LogiQuest

309. Toeplitz Matrix

EasyMatrix

A matrix is Toeplitz if every top-left to bottom-right diagonal has equal elements. Print YES or NO.

Input format

Line 1: r c Next r lines: c integers

Output format

YES or NO

Example 1

Input

3 4
1 2 3 4
5 1 2 3
9 5 1 2

Output

YES

Example 2

Input

2 2
1 2
2 2

Output

NO

Constraints

1 ≤ r, c ≤ 500

Read input from standard input and print the answer to standard output. Your code is judged against 3 test cases, most of them hidden.

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