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Matrix Multiplication
Time Limit:2000MS  Memory Limit:65536K
Total Submit:3582 Accepted:486

Description

You are given three n ¡Á n matrices A, B and C. Does the equation A ¡Á B = C hold true?

Input

The first line of input contains a positive integer n (n ¡Ü 500) followed by the the three matrices A, B and C respectively. Each matrix's description is a block of n ¡Á n integers.

It guarantees that the elements of A and B are less than 100 in absolute value and elements of C are less than 10,000,000 in absolute value.

Output

Output "YES" if the equation holds true, otherwise "NO".

Sample Input

2
1 0
2 3
5 1
0 8
5 1
10 26

Sample Output

YES

Hint
Multiple inputs will be tested. So O(n3) algorithm will get TLE.

Source
POJ Monthly--2007.08.05, qzc

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