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5729: Strictly Positive Matrix

内存限制：256 MB 时间限制：2 S
题面：传统 评测方式：文本比较 上传者：
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题目描述

E. Strictly Positive Matrix
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output
You have matrix a of size n×n. Let's number the rows of the matrix from 1 to n from top to bottom, let's number the columns from 1 to n from left to right. Let's use aij to represent the element on the intersection of the i-th row and the j-th column.
Matrix a meets the following two conditions:
  • for any numbers i,j (1≤i,j≤n) the following inequality holds: aij≥0;
  • .
Matrix b is strictly positive, if for any numbers i,j (1≤i,j≤n) the inequality bij>0 holds. You task is to determine if there is such integer k≥1, that matrix ak is strictly positive.
Input
The first line contains integer n (2≤n≤2000) − the number of rows and columns in matrix a.
The next n lines contain the description of the rows of matrix a. The i-th line contains n non-negative integers ai1,ai2,...,ain (0≤aij≤50). It is guaranteed that .
Output
If there is a positive integer k≥1, such that matrix ak is strictly positive, print "YES" (without the quotes). Otherwise, print "NO" (without the quotes).
Examples
Input 
2
1 0
0 1
Output 
NO
Input 
5
4 5 6 1 2
1 2 3 4 5
6 4 1 2 4
1 1 1 1 1
4 4 4 4 4
Output 
YES

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