There is an H × W grid (H vertical, W horizontal), where each square contains a lowercase English letter. Specifically, the letter in the square at the i-th row and j-th column is equal to the j-th character in the string Si.
Snuke can apply the following operation to this grid any number of times:
Snuke wants this grid to be symmetric. That is, for any 1 ≤ i ≤ H and 1 ≤ j ≤ W, the letter in the square at the i-th row and j-th column and the letter in the square at the (H + 1 - i)-th row and (W + 1 - j)-th column should be equal.
Determine if Snuke can achieve this objective.
Input is given from Standard Input in the following format:
H W S1 S2 : SH
If Snuke can make the grid symmetric, print
YES; if he cannot, print
2 3 arc rac
If the second and third columns from the left are swapped, the grid becomes symmetric, as shown in the image below:
3 7 atcoder regular contest
12 12 bimonigaloaf faurwlkbleht dexwimqxzxbb lxdgyoifcxid ydxiliocfdgx nfoabgilamoi ibxbdqmzxxwe pqirylfrcrnf wtehfkllbura yfrnpflcrirq wvcclwgiubrk lkbrwgwuiccv