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
21 00 1
Output
NO
Input
54 5 6 1 21 2 3 4 56 4 1 2 41 1 1 1 14 4 4 4 4
Output
YES