Problem
Given an N x M matrix, a zigzag path starts at any cell in the top row, and at each step moves to the next row to a cell that's NOT in the same column as the previous step. Find the maximum possible sum along such a path (N ≥ 1, M ≥ 2).
Input format
Input
input.txt
- Two integers N, M (1 ≤ N ≤ 10, 2 ≤ M ≤ 10) - N rows with M integers
Output format
Output
output.txt
- The maximum sum.
Example
input
3 3 1 2 3 9 8 7 4 5 6
output
18
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Sample cases (from the problem)
Sample Case 1
Input
3 3 1 2 3 9 8 7 4 5 6
Expected output
18
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