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문제

단어 덧셈이란 905 + 125 = 1030과 같은 덧셈의 각 숫자를 알파벳으로 바꾼 것이다.

9를 A로, 0을 C로, 5를 M으로, 1을 I로, 2를 B로, 0을 C로, 3을 P로 바꾸면 다음과 같이 된다.

ACM + IBM = ICPC

이렇게 905 + 125 = 1030의 경우에는 바꾸는 방법이 총 4가지가 있다.

방법 A B C I M P
방법 1 9 2 0 1 5 3
방법 2 9 3 0 1 5 4
방법 2 9 6 0 1 5 7
방법 2 9 7 0 1 5 8

 

단어 덧셈이 주어졌을 때, 이 단어 덧셈을 푸는 방법의 수를 구하는 프로그램을 작성하시오. 단, 다음 조건을 만족해야 한다.

1. 덧셈의 각 항은 숫자 '0'-'9'로 이루어져 있다. 모든 숫자는 알파벳 'A'-Z'로 바뀌어져 있다.

2. 한 알파벳은 하나의 숫자만을 나타낼 수 있다. 또, 어떤 숫자에 해당하는 알파벳은 반드시 하나 이어야 한다.

3. 0을 제외한 숫자는 0으로 시작할 수 없다. 즉, 00이나 0123과 같은 경우는 허용하지 않는다.

 

입력

입력은 여러 개의 테스트 케이스로 이루어져 있다. 테스트 케이스의 마지막 줄에는 0이 주어진다.

각 테스트 케이스는 첫째 줄에 단어의 개수 N이 주어지고, 그 다음 줄에는 단어 N개가 주어진다. 단어는 알파벳 'A'-'Z'로만 이루어져 있다.

각 단어는 다음과 같은 방정식을 나타낸다.

단어1+단어2+...+단어N-1 = 단어N

N은 2보다 크고, 13보다 작다. 단어의 길이는 0보다 크고, 9보다 작다. 단어에 등장하는 서로 다른 알파벳의 개수는 0보다 크고, 11보다 작다.

출력

각 테스트 케이스에 대해서, 단어 덧셈을 풀 수 있는 방법의 수를 출력한다.

예제 입력 1

3
ACM
IBM
ICPC
3
GAME
BEST
GAMER
4
A
B
C
AB
3
A
B
CD
3
ONE
TWO
THREE
3
TWO
THREE
FIVE
3
MOV
POP
DIV
9
A
B
C
D
E
F
G
H
IJ
0

예제 출력 1

4
1
8
30
0
0
0
40320
[{"problem_id":"4964","problem_lang":"0","title":"\ub2e8\uc5b4 \ub367\uc148","description":"<p>\ub2e8\uc5b4 \ub367\uc148\uc774\ub780 905 + 125 = 1030\uacfc \uac19\uc740 \ub367\uc148\uc758 \uac01 \uc22b\uc790\ub97c \uc54c\ud30c\ubcb3\uc73c\ub85c \ubc14\uafbc \uac83\uc774\ub2e4.<\/p>\r\n\r\n<p>9\ub97c A\ub85c, 0\uc744 C\ub85c, 5\ub97c M\uc73c\ub85c, 1\uc744 I\ub85c, 2\ub97c B\ub85c, 0\uc744 C\ub85c, 3\uc744 P\ub85c \ubc14\uafb8\uba74 \ub2e4\uc74c\uacfc \uac19\uc774 \ub41c\ub2e4.<\/p>\r\n\r\n<p>ACM + IBM = ICPC<\/p>\r\n\r\n<p>\uc774\ub807\uac8c 905 + 125 = 1030\uc758 \uacbd\uc6b0\uc5d0\ub294 \ubc14\uafb8\ub294 \ubc29\ubc95\uc774 \ucd1d 4\uac00\uc9c0\uac00 \uc788\ub2e4.<\/p>\r\n\r\n<table class=\"table table-bordered\" style=\"width:28%\">\r\n\t<thead>\r\n\t\t<tr>\r\n\t\t\t<th style=\"width:10%\">\ubc29\ubc95<\/th>\r\n\t\t\t<th style=\"width:3%\">A<\/th>\r\n\t\t\t<th style=\"width:3%\">B<\/th>\r\n\t\t\t<th style=\"width:3%\">C<\/th>\r\n\t\t\t<th style=\"width:3%\">I<\/th>\r\n\t\t\t<th style=\"width:3%\">M<\/th>\r\n\t\t\t<th style=\"width:3%\">P<\/th>\r\n\t\t<\/tr>\r\n\t<\/thead>\r\n\t<tbody>\r\n\t\t<tr>\r\n\t\t\t<td>\ubc29\ubc95 1<\/td>\r\n\t\t\t<td>9<\/td>\r\n\t\t\t<td>2<\/td>\r\n\t\t\t<td>0<\/td>\r\n\t\t\t<td>1<\/td>\r\n\t\t\t<td>5<\/td>\r\n\t\t\t<td>3<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td>\ubc29\ubc95 2<\/td>\r\n\t\t\t<td>9<\/td>\r\n\t\t\t<td>3<\/td>\r\n\t\t\t<td>0<\/td>\r\n\t\t\t<td>1<\/td>\r\n\t\t\t<td>5<\/td>\r\n\t\t\t<td>4<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td>\ubc29\ubc95 2<\/td>\r\n\t\t\t<td>9<\/td>\r\n\t\t\t<td>6<\/td>\r\n\t\t\t<td>0<\/td>\r\n\t\t\t<td>1<\/td>\r\n\t\t\t<td>5<\/td>\r\n\t\t\t<td>7<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td>\ubc29\ubc95 2<\/td>\r\n\t\t\t<td>9<\/td>\r\n\t\t\t<td>7<\/td>\r\n\t\t\t<td>0<\/td>\r\n\t\t\t<td>1<\/td>\r\n\t\t\t<td>5<\/td>\r\n\t\t\t<td>8<\/td>\r\n\t\t<\/tr>\r\n\t<\/tbody>\r\n<\/table>\r\n\r\n<p>&nbsp;<\/p>\r\n\r\n<p>\ub2e8\uc5b4 \ub367\uc148\uc774 \uc8fc\uc5b4\uc84c\uc744 \ub54c, \uc774 \ub2e8\uc5b4 \ub367\uc148\uc744 \ud478\ub294 \ubc29\ubc95\uc758 \uc218\ub97c \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624. \ub2e8, \ub2e4\uc74c \uc870\uac74\uc744 \ub9cc\uc871\ud574\uc57c \ud55c\ub2e4.<\/p>\r\n\r\n<p>1. \ub367\uc148\uc758 \uac01 \ud56d\uc740 \uc22b\uc790 &#39;0&#39;-&#39;9&#39;\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\ub2e4. \ubaa8\ub4e0 \uc22b\uc790\ub294 \uc54c\ud30c\ubcb3 &#39;A&#39;-Z&#39;\ub85c \ubc14\ub00c\uc5b4\uc838 \uc788\ub2e4.<\/p>\r\n\r\n<p>2. \ud55c \uc54c\ud30c\ubcb3\uc740 \ud558\ub098\uc758 \uc22b\uc790\ub9cc\uc744 \ub098\ud0c0\ub0bc \uc218 \uc788\ub2e4. \ub610, \uc5b4\ub5a4 \uc22b\uc790\uc5d0 \ud574\ub2f9\ud558\ub294 \uc54c\ud30c\ubcb3\uc740 \ubc18\ub4dc\uc2dc \ud558\ub098 \uc774\uc5b4\uc57c \ud55c\ub2e4.<\/p>\r\n\r\n<p>3. 0\uc744 \uc81c\uc678\ud55c \uc22b\uc790\ub294 0\uc73c\ub85c \uc2dc\uc791\ud560 \uc218 \uc5c6\ub2e4. \uc989, 00\uc774\ub098 0123\uacfc \uac19\uc740 \uacbd\uc6b0\ub294 \ud5c8\uc6a9\ud558\uc9c0 \uc54a\ub294\ub2e4.<\/p>\r\n\r\n<p>&nbsp;<\/p>\r\n","input":"<p>\uc785\ub825\uc740 \uc5ec\ub7ec \uac1c\uc758 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\ub2e4. \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \ub9c8\uc9c0\ub9c9 \uc904\uc5d0\ub294 0\uc774 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub294 \uccab\uc9f8 \uc904\uc5d0 \ub2e8\uc5b4\uc758 \uac1c\uc218 N\uc774 \uc8fc\uc5b4\uc9c0\uace0, \uadf8 \ub2e4\uc74c \uc904\uc5d0\ub294 \ub2e8\uc5b4 N\uac1c\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \ub2e8\uc5b4\ub294 \uc54c\ud30c\ubcb3 &#39;A&#39;-&#39;Z&#39;\ub85c\ub9cc \uc774\ub8e8\uc5b4\uc838 \uc788\ub2e4.<\/p>\r\n\r\n<p>\uac01 \ub2e8\uc5b4\ub294 \ub2e4\uc74c\uacfc \uac19\uc740 \ubc29\uc815\uc2dd\uc744 \ub098\ud0c0\ub0b8\ub2e4.<\/p>\r\n\r\n<p>\ub2e8\uc5b4<sub>1<\/sub>+\ub2e8\uc5b4<sub>2<\/sub>+...+\ub2e8\uc5b4<sub>N-1<\/sub> = \ub2e8\uc5b4<sub>N<\/sub><\/p>\r\n\r\n<p>N\uc740 2\ubcf4\ub2e4 \ud06c\uace0, 13\ubcf4\ub2e4 \uc791\ub2e4. \ub2e8\uc5b4\uc758 \uae38\uc774\ub294 0\ubcf4\ub2e4 \ud06c\uace0, 9\ubcf4\ub2e4 \uc791\ub2e4. \ub2e8\uc5b4\uc5d0 \ub4f1\uc7a5\ud558\ub294 \uc11c\ub85c \ub2e4\ub978 \uc54c\ud30c\ubcb3\uc758 \uac1c\uc218\ub294 0\ubcf4\ub2e4 \ud06c\uace0, 11\ubcf4\ub2e4 \uc791\ub2e4.<\/p>\r\n","output":"<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc5d0 \ub300\ud574\uc11c, \ub2e8\uc5b4 \ub367\uc148\uc744 \ud480 \uc218 \uc788\ub294 \ubc29\ubc95\uc758 \uc218\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"Korean"},{"problem_id":"4964","problem_lang":"1","title":"Verbal Arithmetic","description":"<p>Let&#39;s think about verbal arithmetic.<\/p>\r\n\r\n<p>The material of this puzzle is a summation of non-negative integers represented in a decimal format, for example, as follows.<\/p>\r\n\r\n<pre>\r\n    905 +  125 = 1030<\/pre>\r\n\r\n<p>In verbal arithmetic, every digit appearing in the equation is masked with an alphabetic character. A problem which has the above equation as one of its answers, for example, is the following.<\/p>\r\n\r\n<pre>\r\n    ACM + IBM = ICPC<\/pre>\r\n\r\n<p>Solving this puzzle means finding possible digit assignments to the alphabetic characters in the verbal equation.<\/p>\r\n\r\n<p>The rules of this puzzle are the following.<\/p>\r\n\r\n<ul>\r\n\t<li>Each integer in the equation is expressed in terms of one or more digits &#39;0&#39;-&#39;9&#39;, but all the digits are masked with some alphabetic characters &#39;A&#39;-&#39;Z&#39;.<\/li>\r\n\t<li>The same alphabetic character appearing in multiple places of the equation masks the same digit. Moreover, all appearances of the same digit are masked with a single alphabetic character. That is, different alphabetic characters mean different digits.<\/li>\r\n\t<li>The most significant digit must not be &#39;0&#39;, except when a zero is expressed as a single digit &#39;0&#39;. That is, expressing numbers as &quot;00&quot; or &quot;0123&quot; is not permitted.<\/li>\r\n<\/ul>\r\n\r\n<p>There are 4 different digit assignments for the verbal equation above as shown in the following table.<\/p>\r\n\r\n<table class=\"table table-bordered\" style=\"width:28%\">\r\n\t<thead>\r\n\t\t<tr>\r\n\t\t\t<th style=\"width:10%\">Mask<\/th>\r\n\t\t\t<th style=\"width:3%\">A<\/th>\r\n\t\t\t<th style=\"width:3%\">B<\/th>\r\n\t\t\t<th style=\"width:3%\">C<\/th>\r\n\t\t\t<th style=\"width:3%\">I<\/th>\r\n\t\t\t<th style=\"width:3%\">M<\/th>\r\n\t\t\t<th style=\"width:3%\">P<\/th>\r\n\t\t<\/tr>\r\n\t<\/thead>\r\n\t<tbody>\r\n\t\t<tr>\r\n\t\t\t<td>Case 1<\/td>\r\n\t\t\t<td>9<\/td>\r\n\t\t\t<td>2<\/td>\r\n\t\t\t<td>0<\/td>\r\n\t\t\t<td>1<\/td>\r\n\t\t\t<td>5<\/td>\r\n\t\t\t<td>3<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td>Case 2<\/td>\r\n\t\t\t<td>9<\/td>\r\n\t\t\t<td>3<\/td>\r\n\t\t\t<td>0<\/td>\r\n\t\t\t<td>1<\/td>\r\n\t\t\t<td>5<\/td>\r\n\t\t\t<td>4<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td>Case 2<\/td>\r\n\t\t\t<td>9<\/td>\r\n\t\t\t<td>6<\/td>\r\n\t\t\t<td>0<\/td>\r\n\t\t\t<td>1<\/td>\r\n\t\t\t<td>5<\/td>\r\n\t\t\t<td>7<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td>Case 2<\/td>\r\n\t\t\t<td>9<\/td>\r\n\t\t\t<td>7<\/td>\r\n\t\t\t<td>0<\/td>\r\n\t\t\t<td>1<\/td>\r\n\t\t\t<td>5<\/td>\r\n\t\t\t<td>8<\/td>\r\n\t\t<\/tr>\r\n\t<\/tbody>\r\n<\/table>\r\n\r\n<p>Your job is to write a program which solves this puzzle.<\/p>","input":"<p>The input consists of a number of datasets. The end of the input is indicated by a line containing a zero.<\/p>\r\n\r\n<p>The number of datasets is no more than 100. Each dataset is formatted as follows.<\/p>\r\n<pre>N \r\nSTRING 1 \r\nSTRING 2 \r\n... \r\nSTRING N \r\n<\/pre>\r\n<p>The first line of a dataset contains an integer N which is the number of integers appearing in the equation. Each of the following N lines contains a string composed of uppercase alphabetic characters &#39;A&#39;-&#39;Z&#39; which mean masked digits.<\/p>\r\n\r\n<p>Each dataset expresses the following equation.<\/p>\r\n\r\n<pre>STRING 1 + STRING 2 + ... + STRING N -1 = STRING N<\/pre>\r\n\r\n<p>The integer N is greater than 2 and less than 13. The length of STRING i is greater than 0 and less than 9. The number of different alphabetic characters appearing in each dataset is greater than 0 and less than 11.<\/p>\r\n","output":"<p>For each dataset, output a single line containing the number of different digit assignments that satisfy the equation.<\/p>\r\n\r\n<p>The output must not contain any superfluous characters.<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"English"}]

출처

ICPC > Regionals > Asia Pacific > Japan > Japan Domestic Contest > 2009 Japan Domestic Contest C번

  • 문제를 번역한 사람: baekjoon
  • 문제의 오타를 찾은 사람: kazel