You are given an ~R \times C~ matrix ~M~. Each of its elements is either ~0~ or ~1~.

A cross of size ~k~ is a subregion of ~M~, centering at one of its elements, containing the center and ~k~ elements in each of the four orthogonal directions (i.e., horizontal and vertical directions).

A cross is called "symmetric" if it does not change after being rotated by ~90~ degrees. Please find the cross with the largest size in ~M~. It is guaranteed that there is exactly one such cross.

Input Specification

The first line contains two integers ~R~ and ~C~, the number of rows and columns of ~M~. The next ~R~ lines each contain ~C~ numbers separated by one space, representing ~M~.

• In ~50\%~ of the test cases, ~3 \le R,C \le 500~.
• In ~100\%~ of the test cases, ~3 \le R,C \le 2000~.

Output Specification

The output contains a single line with three integers: the size of the largest symmetric cross in ~M~, and the row and column number of its center.

Sample Input 1

5 5
0 0 1 0 0
0 0 0 0 0
1 0 1 0 1
0 0 0 0 0
0 0 1 0 0

Sample Output 1

2 3 3

Sample Input 2

5 5
0 0 1 0 0
0 1 0 0 1
1 0 1 0 0
0 0 1 0 1
0 0 1 0 0

Sample Output 2

1 2 2