# #P402E. Strictly Positive Matrix

ID: 5322 Type: RemoteJudge 1000ms 256MiB 尝试: 1 已通过: 1 难度: 8 上传者: 标签>graphsmath*2200

# Strictly Positive Matrix

## Description

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.

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 .

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).

## 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).

## Samples

``````2
1 0
0 1

``````
``````NO

``````
``````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

``````
``````YES

``````