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문제

다각형의 삼각분할이란 다각형을 삼각형으로 나누는 꼭짓점을 연결하는 직선의 집합이다. 직선은 반드시 다각형 내부에 있어야 하며, 꼭짓점을 제외한 다른 곳에서 다른 직선과 교차하면 안된다. 

위의 그림에서 굵은 선은 다각형의 변을 나타내고, 가는 선은 삼각분할을 나타낸다. 꼭짓점이 n개인 다각형을 삼각분할하면 (n-2)개의 삼각형을 만들 수 있다.

한 꼭짓점에서 시작해 변을 따라 이동하면서 각 꼭짓점에 있는 삼각형의 개수를 나열한 것을 삼각형 개수 수열이라고 한다. 위의 그림에 나와있는 다각형의 삼각형 개수 수열은 아래와 같다. 가장 왼쪽 위에 있는 꼭짓점에서 시작한다.

  • A: 1 3 1 3 1 3
  • B: 2 2 1 4 1 2
  • C: 1 2 3 2 1 6 1 2 3 2 1 6

N개의 양의 정수로 이루어진 삼각형 개수 수열이 주어졌을 때, 이러한 수열을 만드는 다각형이 존재하는지 안하는지를 구하는 프로그램을 작성하시오. 존재하는 경우에는 삼각형을 모두 출력한다.

입력

첫째 줄에 테스트 케이스의 개수 P (1 ≤ P ≤ 1000)가 주어진다.

각 테스트 케이스는 한 줄로 이루어져 있다. 첫 번째 숫자는 테스트 케이스 번호 K이며, 두 번째 숫자는 수열의 길이 N (4 ≤ N ≤ 20)이다. 다음 N개의 숫자는 삼각형 개수 수열이다.

출력

입력으로 주어진 수열이 삼각형 개수 수열이 아닌 경우에는 테스트 케이스 번호 K와 알파벳 대문자 "N"을 출력한다.

올바른 경우에는 테스트 케이스 번호 K와 알파벳 대문자 "Y"를 출력한다. 다음 (N-2)개 줄에는 어떤 꼭짓점이 삼각형을 이루는지 한 줄에 하나씩 출력한다. 꼭짓점은 입력으로 주어진 순서대로 1번부터 시작하며, 사전순으로 정렬해서 출력한다. k < l < m이 한 삼각형이고, r < s < t가 다른 삼각형일 때, 아래 조건을 만족하면 첫 번째 삼각형이 두 번째보다 사전순으로 앞선다.

k<r OR (k==r AND l<s) OR (k==r AND l==s AND m<t)

예제 입력 1

4
1 6 1 3 1 3 1 3
2 6 1 3 2 2 1 3
3 12 1 2 3 2 1 6 1 2 3 2 1 6
4 20 1 2 3 2 1 6 1 2 3 2 1 6 1 3 2 2 1 3 1 2

예제 출력 1

1 Y
1 2 6
2 3 4
2 4 6
4 5 6
2 N
3 Y
1 2 12
2 3 12
3 4 6
3 6 12
4 5 6
6 7 8
6 8 9
6 9 12
9 10 12
10 11 12
4 N
[{"problem_id":"9474","problem_lang":"0","title":"\uc0bc\uac01 \ubd84\ud560\uacfc \uc0bc\uac01\ud615","description":"<p>\ub2e4\uac01\ud615\uc758 \uc0bc\uac01\ubd84\ud560\uc774\ub780 \ub2e4\uac01\ud615\uc744 \uc0bc\uac01\ud615\uc73c\ub85c \ub098\ub204\ub294 \uaf2d\uc9d3\uc810\uc744 \uc5f0\uacb0\ud558\ub294 \uc9c1\uc120\uc758 \uc9d1\ud569\uc774\ub2e4. \uc9c1\uc120\uc740 \ubc18\ub4dc\uc2dc \ub2e4\uac01\ud615 \ub0b4\ubd80\uc5d0 \uc788\uc5b4\uc57c \ud558\uba70, \uaf2d\uc9d3\uc810\uc744 \uc81c\uc678\ud55c \ub2e4\ub978 \uacf3\uc5d0\uc11c \ub2e4\ub978 \uc9c1\uc120\uacfc \uad50\ucc28\ud558\uba74 \uc548\ub41c\ub2e4.&nbsp;<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/triangula.png\" style=\"height:233px; width:620px\" \/><\/p>\r\n\r\n<p>\uc704\uc758 \uadf8\ub9bc\uc5d0\uc11c \uad75\uc740 \uc120\uc740 \ub2e4\uac01\ud615\uc758 \ubcc0\uc744 \ub098\ud0c0\ub0b4\uace0, \uac00\ub294 \uc120\uc740 \uc0bc\uac01\ubd84\ud560\uc744 \ub098\ud0c0\ub0b8\ub2e4. \uaf2d\uc9d3\uc810\uc774 n\uac1c\uc778 \ub2e4\uac01\ud615\uc744 \uc0bc\uac01\ubd84\ud560\ud558\uba74 (n-2)\uac1c\uc758 \uc0bc\uac01\ud615\uc744 \ub9cc\ub4e4 \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<p>\ud55c \uaf2d\uc9d3\uc810\uc5d0\uc11c \uc2dc\uc791\ud574 \ubcc0\uc744 \ub530\ub77c \uc774\ub3d9\ud558\uba74\uc11c \uac01 \uaf2d\uc9d3\uc810\uc5d0 \uc788\ub294 \uc0bc\uac01\ud615\uc758 \uac1c\uc218\ub97c \ub098\uc5f4\ud55c \uac83\uc744 \uc0bc\uac01\ud615 \uac1c\uc218 \uc218\uc5f4\uc774\ub77c\uace0 \ud55c\ub2e4. \uc704\uc758 \uadf8\ub9bc\uc5d0 \ub098\uc640\uc788\ub294 \ub2e4\uac01\ud615\uc758 \uc0bc\uac01\ud615 \uac1c\uc218 \uc218\uc5f4\uc740 \uc544\ub798\uc640 \uac19\ub2e4. \uac00\uc7a5 \uc67c\ucabd \uc704\uc5d0 \uc788\ub294 \uaf2d\uc9d3\uc810\uc5d0\uc11c \uc2dc\uc791\ud55c\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>A: 1 3 1 3 1 3<\/li>\r\n\t<li>B: 2 2 1 4 1 2<\/li>\r\n\t<li>C: 1 2 3 2 1 6 1 2 3 2 1 6<\/li>\r\n<\/ul>\r\n\r\n<p>N\uac1c\uc758 \uc591\uc758 \uc815\uc218\ub85c \uc774\ub8e8\uc5b4\uc9c4 \uc0bc\uac01\ud615 \uac1c\uc218 \uc218\uc5f4\uc774 \uc8fc\uc5b4\uc84c\uc744 \ub54c, \uc774\ub7ec\ud55c \uc218\uc5f4\uc744 \ub9cc\ub4dc\ub294 \ub2e4\uac01\ud615\uc774 \uc874\uc7ac\ud558\ub294\uc9c0 \uc548\ud558\ub294\uc9c0\ub97c \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624. \uc874\uc7ac\ud558\ub294 \uacbd\uc6b0\uc5d0\ub294 \uc0bc\uac01\ud615\uc744 \ubaa8\ub450 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uac1c\uc218 P (1 &le; P &le; 1000)\uac00 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub294 \ud55c \uc904\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\ub2e4. \uccab \ubc88\uc9f8 \uc22b\uc790\ub294 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4 \ubc88\ud638 K\uc774\uba70, \ub450 \ubc88\uc9f8 \uc22b\uc790\ub294 \uc218\uc5f4\uc758 \uae38\uc774 N (4 &le; N &le; 20)\uc774\ub2e4. \ub2e4\uc74c N\uac1c\uc758 \uc22b\uc790\ub294 \uc0bc\uac01\ud615 \uac1c\uc218 \uc218\uc5f4\uc774\ub2e4.<\/p>\r\n","output":"<p>\uc785\ub825\uc73c\ub85c \uc8fc\uc5b4\uc9c4 \uc218\uc5f4\uc774 \uc0bc\uac01\ud615 \uac1c\uc218 \uc218\uc5f4\uc774 \uc544\ub2cc \uacbd\uc6b0\uc5d0\ub294 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4 \ubc88\ud638 K\uc640 \uc54c\ud30c\ubcb3 \ub300\ubb38\uc790 &quot;N&quot;\uc744 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n\r\n<p>\uc62c\ubc14\ub978 \uacbd\uc6b0\uc5d0\ub294 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4 \ubc88\ud638 K\uc640 \uc54c\ud30c\ubcb3 \ub300\ubb38\uc790 &quot;Y&quot;\ub97c \ucd9c\ub825\ud55c\ub2e4. \ub2e4\uc74c (N-2)\uac1c \uc904\uc5d0\ub294 \uc5b4\ub5a4 \uaf2d\uc9d3\uc810\uc774 \uc0bc\uac01\ud615\uc744 \uc774\ub8e8\ub294\uc9c0 \ud55c \uc904\uc5d0 \ud558\ub098\uc529 \ucd9c\ub825\ud55c\ub2e4. \uaf2d\uc9d3\uc810\uc740 \uc785\ub825\uc73c\ub85c \uc8fc\uc5b4\uc9c4 \uc21c\uc11c\ub300\ub85c 1\ubc88\ubd80\ud130 \uc2dc\uc791\ud558\uba70, \uc0ac\uc804\uc21c\uc73c\ub85c \uc815\ub82c\ud574\uc11c \ucd9c\ub825\ud55c\ub2e4. k &lt; l &lt; m\uc774 \ud55c \uc0bc\uac01\ud615\uc774\uace0, r &lt; s &lt; t\uac00 \ub2e4\ub978 \uc0bc\uac01\ud615\uc77c \ub54c, \uc544\ub798 \uc870\uac74\uc744 \ub9cc\uc871\ud558\uba74 \uccab \ubc88\uc9f8 \uc0bc\uac01\ud615\uc774 \ub450 \ubc88\uc9f8\ubcf4\ub2e4 \uc0ac\uc804\uc21c\uc73c\ub85c \uc55e\uc120\ub2e4.<\/p>\r\n\r\n<pre>\r\nk&lt;r OR (k==r AND l&lt;s) OR (k==r AND l==s AND m&lt;t)<\/pre>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"9474","problem_lang":"1","title":"Triangle Count Sequences of Polygon Triangulations","description":"<p>A Triangulation of a polygon is a set of lines between vertices of the polygon that divide the polygoninto triangles. The lines must be inside the polygon and may not intersect each other except atvertices of the polygon. For example:<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/triangula.png\" style=\"height:233px; width:620px\" \/><\/p>\r\n\r\n<p>In the examples, the heavy line is the outline of the polygon and the lighter lines give the triangulation. In each case a triangulation of a polygon with n vertices will result in (n-2) triangles.<\/p>\r\n\r\n<p>The triangle count sequence of a triangulation is obtained by starting at some vertex, proceedingaround the polygon and for each vertex of the polygon recording the number of triangles of thetriangulation incident on that vertex. In the examples above the triangle count sequences starting atthe top (left) are:<\/p>\r\n\r\n<ul>\r\n\t<li>A: 1 3 1 3 1 3<\/li>\r\n\t<li>B: 2 2 1 4 1 2<\/li>\r\n\t<li>C: 1 2 3 2 1 6 1 2 3 2 1 6<\/li>\r\n<\/ul>\r\n\r\n<p>Write a program which takes as input a sequence of N positive integers and determines whether thesequence is the triangle count sequence of a polygon of N vertices. If so, list the triangles of thetriangulation in lexicographical order.<\/p>\r\n","input":"<p>The first line of input contains a single integer P, (1 &le; P &le; 1000), which is the number of data setsthat follow. Each data set should be processed identically and independently.<\/p>\r\n\r\n<p>Each data set consists of a single line of input. It contains the data set number, K, followed by thenumber, N, (4 &lt;= N &lt;= 20) of integers in the sequence, followed by the N integers of the sequencein order, all separated by a single space.<\/p>\r\n","output":"<p>For each data set there may be multiple lines of output. If the input sequence is NOT the trianglecount sequence of a polygon of N vertices, the single output line consists of the data set number, K,followed by a single space followed by the (capital) letter N. Otherwise (the input sequence is thetriangle count sequence of a polygon of N vertices), the first output line consists of the data setnumber, K, followed by a single space followed by the (capital) letter Y. Following this line are (N-2)lines each containing the indices of the vertices of a triangle of the triangulation, one triangle per line,with the vertex indices in increasing order. The triangles should be sorted in lexicographic orderleast first. That is, if k &lt; l &lt; m are the vertex indices of one triangle and r &lt; s &lt; t are the vertexindices of another, then the first precedes the second in lexicographical order if:<\/p>\r\n\r\n<pre>\r\nk &lt; r OR (k == r AND l &lt; s) OR (k == r AND l == s AND m &lt; t)<\/pre>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]