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문제

상근이는 매일 저녁으로 파스타를 만들어 먹는다. 상근이가 만들 수 있는 파스타는 총 세 종류로 토마토 소스, 크림 소스, 바질 소스이다.

상근이는 앞으로 N일 동안 먹을 파스타를 계획하려고 한다. 매일 매일 세 종류의 파스타 중 한 종류를 선택할 것이다. 하지만, 같은 파스타를 계속해서 먹으면 질려버릴 수 있기 때문에, 3일 이상 연속해서 같은 파스타를 먹지 않는다.

또, N일 중 K일에 먹을 파스타는 미리 정해두었다.

N과 K일에 먹을 파스타가 주어졌을 때, 가능한 계획의 수를 구하는 프로그램을 작성하시오.

입력

첫째 줄에 N과 K가 주어진다. (3 ≤ N ≤ 100, 1 ≤ K ≤ N)

둘째 줄부터 K개 줄에는, 미리 파스타를 정해놓은 날의 정보가 주어진다. 이 정보는 Ai Bi와 같은 형식이며, Ai일에 먹을 파스타는 Bi라는 뜻이다. 이때, Bi = 1이면 토마토 소스, 2이면 크림 소스, 3이면 바질 소스이다. Ai는 모두 다르다.

출력

상근이가 세울 수 있는 계획의 수를 10000으로 나눈 나머지를 출력한다.

예제 입력 1

5 3
3 1
1 1
4 2

예제 출력 1

6

힌트

예제의 경우에는 총 6가지가 가능하다.

1,2,1,2,1

1,2,1,2,2

1,2,1,2,3

1,3,1,2,1

1,3,1,2,2

1,3,1,2,3

[{"problem_id":"5546","problem_lang":"0","title":"\ud30c\uc2a4\ud0c0","description":"<p>\r\n\t\uc0c1\uadfc\uc774\ub294 \ub9e4\uc77c \uc800\ub141\uc73c\ub85c \ud30c\uc2a4\ud0c0\ub97c \ub9cc\ub4e4\uc5b4 \uba39\ub294\ub2e4. \uc0c1\uadfc\uc774\uac00 \ub9cc\ub4e4 \uc218 \uc788\ub294 \ud30c\uc2a4\ud0c0\ub294 \ucd1d \uc138 \uc885\ub958\ub85c \ud1a0\ub9c8\ud1a0 \uc18c\uc2a4, \ud06c\ub9bc \uc18c\uc2a4, \ubc14\uc9c8 \uc18c\uc2a4\uc774\ub2e4.<\/p>\r\n\r\n<p>\r\n\t\uc0c1\uadfc\uc774\ub294 \uc55e\uc73c\ub85c N\uc77c \ub3d9\uc548 \uba39\uc744 \ud30c\uc2a4\ud0c0\ub97c \uacc4\ud68d\ud558\ub824\uace0 \ud55c\ub2e4. \ub9e4\uc77c \ub9e4\uc77c \uc138 \uc885\ub958\uc758 \ud30c\uc2a4\ud0c0 \uc911 \ud55c \uc885\ub958\ub97c \uc120\ud0dd\ud560 \uac83\uc774\ub2e4. \ud558\uc9c0\ub9cc, \uac19\uc740 \ud30c\uc2a4\ud0c0\ub97c \uacc4\uc18d\ud574\uc11c \uba39\uc73c\uba74 \uc9c8\ub824\ubc84\ub9b4 \uc218 \uc788\uae30 \ub54c\ubb38\uc5d0, 3\uc77c \uc774\uc0c1 \uc5f0\uc18d\ud574\uc11c \uac19\uc740 \ud30c\uc2a4\ud0c0\ub97c \uba39\uc9c0 \uc54a\ub294\ub2e4.<\/p>\r\n\r\n<p>\r\n\t\ub610, N\uc77c \uc911 K\uc77c\uc5d0 \uba39\uc744 \ud30c\uc2a4\ud0c0\ub294 \ubbf8\ub9ac \uc815\ud574\ub450\uc5c8\ub2e4.<\/p>\r\n\r\n<p>\r\n\tN\uacfc K\uc77c\uc5d0 \uba39\uc744 \ud30c\uc2a4\ud0c0\uac00 \uc8fc\uc5b4\uc84c\uc744 \ub54c, \uac00\ub2a5\ud55c \uacc4\ud68d\uc758 \uc218\ub97c \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>\r\n","input":"<p>\r\n\t\uccab\uc9f8 \uc904\uc5d0 N\uacfc K\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. (3 &le; N &le; 100, 1 &le; K &le; N)<\/p>\r\n\r\n<p>\r\n\t\ub458\uc9f8 \uc904\ubd80\ud130 K\uac1c \uc904\uc5d0\ub294, \ubbf8\ub9ac \ud30c\uc2a4\ud0c0\ub97c \uc815\ud574\ub193\uc740 \ub0a0\uc758 \uc815\ubcf4\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \uc774 \uc815\ubcf4\ub294 A<sub>i<\/sub> B<sub>i<\/sub>\uc640 \uac19\uc740 \ud615\uc2dd\uc774\uba70, A<sub>i<\/sub>\uc77c\uc5d0 \uba39\uc744 \ud30c\uc2a4\ud0c0\ub294 B<sub>i<\/sub>\ub77c\ub294 \ub73b\uc774\ub2e4. \uc774\ub54c, B<sub>i<\/sub> = 1\uc774\uba74 \ud1a0\ub9c8\ud1a0 \uc18c\uc2a4, 2\uc774\uba74 \ud06c\ub9bc \uc18c\uc2a4, 3\uc774\uba74 \ubc14\uc9c8 \uc18c\uc2a4\uc774\ub2e4. Ai\ub294 \ubaa8\ub450 \ub2e4\ub974\ub2e4.<\/p>\r\n","output":"<p>\r\n\t\uc0c1\uadfc\uc774\uac00 \uc138\uc6b8 \uc218 \uc788\ub294 \uacc4\ud68d\uc758 \uc218\ub97c 10000\uc73c\ub85c \ub098\ub208 \ub098\uba38\uc9c0\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"<p>\r\n\t\uc608\uc81c\uc758 \uacbd\uc6b0\uc5d0\ub294 \ucd1d 6\uac00\uc9c0\uac00 \uac00\ub2a5\ud558\ub2e4.<\/p>\r\n\r\n<p>\r\n\t1,2,1,2,1<\/p>\r\n<p>\r\n\t1,2,1,2,2<\/p>\r\n<p>\r\n\t1,2,1,2,3<\/p>\r\n<p>\r\n\t1,3,1,2,1<\/p>\r\n<p>\r\n\t1,3,1,2,2<\/p>\r\n<p>\r\n\t1,3,1,2,3<\/p>\r\n\r\n","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"5546","problem_lang":"2","title":"\u30d1\u30b9\u30bf (Pasta)","description":"<p>\u3042\u306a\u305f\u306f\u30d1\u30b9\u30bf\u304c\u5927\u597d\u7269\u3067\u3042\u308a\uff0c\u6bce\u65e5\uff0c\u6669\u5fa1\u98ef\u306b\u30d1\u30b9\u30bf\u3092\u4f5c\u3063\u3066\u98df\u3079\u3066\u3044\u308b\uff0e\u3042\u306a\u305f\u306f\u30c8\u30de\u30c8\u30bd\u30fc\u30b9\uff0c\u30af\u30ea\u30fc\u30e0\u30bd\u30fc\u30b9\uff0c\u30d0\u30b8\u30eb\u30bd\u30fc\u30b9\u306e 3 \u7a2e\u985e\u306e\u30d1\u30b9\u30bf\u3092\u4f5c\u308b\u3053\u3068\u304c\u3067\u304d\u308b\uff0e<\/p>\r\n\r\n<p>N \u65e5\u9593\u306e\u6669\u5fa1\u98ef\u306e\u4e88\u5b9a\u3092\u8003\u3048\u308b\u3053\u3068\u306b\u3057\u305f\uff0e\u305d\u308c\u305e\u308c\u306e\u65e5\u306b 3 \u7a2e\u985e\u306e\u30d1\u30b9\u30bf\u304b\u3089 1 \u7a2e\u985e\u3092\u9078\u3076\uff0e\u305f\u3060\u3057\uff0c\u540c\u3058\u30d1\u30b9\u30bf\u304c\u7d9a\u304f\u3068\u98fd\u304d\u3066\u3057\u307e\u3046\u306e\u3067\uff0c3 \u65e5\u4ee5\u4e0a\u9023\u7d9a\u3057\u3066\u540c\u3058\u30d1\u30b9\u30bf\u3092\u9078\u3093\u3067\u306f\u3044\u3051\u306a\u3044\uff0e\u307e\u305f\uff0cN \u65e5\u306e\u3046\u3061\u306e K \u65e5\u5206\u306e\u30d1\u30b9\u30bf\u306f\u3059\u3067\u306b\u6c7a\u3081\u3066\u3042\u308b\uff0e<\/p>\r\n\r\n<p>\u5165\u529b\u3068\u3057\u3066 N \u306e\u5024\u3068\uff0cK \u65e5\u5206\u306e\u30d1\u30b9\u30bf\u306e\u60c5\u5831\u304c\u4e0e\u3048\u3089\u308c\u305f\u3068\u304d\uff0c\u6761\u4ef6\u3092\u307f\u305f\u3059\u4e88\u5b9a\u304c\u4f55\u901a\u308a\u3042\u308b\u304b\u3092 10000 \u3067\u5272\u3063\u305f\u4f59\u308a\u3092\u6c42\u3081\u308b\u30d7\u30ed\u30b0\u30e9\u30e0\u3092\u4f5c\u6210\u305b\u3088\uff0e<\/p>\r\n","input":"<p>\u5165\u529b\u306f K + 1 \u884c\u304b\u3089\u306a\u308b\uff0e<\/p>\r\n\r\n<p>1 \u884c\u76ee\u306b\u306f 2 \u3064\u306e\u6574\u6570 N, K (3 \u2266 N \u2266 100\uff0c1 \u2266 K \u2266 N) \u304c\u7a7a\u767d\u3092\u533a\u5207\u308a\u3068\u3057\u3066\u66f8\u304b\u308c\u3066\u3044\u308b\uff0e<\/p>\r\n\r\n<p>1 + i \u884c\u76ee (1 \u2266 i \u2266 K) \u306b\u306f 2 \u3064\u306e\u6574\u6570 Ai, Bi (1 \u2266 Ai \u2266 N\uff0c1 \u2266 Bi \u2266 3) \u304c\u7a7a\u767d\u3092\u533a\u5207\u308a\u3068\u3057\u3066\u66f8\u304b\u308c\u3066\u3044\u308b\uff0e\u3053\u308c\u306f\uff0cAi \u65e5\u76ee\u306e\u30d1\u30b9\u30bf\u306f\u3059\u3067\u306b\u6c7a\u307e\u3063\u3066\u304a\u308a\uff0cBi = 1 \u306e\u3068\u304d\u306f\u30c8\u30de\u30c8\u30bd\u30fc\u30b9\u3067\u3042\u308a\uff0cBi = 2 \u306e\u3068\u304d\u306f\u30af\u30ea\u30fc\u30e0\u30bd\u30fc\u30b9\u3067\u3042\u308a\uff0cBi = 3 \u306e\u3068\u304d\u306f\u30d0\u30b8\u30eb\u30bd\u30fc\u30b9\u3067\u3042\u308b\u3053\u3068\u3092\u8868\u3059\uff0eAi (1 \u2266 i \u2266 K) \u306f\u5168\u3066\u7570\u306a\u308b\uff0e\u4e0e\u3048\u3089\u308c\u308b\u5165\u529b\u30c7\u30fc\u30bf\u306b\u304a\u3044\u3066\uff0c\u6761\u4ef6\u3092\u307f\u305f\u3059\u4e88\u5b9a\u306f 1 \u901a\u308a\u4ee5\u4e0a\u3042\u308b\u3053\u3068\u304c\u4fdd\u8a3c\u3055\u308c\u3066\u3044\u308b\uff0e<\/p>\r\n","output":"<p>\u6761\u4ef6\u3092\u307f\u305f\u3059\u4e88\u5b9a\u304c\u4f55\u901a\u308a\u3042\u308b\u304b\u3092 10000 \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":"","original":"1","problem_lang_code":"\uc77c\ubcf8\uc5b4"}]