# 「CF403C」Strictly Positive Matrix

2015年1月24日1,8730

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 integersai1, 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).

Sample test(s)
input

output

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（利用上面一段证明我们可以如果k存在那么其上界为2n，因此50分做法只需要取一个矩阵的2n次幂判断即可。）