Minimum Path Sum

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

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

Examples

Example 1:

Input: grid = [[1,3,1],[1,5,1],[4,2,1]]

Output: 7

Explanation: The path 1 → 3 → 1 → 1 → 1 minimizes the sum to 7.

Example 2:

Input: grid = [[1,2,3],[4,5,6]]

Output: 12

Explanation: The path 1 → 2 → 3 → 6 minimizes the sum to 12.

Example 3:

Input: grid = [[5]]

Output: 5

Explanation: The grid has only one cell, so the minimum path sum is 5.

Constraints

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