시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
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문제

상근이와 선영이는 메시지를 자주 주고 받는다. 하지만, 그들은 다른 사람이 자신이 작성한 메시지를 읽는 것을 매우 싫어한다. 정인이는 이 두 사람이 서로 보내는 메시지에 큰 관심을 가지고 있고, 메시지를 가로채고 있다. 하지만, 상근이와 선영이는 메시지를 암호화 하기 때문에 정인이는 메시지를 읽을 수 없다. 정인이가 가로채는 메시지는 암호화된 메시지(암호문)이다.

최근에 정인이는 우연히 메시지 원본(평문)을 얻었다. 정인이는 다른 메시지도 해독하기 위해서 암호키를 찾기로 했다.

상근이와 선영이는 메시지를 k개의 글자씩 블럭으로 나눈 다음에 각 블럭에 들어있는 글자의 순서를 바꾸는 것이다. 순서를 바꾸는 방법은 총 k!가지가 있으며, 이 중 한 순열을 골라서 모든 블럭에 동일하게 적용한다. 이 때 사용한 순열을 암호키라고 한다. 아래 그림은 secret을 암호키 (514362)를 이용해서 암호화한 것이고, 블럭의 크기는 6이다.

정인이는 블럭의 크기도 알고 있다. 또, 평문과 암호문의 길이는 같고, 길이는 항상 k로 나누어 떨어진다. 또, 모든 블럭은 같은 암호키를 이용해서 암호화 한다.

평문 M과 암호문 C, 그리고 블럭의 크기 k가 주어졌을 때, M을 C로 암호화하는 암호키의 수를 구하는 프로그램을 작성하시오.

입력

입력은 여러 개의 테스트 케이스로 이루어져 있따. 각 테스트 케이스는 세 줄로 이루어져 있고, 블럭의 크기 k, 평문 M, 암호문 C가 한 줄에 하나씩 주어진다. k는 1보다 큰 양의 정수이고, M과 C는 알파벳 소문자로만 이루어져 있으며, 길이는 최대 100이다. M과 C의 길이는 같고, M의 길이는 k의 배수이다. 

출력

각 테스트 케이스에 대해서, 가능한 암호키의 개수를 출력한다. 암호키의 수는 263-1을 넘지 않는다. 만약, M에서 C를 만들 수 없다면 0을 출력한다.

예제 입력 1

4
treewood
ertedowo
6
secret
etrcse
1
impossibru
youdontsay

예제 출력 1

1
2
0

힌트

[{"problem_id":"3650","problem_lang":"0","title":"\uc554\ud638 \ud574\ub3c5","description":"<p>\uc0c1\uadfc\uc774\uc640 \uc120\uc601\uc774\ub294 \uba54\uc2dc\uc9c0\ub97c \uc790\uc8fc \uc8fc\uace0 \ubc1b\ub294\ub2e4. \ud558\uc9c0\ub9cc, \uadf8\ub4e4\uc740 \ub2e4\ub978 \uc0ac\ub78c\uc774 \uc790\uc2e0\uc774 \uc791\uc131\ud55c \uba54\uc2dc\uc9c0\ub97c \uc77d\ub294 \uac83\uc744 \ub9e4\uc6b0 \uc2eb\uc5b4\ud55c\ub2e4. \uc815\uc778\uc774\ub294 \uc774 \ub450 \uc0ac\ub78c\uc774 \uc11c\ub85c \ubcf4\ub0b4\ub294 \uba54\uc2dc\uc9c0\uc5d0 \ud070 \uad00\uc2ec\uc744 \uac00\uc9c0\uace0 \uc788\uace0, \uba54\uc2dc\uc9c0\ub97c \uac00\ub85c\ucc44\uace0 \uc788\ub2e4. \ud558\uc9c0\ub9cc, \uc0c1\uadfc\uc774\uc640 \uc120\uc601\uc774\ub294 \uba54\uc2dc\uc9c0\ub97c \uc554\ud638\ud654 \ud558\uae30 \ub54c\ubb38\uc5d0 \uc815\uc778\uc774\ub294 \uba54\uc2dc\uc9c0\ub97c \uc77d\uc744 \uc218 \uc5c6\ub2e4. \uc815\uc778\uc774\uac00 \uac00\ub85c\ucc44\ub294 \uba54\uc2dc\uc9c0\ub294 \uc554\ud638\ud654\ub41c \uba54\uc2dc\uc9c0(\uc554\ud638\ubb38)\uc774\ub2e4.<\/p>\r\n\r\n<p>\ucd5c\uadfc\uc5d0 \uc815\uc778\uc774\ub294 \uc6b0\uc5f0\ud788 \uba54\uc2dc\uc9c0 \uc6d0\ubcf8(\ud3c9\ubb38)\uc744 \uc5bb\uc5c8\ub2e4. \uc815\uc778\uc774\ub294 \ub2e4\ub978 \uba54\uc2dc\uc9c0\ub3c4 \ud574\ub3c5\ud558\uae30 \uc704\ud574\uc11c \uc554\ud638\ud0a4\ub97c \ucc3e\uae30\ub85c \ud588\ub2e4.<\/p>\r\n\r\n<p>\uc0c1\uadfc\uc774\uc640 \uc120\uc601\uc774\ub294 \uba54\uc2dc\uc9c0\ub97c k\uac1c\uc758 \uae00\uc790\uc529 \ube14\ub7ed\uc73c\ub85c \ub098\ub208 \ub2e4\uc74c\uc5d0 \uac01 \ube14\ub7ed\uc5d0 \ub4e4\uc5b4\uc788\ub294 \uae00\uc790\uc758 \uc21c\uc11c\ub97c \ubc14\uafb8\ub294 \uac83\uc774\ub2e4. \uc21c\uc11c\ub97c \ubc14\uafb8\ub294 \ubc29\ubc95\uc740 \ucd1d k!\uac00\uc9c0\uac00 \uc788\uc73c\uba70, \uc774 \uc911 \ud55c \uc21c\uc5f4\uc744 \uace8\ub77c\uc11c \ubaa8\ub4e0 \ube14\ub7ed\uc5d0 \ub3d9\uc77c\ud558\uac8c \uc801\uc6a9\ud55c\ub2e4. \uc774 \ub54c \uc0ac\uc6a9\ud55c \uc21c\uc5f4\uc744 \uc554\ud638\ud0a4\ub77c\uace0 \ud55c\ub2e4. \uc544\ub798 \uadf8\ub9bc\uc740 secret\uc744 \uc554\ud638\ud0a4 (514362)\ub97c \uc774\uc6a9\ud574\uc11c \uc554\ud638\ud654\ud55c \uac83\uc774\uace0, \ube14\ub7ed\uc758 \ud06c\uae30\ub294 6\uc774\ub2e4.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/keysecret.png\" style=\"height:133px; width:246px\" \/><\/p>\r\n\r\n<p>\uc815\uc778\uc774\ub294 \ube14\ub7ed\uc758 \ud06c\uae30\ub3c4 \uc54c\uace0 \uc788\ub2e4. \ub610, \ud3c9\ubb38\uacfc \uc554\ud638\ubb38\uc758 \uae38\uc774\ub294 \uac19\uace0, \uae38\uc774\ub294 \ud56d\uc0c1 k\ub85c \ub098\ub204\uc5b4 \ub5a8\uc5b4\uc9c4\ub2e4. \ub610, \ubaa8\ub4e0 \ube14\ub7ed\uc740 \uac19\uc740 \uc554\ud638\ud0a4\ub97c \uc774\uc6a9\ud574\uc11c \uc554\ud638\ud654 \ud55c\ub2e4.<\/p>\r\n\r\n<p>\ud3c9\ubb38 M\uacfc \uc554\ud638\ubb38 C, \uadf8\ub9ac\uace0 \ube14\ub7ed\uc758 \ud06c\uae30 k\uac00 \uc8fc\uc5b4\uc84c\uc744 \ub54c, M\uc744 C\ub85c \uc554\ud638\ud654\ud558\ub294 \uc554\ud638\ud0a4\uc758 \uc218\ub97c \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>\r\n","input":"<p>\uc785\ub825\uc740 \uc5ec\ub7ec \uac1c\uc758 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\ub530. \uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub294 \uc138 \uc904\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\uace0, \ube14\ub7ed\uc758 \ud06c\uae30 k, \ud3c9\ubb38 M, \uc554\ud638\ubb38 C\uac00 \ud55c \uc904\uc5d0 \ud558\ub098\uc529 \uc8fc\uc5b4\uc9c4\ub2e4. k\ub294 1\ubcf4\ub2e4 \ud070 \uc591\uc758 \uc815\uc218\uc774\uace0, M\uacfc C\ub294 \uc54c\ud30c\ubcb3 \uc18c\ubb38\uc790\ub85c\ub9cc \uc774\ub8e8\uc5b4\uc838 \uc788\uc73c\uba70, \uae38\uc774\ub294 \ucd5c\ub300 100\uc774\ub2e4. M\uacfc C\uc758 \uae38\uc774\ub294 \uac19\uace0, M\uc758 \uae38\uc774\ub294 k\uc758 \ubc30\uc218\uc774\ub2e4.&nbsp;<\/p>\r\n","output":"<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc5d0 \ub300\ud574\uc11c, \uac00\ub2a5\ud55c \uc554\ud638\ud0a4\uc758 \uac1c\uc218\ub97c \ucd9c\ub825\ud55c\ub2e4. \uc554\ud638\ud0a4\uc758 \uc218\ub294 2<sup>63<\/sup>-1\uc744 \ub118\uc9c0 \uc54a\ub294\ub2e4. \ub9cc\uc57d, M\uc5d0\uc11c C\ub97c \ub9cc\ub4e4 \uc218 \uc5c6\ub2e4\uba74 0\uc744 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"3650","problem_lang":"1","title":"Key Insight","description":"<p>Alice and Bob love to send each other messages, but they don&rsquo;t like it when other people read their messages. Your friend Charles is very interested in what Alice and Bob send to each other, but since Alice and Bob are encrypting their messages he is unable to read them, even though he is able to intercept the encrypted messages (called &ldquo;ciphertext&rdquo;).<\/p>\r\n\r\n<p>Recently, Charles has not only intercepted an encrypted message, he also knows the original content of this message (which is called &ldquo;plaintext&rdquo;). To help him decrypt future messages between Alice and Bob, you are asked to write a program that will help him look for the encryption key.<\/p>\r\n\r\n<p>Charles has informed you that he knows that Alice and Bob are using a transposition block cipher. This means that for each block of k characters in the message, the characters within the block are re-ordered into one of k! possible permutations during encryption. Each permutation is determined by its unique corresponding encryption key. The key corresponding to the permutation shown in Figure 1 would be some representation of (123456) -&gt; (514362). Since your only task is counting (possible) keys, the actual representation is not relevant.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/keysecret.png\" style=\"height:133px; width:246px\" \/><\/p>\r\n\r\n<p>Figure 1: Example of transposition<\/p>\r\n\r\n<p>Fortunately, Charles does know the block size k, and he knows that the plaintext and ciphertext that he intercepted consist of one or more full blocks of length k (i.e., no incomplete blocks) that have each been encrypted with the same key.<\/p>\r\n\r\n<p>Given the plaintext M and ciphertext C that Charles has intercepted, your program will compute the number of possible encryption keys.<\/p>\r\n","input":"<p>For each test case, the input contains three lines:<\/p>\r\n\r\n<ul>\r\n\t<li>One line containing a positive integer k, the block size (k &ge; 1).<\/li>\r\n\t<li>One line containing M, the plaintext (1 &le; |M| &le; 100, |M| is a multiple of k).<\/li>\r\n\t<li>One line containing C, the ciphertext (|C| = |M|)<\/li>\r\n<\/ul>\r\n\r\n<p>Both plaintext and ciphertext consist only of lower-case letters.<\/p>\r\n","output":"<p>For each test case, print one line containing the number of possible encryption keys of size k. This number will not exceed 2<sup>63<\/sup>-1. If it is impossible to obtain M from C by a transposition cipher of block size k, print &lsquo;0&rsquo; (the number zero).<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]