Given a m x n grid filled with non-negative numbers, find a path from the top-left to the bottom-right, which minimizes the sum of all numbers along its path.

Note: You can only move either down or right at any point in time.

Example 1:

Input:
1 3 1
1 5 1
4 2 1
Output: 7

(1→3→1→1→1)

Example 2:

Input:
1 2 3
4 5 6
Output: 12

Constraints:

• m == grid.length, n == grid[i].length
• 1 ≤ m, n ≤ 200
• 0 ≤ grid[i][j] ≤ 200

Input format: First line: two integers m n. Next m lines: n space-separated integers.

Output format: Minimum path sum.