n\r\n\r\n<p>\ub2e4\uc74c\uc740 &quot;\uc88b\uc740 \uae43\ubc1c&quot;\uc758 \uc608\uc774\ub2e4.<\/p>\r\n\r\n\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/joi2.png\" style=\"height:148px; width:340px\" \/><\/p>\r\n\r\n\r\n\r\n<p>\ub2e4\uc74c\uc740 &quot;\uc88b\uc740 \uae43\ubc1c&quot;\uc774 \uc544\ub2cc \uc608\uc774\ub2e4.<\/p>\r\n\r\n\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/joi3.png\" style=\"height:148px; width:340px\" \/><\/p>\r\n\r\n\r\n\r\n<p>\uc77c\ubd80 \uc704\uce58\uc5d0\ub294 \uc774\ubbf8 \uadf8 \uce78\uc744 \ucc44\uc6b8 \ubb38\uc790\uac00 \uc815\ud574\uc838 \uc788\ub2e4. \uc774\ub54c, M, N\uc774 \uc8fc\uc5b4\uc84c\uc744 \ub54c, \uc88b\uc740 \uae43\ubc1c\uc744 \ub9cc\ub4e4 \uc218 \uc788\ub294 \ubc29\ubc95\uc758 \uc218\ub97c \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0 \uae43\ubc1c\uc758 \ud06c\uae30 M\uacfc N\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. (2 &le; M, N &le; 20)<\/p>\r\n\r\n\r\n\r\n<p>\ub2e4\uc74c M\uac1c \uc904\uc5d0\ub294 \uae43\ubc1c\uc758 \ubaa8\uc591\uc778 N\uac1c \ubb38\uc790\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \uac01 \ubb38\uc790\ub294 J, O, I, ?\uc911 \ud558\ub098\uc774\ub2e4. J, O, I\uc778 \uacbd\uc6b0\uc5d0\ub294 i\ud589 j\uc5f4 \uc704\uce58\uc758 \ubb38\uc790\uac00 \uc774\ubbf8 \uadf8 \ubb38\uc790\ub85c \uc815\ud574\uc838 \uc788\ub294 \ub73b\uc774\uace0, ?\ub294 \uc544\uc9c1 \uc815\ud574\uc838 \uc788\uc9c0 \uc54a\ub2e4\ub294 \ub73b\uc774\ub2e4.<\/p>\r\n","output":"<p>\uccab\uc9f8 \uc904\uc5d0 &quot;\uc88b\uc740 \uae43\ubc1c&quot;\uc744 \ub9cc\ub4e4 \uc218 \uc788\ub294 \ubc29\ubc95\uc758 \uc218\ub97c 100000\uc73c\ub85c \ub098\ub208 \ub098\uba38\uc9c0\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"<p><img alt=\"\" src=\"\/upload\/images\/joi4.png\" style=\"height:244px; width:340px\" \/><\/p>\r\n","original":"0","html_title":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"5559","problem_lang":"2","title":"JOI \u65d7 (JOI Flag)","description":"<p>\u30aa\u30ea\u30f3\u30d4\u30c3\u30af\u65e5\u672c\u59d4\u54e1\u4f1a\u3067\u306f\uff0c\u4eca\u5e74\u306e\u65e5\u672c\u60c5\u5831\u30aa\u30ea\u30f3\u30d4\u30c3\u30af (JOI) \u3092\u5ba3\u4f1d\u3059\u308b\u305f\u3081\u306b\uff0c JOI \u306e\u30ed\u30b4\u3092\u30e2\u30c1\u30fc\u30d5\u306b\u3057\u305f\u65d7\u3092\u4f5c\u308b\u3053\u3068\u306b\u306a\u3063\u305f\uff0e \u65d7\u306f\u300c\u826f\u3044\u65d7\u300d\u3067\u306a\u3051\u308c\u3070\u306a\u3089\u306a\u3044\uff0e \u300c\u826f\u3044\u65d7\u300d\u3068\u306f\uff0c\u30a2\u30eb\u30d5\u30a1\u30d9\u30c3\u30c8\u306e J, O, I \u306e\u3044\u305a\u308c\u304b\u306e\u6587\u5b57\u3092\uff0c\u7e26 M \u884c\uff0c\u6a2a N \u5217\u306e\u9577\u65b9\u5f62\u72b6\u306b\u4e26\u3079\u305f\u3082\u306e\u3067\uff0c J, O, I \u304c\u4ee5\u4e0b\u306e\u56f3\u306e\u3088\u3046\u306b (\u3059\u306a\u308f\u3061\uff0cJ \u306e\u53f3\u96a3\u306b O \u304c\uff0c\u305d\u306e J \u306e\u4e0b\u96a3\u306b I \u304c) \u4e26\u3093\u3067\u3044\u308b\u7b87\u6240\u304c\u65d7\u306e\u5c11\u306a\u304f\u3068\u3082 1 \u304b\u6240\u306b\u3042\u308b\u3082\u306e\u3067\u3042\u308b\uff0e<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/joi1.png\" style=\"height:100px; width:100px\" \/><\/p>\r\n\r\n<p>\u4ee5\u4e0b\u306e\u56f3\u306b\uff0c\u300c\u826f\u3044\u65d7\u300d\u306e\u4f8b\u3092 2 \u3064\u793a\u3059\uff0e<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/joi2.png\" style=\"height:148px; width:340px\" \/><\/p>\r\n\r\n<p>\u4ee5\u4e0b\u306e\u56f3\u306b\uff0c\u300c\u826f\u3044\u65d7\u300d\u3067\u306f\u306a\u3044\u4f8b\u3092 2 \u3064\u793a\u3059\uff0e<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/joi3.png\" style=\"height:148px; opacity:0.9; width:340px\" \/><\/p>\r\n\r\n<p>\u3044\u307e M, N \u306e\u5024\uff0c\u304a\u3088\u3073\u65d7\u306e\u4e00\u90e8\u306e\u5834\u6240\u306b\u3064\u3044\u3066 J, O, I \u306e\u3069\u306e\u6587\u5b57\u306b\u3059\u308b\u304b\u304c\u6c7a\u307e\u3063\u3066\u304a\u308a\uff0c\u5165\u529b\u3068\u3057\u3066\u305d\u306e\u60c5\u5831\u304c\u4e0e\u3048\u3089\u308c\u308b\uff0e \u8003\u3048\u3089\u308c\u308b\u300c\u826f\u3044\u65d7\u300d\u306f\u4f55\u901a\u308a\u3042\u308b\u304b\u3092\u8a08\u7b97\u3057\uff0c\u305d\u306e\u6570\u3092 100000 (=10<sup>5<\/sup>) \u3067\u5272\u3063\u305f\u4f59\u308a\u3092\u51fa\u529b\u3059\u308b\u30d7\u30ed\u30b0\u30e9\u30e0\u3092\u4f5c\u6210\u305b\u3088\uff0e<\/p>\r\n","input":"<p>\u5165\u529b\u306f 1 + M \u884c\u304b\u3089\u306a\u308b\uff0e<\/p>\r\n\r\n<p>1 \u884c\u76ee\u306b\u306f\u65d7\u306e\u5927\u304d\u3055\u3092\u8868\u3059 2 \u3064\u306e\u6574\u6570 M, N (2 \u2266 M \u2266 20, 2 \u2266 N \u2266 20) \u304c\u7a7a\u767d\u3067\u533a\u5207\u3089\u308c\u3066\u66f8\u304b\u308c\u3066\u3044\u308b\uff0e<\/p>\r\n\r\n<p>1 + i \u884c\u76ee (1 \u2266 i \u2266 M) \u306b\u306f\uff0cN \u6587\u5b57\u304b\u3089\u306a\u308b\u6587\u5b57\u5217\u304c\u66f8\u304b\u308c\u3066\u3044\u308b\uff0e \u5404\u6587\u5b57\u306f J, O, I, ? \u306e\u3044\u305a\u308c\u304b\u3067\u3042\u308a\uff0c j \u6587\u5b57\u76ee (1 \u2266 j \u2266 N) \u304c J, O, I \u306e\u3044\u305a\u308c\u304b\u3067\u3042\u308b\u5834\u5408\u306f i \u884c j \u5217\u306e\u5834\u6240\u306e\u6587\u5b57\u304c\u305d\u308c\u305e\u308c J, O, I \u306b\u6c7a\u307e\u3063\u3066\u3044\u308b\u3053\u3068\uff0c ? \u3067\u3042\u308b\u5834\u5408\u306f\u307e\u3060\u6c7a\u307e\u3063\u3066\u3044\u306a\u3044\u3053\u3068\u3092\u8868\u3059\uff0e<\/p>\r\n","output":"<p>\u8003\u3048\u3089\u308c\u308b\u300c\u826f\u3044\u65d7\u300d\u306e\u500b\u6570\u3092 100000 (=10<sup>5<\/sup>) \u3067\u5272\u3063\u305f\u4f59\u308a\u3092 1 \u884c\u3067\u51fa\u529b\u305b\u3088\uff0e<\/p>\r\n\r\n<p>&nbsp;<\/p>\r\n","hint":"<p><img alt=\"\" src=\"\/upload\/images\/joi4.png\" style=\"height:244px; opacity:0.9; width:340px\" \/><\/p>\r\n","original":"1","html_title":"0","problem_lang_code":"\uc77c\ubcf8\uc5b4"}]