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문제

축구 토너먼트에는 총 n개 팀이 참가한다. 첫 번째 라운드에서 총 n/2개의 경기가 열리게 된다. 매 라운드가 끝난 다음에, 승리한 팀은 다음 라운드에 진출한다. 두 번째 라운드에는 총 n/4개의 경기가 열리게 된다. 마지막에는 두 팀이 결승전에 올라오게 된다. 결승전의 승자는 토너먼트의 승자가 된다.

선영이는 한 축구 팀의 구단주이다. 이 팀은 세계에서 가장 축구를 잘하는 팀은 아니지만, 꽤 잘하는 팀이다. 선영이네 축구팀은 토너먼트에 참가한 팀중 적어도 절반은 쉽게 이길 수 있다. 또, 선영이네 팀이 이기지 못하는 모든 팀 t에 대해서, 그 팀을 이길 수 있으면서 선영이네 팀에게 지는 팀 t'가 항상 존재한다.

선영이네 팀이 토너먼트에 우승할 수 있게 토너먼트 스케줄을 작성하는 프로그램을 작성하시오.

입력

입력은 여러 개의 테스트 케이스로 이루어져 있다.

각 테스트 케이스의 첫째 줄에는 토너먼트에 참가하는 팀의 수 n이 주어진다. (2 ≤ n ≤ 1024, n은 2의 제곱꼴) 팀은 1번부터 n번까지 번호가 매겨져 있으며, 선영이네 팀의 번호는 1이다.

다음 n개 줄에는 n자리 바이너리 스트링이 주어진다. j번째 줄의 k번째 숫자가 1인 경우에는 팀 j가 팀 k를 이길 수 있는 것이고, 다른 경우는 모두 0이다. (토너먼트 경기이기 때문에, 비기는 경우는 존재하지 않는다)

팀은 자기 자신과 경기를 할 수 없기 때문에, j번째 줄의 j번째 숫자는 항상 0이다. j와 k가 다른 경우에, j번째 줄의 k번째 숫자와 k번째 줄의 j번째 숫자는 다르다.

출력

각 테스트 케이스에 대해서, 선영이네 팀이 승리할 수 있는 토너먼트 스케줄 n-1개 줄을 출력한다.

첫 n/2개 줄은 토너먼트의 첫 번째 라운드, 다음 n/4개 줄은 두 번째 라운드, ... 마지막 줄은 결승전이다.

각 줄은 두 정수 x와 y로 이루어져 있어야 한다. 이 뜻은 팀 x와 팀 y가 경기를 한다는 뜻이다.

만약, 팀1이 우승할 수 있는 스케줄이 여러 가지인 경우 아무거나 출력한다.

예제 입력 1

4
0110
0011
0000
1010
8
00111010
10101111
00010010
01000101
00110010
10101011
00010000
10101010

예제 출력 1

1 3
2 4
1 2
1 5
3 7
4 8
2 6
1 3
4 2
1 4
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In the \ufb01rst round, n\/2 matches are played such that each team plays against one other team. After every round, only the winning teams advance to the next round. In the second round, n\/4 matches are played such that each \ufb01rst-round winner plays against one other \ufb01rst-round winner. Eventually, only two teams are left to play a \ufb01nal match. The winner of the \ufb01nal match is the champion of the tournament.<\/p>\r\n\r\n<p>The Dutch soccer team is probably not the best team in the world. However, they are still a pretty good team. They can easily win from at least half of the other teams. Moreover, for every team t that the Dutch cannot beat in a direct confrontation, there is another team t&#39; that beats t, but is beaten by the Dutch team.<\/p>\r\n\r\n<p>The Dutch coach wants to manipulate the tournament such that the Dutch team will become champion. He happens to know, for each pair of teams, which team would certainly win if a match was played between them.<\/p>\r\n\r\n<p>For each two teams, you know beforehand which one would win if they played against each other. (Since this is a knock-out tournament, no ties will occur.) Furthermore, you know for sure that your favourite team can beat at least half of the other teams, and for every team t that your favourite team cannot beat, there is a team t&#39; that beats t but is itself beaten by your favourite team.<\/p>\r\n\r\n<p>Determine a tournament schedule such that your favourite team wins the tournament.<\/p>\r\n","input":"<p>For each test case, the input is as follows:<\/p>\r\n\r\n<ul>\r\n\t<li>One line containing the number of teams n, where n is a power of two and 2 &le;&nbsp;n &le;&nbsp;1024. Teams are numbered from 1 to n, where team 1 is your favourite team.<\/li>\r\n\t<li>n lines, each containing a string of n binary digits. The k-th digit on the j-th line is &lsquo;1&rsquo; if team j would certainly win from team k, otherwise it is &lsquo;0&rsquo;.<\/li>\r\n<\/ul>\r\n\r\n<p>A team cannot play against itself, therefore the j-th digit on the j-th line is &lsquo;0&rsquo;.<\/p>\r\n\r\n<p>If j &ne; k, the k-th digit on the j-th line is different from the j-th digit on the k-th line.<\/p>\r\n","output":"<p>For each test case, print n - 1 lines of output, specifying a tournament schedule that ensures victory for team 1.<\/p>\r\n\r\n<p>The \ufb01rst n\/2 lines describe the \ufb01rst round of the tournament. 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출처

ICPC > Regionals > Europe > Northwestern European Regional Contest > NWERC 2012 F번