A textile designer represents a rectangular tapestry swatch as a grid with r rows and c columns, where each cell holds an integer thread-color code. The swatch is called a harmonious weave if, along every diagonal running from the upper-left toward the lower-right, all cells carry the same color code (a diagonal here means the set of cells (row, col) that share the same value of row - col). Given the swatch, decide whether it is a harmonious weave.

Input format

Line 1: two integers r and c. Next r lines: each contains c integers, the color codes of that row, left to right.

Output format

Print true if the swatch is a harmonious weave, or false otherwise.

Constraints

• 1 <= r, c <= 200
• 0 <= color code <= 10^5

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

true

2 2
1 2
2 2

false