图 - المسألة

#7995. 图

الإحصائيات

This problem is prepared by gyh20 .

题目描述

给定一个 $n$ 个点的无向正权完全图，请对于每一条边 $(a,b)$，求出是否存在一个点对 $(x,y)$ 使得 $x\rightarrow y$ 的所有最短路都经过 $(a,b)$。

输入格式

从标准输入读入数据。

第一行一个正整数 $n (1 \le n \le 500)$ 表示图的点数。

接下来 $n$ 行每行 $n$ 个数，构成一个大小为 $n\times n$ 的矩阵，第 $i$ 行第 $j$ 个数 $a_{i,j}(1\leq a_{i,j}\leq 10^6)$ 表示 $(i,j)$ 之间的边长度，特别地，$a_{i,i} = 0$.

保证 $a_{i,j}=a_{j,i}$。

输出格式

输出到标准输出。

输出一个大小为 $n$ 的 $01$ 矩阵，其中第 $i$ 行第 $j$ 列为 $1$ 表示边 $(i,j)$ 满足题目中提出的要求，$0$ 表示不满足。

特别的，当 $i=j$ 时输出 $0$。

样例

输入

4
0 3 2 100
3 0 8 100
2 8 0 10
100 100 10 0

输出

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