CF117C.Cycle

A tournament is a directed graph without self-loops in which every pair of vertexes is connected by exactly one directed edge. That is, for any two vertexes u and v (u ≠ v) exists either an edge going from u to v, or an edge from v to u.

You are given a tournament consisting of n vertexes. Your task is to find there a cycle of length three.

锦标赛是一个无自环的有向图，其中每对顶点之间恰好存在一条有向边。也就是说，对任意两个顶点 $u$ 和 $v$（$u \ne v$），要么存在一条从 $u$ 指向 $v$ 的边，要么存在一条从 $v$ 指向 $u$ 的边。

你被给定一个包含 $n$ 个顶点的锦标赛。你的任务是在其中找出一个长度为三的环。

The first line contains an integer n (1 ≤ n ≤ 5000). Next n lines contain the adjacency matrix A of the graph (without spaces). A__i, j = 1 if the graph has an edge going from vertex i to vertex j, otherwise A__i, j = 0. A__i, j stands for the j-th character in the i-th line.

It is guaranteed that the given graph is a tournament, that is, A__i, i = 0, A__i, j ≠ A__j, i (1 ≤ i, j ≤ n, i ≠ j).

第一行包含一个整数 $n$（$1 \leq n \leq 5000$）。接下来的 $n$ 行包含图的邻接矩阵 $A$（各行内无空格）。若图中存在一条从顶点 $i$ 指向顶点 $j$ 的边，则 $A_{i,j} = 1$；否则 $A_{i,j} = 0$。$A_{i,j}$ 表示第 $i$ 行中的第 $j$ 个字符。

保证所给图是一个竞赛图，即对所有 $1 \leq i, j \leq n$ 且 $i \neq j$，均有 $A_{i,i} = 0$ 且 $A_{i,j} \neq A_{j,i}$。

Print three distinct vertexes of the graph _a_1, _a_2, _a_3 (1 ≤ a__i ≤ n), such that _A__a_1, _a_2 = _A__a_2, _a_3 = _A__a_3, _a_1 = 1, or "-1", if a cycle whose length equals three does not exist.

If there are several solutions, print any of them.

输出图中三个互不相同的顶点 $a_1, a_2, a_3$（其中 $1 \leq a_i \leq n$），使得 $A_{a_1,a_2} = A_{a_2,a_3} = A_{a_3,a_1} = 1$；若不存在长度为 3 的环，则输出 -1。

若存在多个解，输出任意一个即可。