submatrix

Be there A a matrix with n lines (numbered from 1 to n) and m columns (numbered from 1 to m) with components from the set {0, 1}.
We call a coordinate (L1, C1, L2, C2) submatrix a rectangular area of the matrix that has the upper-left corner on line L1, column C1 and lower-right corner on line L2, column C2 (L1<=L2, C1<=C2).
The size of a submatrix is equal to the number of elements of the submatrix.

Task

Write a program that determines a maximum size submatrix comprised of only 1s.

Input Data

Input file submatrix.in contains on the first line two positive integers n and m, separated by a space.
Each of the following n lines contain m digits of the set {0, 1}. Digits on the same line are not separated by spaces.

Output Data

Output file submatrix.out will contain on the first line the size of the determined submatrix (maximum possible). The second line will contain 4 positive integers separated by a space, L1 C1 L2 C2, where (L1,C1) represent the line and column of the upper-left corner of the determined submatrix and (L2,C2) represent the line and column of the lower-right corner of the submatrix. If there is more than one solution available the solution for which the line of the upper-left corner is minimal will be displayed. If there is still more than one solution available the one for which the column of the upper-left corner is minimal will be displayed. Finally, if there is still more than one solution the one for which the line of the lower-right corner is minimal will be displayed.

Constraints

1 <= n, m <= 100

Examples

Time limit: 0.5 seconds/test

prof. Emanuela Cerchez
"Grigore Moisil" Iaşi IT High School
Contact:emanuela.cerchez@gmail.com