3118: 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).
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