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;
$\text{[math]}$ .

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.

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 a_i1, a_i2, ..., a_in (0 ≤ a_ij ≤ 50). It is guaranteed that $\text{[math]}$ .

Output

If there is a positive integer k ≥ 1, such that matrix a^k is strictly positive, print "YES" (without the quotes). Otherwise, print "NO" (without the quotes).

Strictly Positive Matrix

Examples