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 a ij 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: a ij ≥ 0; . Matrix b is strictly positive, if for any numbers i, j (1 ≤ i, j ≤ n ) the inequality b ij 0 holds. You task is to determine if there is such integer k ≥ 1, that matrix a k is strictly positive.

输入描述:

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 .

输出描述:

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).