시간 제한메모리 제한제출정답맞힌 사람정답 비율
3 초 128 MB3910728.000%

문제

상근이는 도시를 오고가며 짐을 실고 내리는 트럭 운전사이다. 상근이의 트럭은 매우 커서, 짐을 무제한으로 담을 수 있다. 상근이는 대학시절 배운 프로그래밍을 이용해서 자동으로 짐을 실고 내릴 수 있는 기능을 트럭에 추가했다. 유난히도 스택을 좋아하는 상근이는 스택을 이 기능에 이용했다. 따라서, 마지막으로 실은 짐만 내릴 수 있다.

상근이는 짐을 26가지 종류로 구분했다. 이러한 짐은 알파벳으로 나타낼 수 있다. (대소문자는 구분하지 않는다)

도시의 도로는 모두 일방통행이고, 길이는 모두 1 킬로미터이다. 또, 도로는 모두 세 종류로 나눌 수 있다. 이 도로는 1번 도로, 2번 도로, 3번 도로라고 한다.

1번 도로를 지날 때는 그 도로에 해당하는 짐을 하나 실어야 하고, 2번 도로는 짐을 하나 내려야 한다. 3번 도로는 짐을 실거나 내리지 않고 지나가야 한다.

도시는 N개, 도로는 E개가 있다 상근이는 1번 도시에서 출발해서 N번 도시에 도착해야 한다. N번 도시에 도착했을 때, 트럭은 비어있어도 되고, 안 비어있어도 된다.

상근이가 N번 도시로 도착하는 방법의 수를 계산하는 프로그램을 작성하시오. 단, 상근이는 최대 K 킬로미터만 이동할 수 있다.

입력

첫째 줄에 도시의 수 N, 도로의 수 E, 이동할 수 있는 최대 거리 K가 주어진다. (2 ≤ N ≤ 50, 1 ≤ E ≤ 2450, 1 ≤ K ≤ 50)

다음 E개 줄에는 도로의 정보가 주어진다. 각 도로의 종류에 따라 다른 형식으로 주어진다.

1번 도로: "x y C" x에서 y로 향하는 도로이다. 이 도로를 지날 때, C(대문자)에 해당하는 짐을 실어야 한다.

2번 도로: "x y c" x에서 y로 향하는 도로이다. 이 도로를 지날 때, c(소문자)에 해당하는 짐을 내려야 한다.

3번 도로: "x y" x에서 y로 향하는 도로이며, 그 어

두 도시를 연결하는 도로의 수가 두 개 이상인 경우는 없다. (단, 방향이 다를 수는 있다) 또, x와 y가 같은 경우도 없다.

출력

첫째 줄에 상근이가 1번 도시에서 출발해서 N번 도시로 도착하는 방법의 수를 출력한다. 수가 매우 커질 수 있기 때문에 10007로 나눈 나머지를 출력해야 한다.

예제 입력 1

2 1 10
1 2 a

예제 출력 1

0

예제 입력 2

7 9 5
1 2 A
2 3 B
2 5
5 3 C
3 4 b
3 6 c
3 7
4 7 a
6 7 a

예제 출력 2

4
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(\ub300\uc18c\ubb38\uc790\ub294 \uad6c\ubd84\ud558\uc9c0 \uc54a\ub294\ub2e4)<\/p>\r\n\r\n<p>\ub3c4\uc2dc\uc758 \ub3c4\ub85c\ub294 \ubaa8\ub450 \uc77c\ubc29\ud1b5\ud589\uc774\uace0, \uae38\uc774\ub294 \ubaa8\ub450 1 \ud0ac\ub85c\ubbf8\ud130\uc774\ub2e4. \ub610, \ub3c4\ub85c\ub294 \ubaa8\ub450 \uc138 \uc885\ub958\ub85c \ub098\ub20c \uc218 \uc788\ub2e4. \uc774 \ub3c4\ub85c\ub294 1\ubc88 \ub3c4\ub85c, 2\ubc88 \ub3c4\ub85c, 3\ubc88 \ub3c4\ub85c\ub77c\uace0 \ud55c\ub2e4.<\/p>\r\n\r\n<p>1\ubc88 \ub3c4\ub85c\ub97c \uc9c0\ub0a0 \ub54c\ub294 \uadf8 \ub3c4\ub85c\uc5d0 \ud574\ub2f9\ud558\ub294 \uc9d0\uc744 \ud558\ub098 \uc2e4\uc5b4\uc57c \ud558\uace0, 2\ubc88 \ub3c4\ub85c\ub294 \uc9d0\uc744 \ud558\ub098 \ub0b4\ub824\uc57c \ud55c\ub2e4. 3\ubc88 \ub3c4\ub85c\ub294 \uc9d0\uc744 \uc2e4\uac70\ub098 \ub0b4\ub9ac\uc9c0 \uc54a\uace0 \uc9c0\ub098\uac00\uc57c \ud55c\ub2e4.<\/p>\r\n\r\n<p>\ub3c4\uc2dc\ub294 N\uac1c, \ub3c4\ub85c\ub294 E\uac1c\uac00 \uc788\ub2e4 \uc0c1\uadfc\uc774\ub294 1\ubc88 \ub3c4\uc2dc\uc5d0\uc11c \ucd9c\ubc1c\ud574\uc11c N\ubc88 \ub3c4\uc2dc\uc5d0 \ub3c4\ucc29\ud574\uc57c \ud55c\ub2e4. N\ubc88 \ub3c4\uc2dc\uc5d0 \ub3c4\ucc29\ud588\uc744 \ub54c, \ud2b8\ub7ed\uc740 \ube44\uc5b4\uc788\uc5b4\ub3c4 \ub418\uace0, \uc548 \ube44\uc5b4\uc788\uc5b4\ub3c4 \ub41c\ub2e4.<\/p>\r\n\r\n<p>\uc0c1\uadfc\uc774\uac00 N\ubc88 \ub3c4\uc2dc\ub85c \ub3c4\ucc29\ud558\ub294 \ubc29\ubc95\uc758 \uc218\ub97c \uacc4\uc0b0\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624. \ub2e8, \uc0c1\uadfc\uc774\ub294 \ucd5c\ub300 K \ud0ac\ub85c\ubbf8\ud130\ub9cc \uc774\ub3d9\ud560 \uc218 \uc788\ub2e4.<\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0 \ub3c4\uc2dc\uc758 \uc218 N, \ub3c4\ub85c\uc758 \uc218 E, \uc774\ub3d9\ud560 \uc218 \uc788\ub294 \ucd5c\ub300 \uac70\ub9ac K\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. (2 &le; N &le; 50, 1 &le; E &le; 2450, 1 &le; K &le; 50)<\/p>\r\n\r\n<p>\ub2e4\uc74c E\uac1c \uc904\uc5d0\ub294 \ub3c4\ub85c\uc758 \uc815\ubcf4\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \uac01 \ub3c4\ub85c\uc758 \uc885\ub958\uc5d0 \ub530\ub77c \ub2e4\ub978 \ud615\uc2dd\uc73c\ub85c \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>1\ubc88 \ub3c4\ub85c: &quot;x y C&quot; x\uc5d0\uc11c y\ub85c \ud5a5\ud558\ub294 \ub3c4\ub85c\uc774\ub2e4. \uc774 \ub3c4\ub85c\ub97c \uc9c0\ub0a0 \ub54c, C(\ub300\ubb38\uc790)\uc5d0 \ud574\ub2f9\ud558\ub294 \uc9d0\uc744 \uc2e4\uc5b4\uc57c \ud55c\ub2e4.<\/p>\r\n\r\n<p>2\ubc88 \ub3c4\ub85c: &quot;x y c&quot; x\uc5d0\uc11c y\ub85c \ud5a5\ud558\ub294 \ub3c4\ub85c\uc774\ub2e4. \uc774 \ub3c4\ub85c\ub97c \uc9c0\ub0a0 \ub54c, c(\uc18c\ubb38\uc790)\uc5d0 \ud574\ub2f9\ud558\ub294 \uc9d0\uc744 \ub0b4\ub824\uc57c \ud55c\ub2e4.<\/p>\r\n\r\n<p>3\ubc88 \ub3c4\ub85c: &quot;x y&quot; x\uc5d0\uc11c y\ub85c \ud5a5\ud558\ub294 \ub3c4\ub85c\uc774\uba70, \uadf8 \uc5b4<\/p>\r\n\r\n<p>\ub450 \ub3c4\uc2dc\ub97c \uc5f0\uacb0\ud558\ub294 \ub3c4\ub85c\uc758 \uc218\uac00 \ub450 \uac1c \uc774\uc0c1\uc778 \uacbd\uc6b0\ub294 \uc5c6\ub2e4. (\ub2e8, \ubc29\ud5a5\uc774 \ub2e4\ub97c \uc218\ub294 \uc788\ub2e4) \ub610, x\uc640 y\uac00 \uac19\uc740 \uacbd\uc6b0\ub3c4 \uc5c6\ub2e4.<\/p>\r\n","output":"<p>\uccab\uc9f8 \uc904\uc5d0 \uc0c1\uadfc\uc774\uac00 1\ubc88 \ub3c4\uc2dc\uc5d0\uc11c \ucd9c\ubc1c\ud574\uc11c N\ubc88 \ub3c4\uc2dc\ub85c \ub3c4\ucc29\ud558\ub294 \ubc29\ubc95\uc758 \uc218\ub97c \ucd9c\ub825\ud55c\ub2e4. \uc218\uac00 \ub9e4\uc6b0 \ucee4\uc9c8 \uc218 \uc788\uae30 \ub54c\ubb38\uc5d0 10007\ub85c \ub098\ub208 \ub098\uba38\uc9c0\ub97c \ucd9c\ub825\ud574\uc57c \ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"Korean"},{"problem_id":"2837","problem_lang":"1","title":"KAMION","description":"<p>Mirko is a truck driver. His job is to travel between cities by roads, loading and unloading the cargo.&nbsp;<\/p>\r\n\r\n<p>His truck is so big that it can load unlimited number of packages, but the automated loading system enables only the last loaded package to be unloaded. There exists 26 different types of packages, each of which is denoted by a letter of english alphabet.&nbsp;<\/p>\r\n\r\n<p>The cities are connected by one-way roads of length 1 kilometer. More precisely, there exists 3 types of roads, conveniently denoted by 1, 2 and 3:&nbsp;<\/p>\r\n\r\n<ol>\r\n\t<li>each time Mirko drives down the road of this type, he must load exactly one package of the appropriate type for that road&nbsp;<\/li>\r\n\t<li>each time Mirko drives down the road of this type, he must unload exactly one package of the appropriate type for that road&nbsp;<\/li>\r\n\t<li>Mirko can drive down the road of this type without loading or unloading packages (no loading\/unloading)&nbsp;<\/li>\r\n<\/ol>\r\n\r\n<p>Mirko is required not to load\/unload any cargo except when driving down the roads of type 2 or 3, as stated above.&nbsp;<\/p>\r\n\r\n<p>Mirko can travel along E roads connecting N cities. His starts in the city denoted by number 1 and his goal is to reach city denoted by number N. When arriving in the city numbered N, Mirko&#39;s truck is not required to be empty.&nbsp;<\/p>\r\n\r\n<p>Write a program which computes the number of different ways that Mirko can travel so that he traverses at most K kilometers.&nbsp;<\/p>\r\n","input":"<p>The first line of input contains positive integers N, E and K (2 &le; N &le; 50, 1 &le; E &le; 2450, 1 &le; K &le; 50), which denote the number of cities, the number of roads and the maximum number of kilometers that&nbsp;<\/p>\r\n\r\n<p>Mirko may traverse before reaching his destination.<\/p>\r\n\r\n<p>The following E lines contain the description of the roads along which Mirko can travel. Each type of road have its own format:&nbsp;<\/p>\r\n\r\n<ol>\r\n\t<li>&quot;x y C&quot;, where x and y are positive integers which describe the direction of the road and C is an uppercase letter of english alphabet which denotes the type of package that Mirko must load onto the truck.&nbsp;<\/li>\r\n\t<li>&quot;x y c&quot;, where x and y are positive integers which describe the direction of the road and C is an lowercase letter of english alphabet which denotes the type of package that Mirko must unload from the truck.&nbsp;<\/li>\r\n\t<li>&quot;x y&quot;, where x and y are positive integers which describe the direction of the road In the above formats, the road are traversible when traveling from the city denoted by x to the city denoted by y. Also, it will always be true that 1 &le; x, y &le; N, x &ne; y, and no two roads will connect two cities in the same direction.&nbsp;<\/li>\r\n<\/ol>\r\n","output":"<p>In a single line of output, print the number of different ways Mirko can arrive in the city numbered N, starting from the city numbered 1, while respecting the aforementioned requirements. Since this number can be quite big, print the remainder of that number when divided by 10007.&nbsp;<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"English"}]