시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
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문제

백준이는 대학에서 ACM-ICPC를 함께 공부한 Sogang ACM-ICPC Team 회원들과 사진을 찍으려고 한다. 

회원들은 여러 줄로 나누어서 설 것이고, 앞 줄에 있는 사람의 수는 뒷 줄에 있는 사람의 수보다 작거나 같다. 그리고, 모든 줄은 왼쪽을 기준으로 정렬해서 줄을 설 것이다.

예를 들어 회원이 12명이라면, 뒤에서부터 앞까지 차례대로 5, 3, 3, 1명이 설 수 있다.

백준이는 모든 사람들이 사진에 나와야 한다고 생각한다. 따라서, 각 줄에 서있는 사람의 키는 왼쪽에서 오른쪽으로 갈 수록 작아져야 하고, 뒤에서 앞으로 올 수록 작아져야 한다.

12명의 학생이 있을 때, 5, 3, 3, 1과 같이 줄을 서는 2가지 경우는 다음과 같다. (1이 제일 키가 큰 사람)

학생의 수와 각 줄에 몇 명이 서야 하는 지가 주어졌을 때, 사진을 찍을 수 있는 서로 다른 대형의 수를 구하려고 한다.

학생이 6명이고, 3, 2, 1과 같이 줄을 서는 방법은 다음과 같이 16가지가 있다.

입력

첫째 줄에 테스트 케이스의 개수 T가 주어진다. 각 테스트 케이스는 다음과 같이 두 줄로 이루어져 있다. 첫째 줄에는 줄의 수 k가 주어진다. 둘째 줄에는 가장 뒷 줄부터 앞 줄까지 몇 명의 사람이 줄을 서야 하는지가 공백으로 구분되어 주어진다. (n1, n2, ..., nk)

k는 5보다 작거나 같은 자연수이고, 전체 학생의 수는 30보다 작거나 같다.

출력

각 테스트 케이스에 대해, 한 줄에 하나씩 사진 찍는 대형의 수를 출력한다. 이 값은 4294967295보다 작거나 같다.

예제 입력 1

6
1
30
5
1 1 1 1 1
3
3 2 1
4
5 3 3 1
5
6 5 4 3 2
2
15 15

예제 출력 1

1
1
16
4158
141892608
9694845

힌트

[{"problem_id":"2764","problem_lang":"0","title":"\ub9c8\uc9c0\ub9c9 \uc0ac\uc9c4 \ucc0d\uae30","description":"<p>\ubc31\uc900\uc774\ub294 \ub300\ud559\uc5d0\uc11c ACM-ICPC\ub97c \ud568\uaed8 \uacf5\ubd80\ud55c Sogang ACM-ICPC Team \ud68c\uc6d0\ub4e4\uacfc \uc0ac\uc9c4\uc744 \ucc0d\uc73c\ub824\uace0 \ud55c\ub2e4.&nbsp;<\/p>\r\n\r\n<p>\ud68c\uc6d0\ub4e4\uc740 \uc5ec\ub7ec \uc904\ub85c \ub098\ub204\uc5b4\uc11c \uc124 \uac83\uc774\uace0, \uc55e \uc904\uc5d0 \uc788\ub294 \uc0ac\ub78c\uc758 \uc218\ub294 \ub4b7 \uc904\uc5d0 \uc788\ub294 \uc0ac\ub78c\uc758 \uc218\ubcf4\ub2e4 \uc791\uac70\ub098 \uac19\ub2e4. \uadf8\ub9ac\uace0, \ubaa8\ub4e0 \uc904\uc740 \uc67c\ucabd\uc744 \uae30\uc900\uc73c\ub85c \uc815\ub82c\ud574\uc11c \uc904\uc744 \uc124 \uac83\uc774\ub2e4.<\/p>\r\n\r\n<p>\uc608\ub97c \ub4e4\uc5b4 \ud68c\uc6d0\uc774 12\uba85\uc774\ub77c\uba74, \ub4a4\uc5d0\uc11c\ubd80\ud130 \uc55e\uae4c\uc9c0 \ucc28\ub840\ub300\ub85c 5, 3, 3, 1\uba85\uc774 \uc124 \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/Screen%20Shot%202012-11-06%20at%20%EC%98%A4%EC%A0%84%202_52_48.png\" style=\"height:69px; width:99px\" \/><\/p>\r\n\r\n<p>\ubc31\uc900\uc774\ub294 \ubaa8\ub4e0 \uc0ac\ub78c\ub4e4\uc774 \uc0ac\uc9c4\uc5d0 \ub098\uc640\uc57c \ud55c\ub2e4\uace0 \uc0dd\uac01\ud55c\ub2e4. \ub530\ub77c\uc11c, \uac01 \uc904\uc5d0 \uc11c\uc788\ub294 \uc0ac\ub78c\uc758 \ud0a4\ub294 \uc67c\ucabd\uc5d0\uc11c \uc624\ub978\ucabd\uc73c\ub85c \uac08 \uc218\ub85d \uc791\uc544\uc838\uc57c \ud558\uace0, \ub4a4\uc5d0\uc11c \uc55e\uc73c\ub85c \uc62c \uc218\ub85d \uc791\uc544\uc838\uc57c \ud55c\ub2e4.<\/p>\r\n\r\n<p>12\uba85\uc758 \ud559\uc0dd\uc774 \uc788\uc744 \ub54c, 5, 3, 3, 1\uacfc \uac19\uc774 \uc904\uc744 \uc11c\ub294 2\uac00\uc9c0 \uacbd\uc6b0\ub294 \ub2e4\uc74c\uacfc \uac19\ub2e4. (1\uc774 \uc81c\uc77c \ud0a4\uac00 \ud070 \uc0ac\ub78c)<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/Screen%20Shot%202012-11-06%20at%20%EC%98%A4%EC%A0%84%202_52_51.png\" style=\"height:75px; width:280px\" \/><\/p>\r\n\r\n<p>\ud559\uc0dd\uc758 \uc218\uc640 \uac01 \uc904\uc5d0 \uba87 \uba85\uc774 \uc11c\uc57c \ud558\ub294 \uc9c0\uac00 \uc8fc\uc5b4\uc84c\uc744 \ub54c, \uc0ac\uc9c4\uc744 \ucc0d\uc744 \uc218 \uc788\ub294 \uc11c\ub85c \ub2e4\ub978 \ub300\ud615\uc758 \uc218\ub97c \uad6c\ud558\ub824\uace0 \ud55c\ub2e4.<\/p>\r\n\r\n<p>\ud559\uc0dd\uc774 6\uba85\uc774\uace0, 3, 2, 1\uacfc \uac19\uc774 \uc904\uc744 \uc11c\ub294 \ubc29\ubc95\uc740 \ub2e4\uc74c\uacfc \uac19\uc774 16\uac00\uc9c0\uac00 \uc788\ub2e4.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/Screen%20Shot%202012-11-06%20at%20%EC%98%A4%EC%A0%84%202_52_54.png\" style=\"height:58px; width:535px\" \/><\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uac1c\uc218 T\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub294 \ub2e4\uc74c\uacfc \uac19\uc774 \ub450 \uc904\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\ub2e4. \uccab\uc9f8 \uc904\uc5d0\ub294 \uc904\uc758 \uc218 k\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \ub458\uc9f8 \uc904\uc5d0\ub294 \uac00\uc7a5 \ub4b7 \uc904\ubd80\ud130 \uc55e \uc904\uae4c\uc9c0 \uba87 \uba85\uc758 \uc0ac\ub78c\uc774 \uc904\uc744 \uc11c\uc57c \ud558\ub294\uc9c0\uac00 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub418\uc5b4 \uc8fc\uc5b4\uc9c4\ub2e4. (n1, n2, ..., nk)<\/p>\r\n\r\n<p>k\ub294 5\ubcf4\ub2e4 \uc791\uac70\ub098 \uac19\uc740 \uc790\uc5f0\uc218\uc774\uace0, \uc804\uccb4 \ud559\uc0dd\uc758 \uc218\ub294 30\ubcf4\ub2e4 \uc791\uac70\ub098 \uac19\ub2e4.<\/p>\r\n","output":"<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc5d0 \ub300\ud574, \ud55c \uc904\uc5d0 \ud558\ub098\uc529 \uc0ac\uc9c4 \ucc0d\ub294 \ub300\ud615\uc758 \uc218\ub97c \ucd9c\ub825\ud55c\ub2e4. \uc774 \uac12\uc740 4294967295\ubcf4\ub2e4 \uc791\uac70\ub098 \uac19\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"2764","problem_lang":"1","title":"Mr. Young\u2019s Picture Permutations","description":"<p>Mr. Young wishes to take a picture of his class. The students will stand in rows with each row no longer than the row behind it and the left ends of the rows aligned. For instance, 12 students could be arranged in rows (from back to front) of 5, 3, 3 and 1 students.&nbsp;<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/Screen%20Shot%202012-11-06%20at%20%EC%98%A4%EC%A0%84%202_52_48.png\" style=\"height:69px; width:99px\" \/><\/p>\r\n\r\n<p>In addition, Mr. Young wants the students in each row arranged so that heights decrease from left to right. Also, student heights should decrease from the back to the front. Thinking about it, Mr. Young sees that for the 12-student example, there are at least two ways to arrange the students (with 1 as the tallest etc.):&nbsp;<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/Screen%20Shot%202012-11-06%20at%20%EC%98%A4%EC%A0%84%202_52_51.png\" style=\"height:75px; width:280px\" \/><\/p>\r\n\r\n<p>Mr. Young wonders how many different arrangements of the students there might be for a given arrangement of rows. He tries counting by hand starting with rows of 3, 2 and 1 and counts 16 arrangements:&nbsp;<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/Screen%20Shot%202012-11-06%20at%20%EC%98%A4%EC%A0%84%202_52_54.png\" style=\"height:58px; width:535px\" \/><\/p>\r\n\r\n<p>Mr. Young sees that counting by hand is not going to be very effective for any reasonable number of students so he asks you to help out by writing a computer program to determine the number of different arrangements of students for a given set of rows.&nbsp;<\/p>\r\n","input":"<p>The input for each problem instance will consist of two lines. The first line gives the number of rows, k, as a decimal integer. The second line contains the lengths of the rows from back to front (n1, n2, &hellip;, nk) as decimal integers separated by a single space. The problem set ends with a line with a row count of 0. There will never be more than 5 rows and the total number of students, N, (sum of the row lengths) will be at most 30.&nbsp;<\/p>\r\n","output":"<p>The output for each problem instance shall be the number of arrangements of the N students into the given rows so that the heights decrease along each row from left to right and along each column from back to front as a decimal integer. (Assume all heights are distinct.) The result of each problem instance should be on a separate line. The input data will be chosen so that the result will always fit in an unsigned 32 bit integer.<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]

출처

ACM-ICPC > Regionals > North America > Greater New York Region > 2004 Greater New York Programming Contest I번