Maximum Sum Submatrix HARD Sorting Searching 50 XP 0 solved

Problem

Given an NΓ—M matrix, find the submatrix with the largest sum. Output the maximal sum.

Input format

Input input.txt

- The first line contains N and M (1 ≀ N, M ≀ 20). - Each of the next N lines contains M integers.

Output format

Output output.txt

- The maximal sum.

Example

input
2 3
1 -2 0
-3 4 5
output
9

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