class Solution:
    def minPathSum(self, grid: List[List[int]]) -> int:
        # Step 1: Initialize the dp array with the same dimensions as the input grid.
        m, n = len(grid), len(grid[0])
        dp = [[0] * n for _ in range(m)]

        # Step 2: Set the starting point.
        dp[0][0] = grid[0][0]

        # Step 3: Populate the first row and first column.
        for i in range(1, m):
            dp[i][0] = dp[i - 1][0] + grid[i][0]
        for j in range(1, n):
            dp[0][j] = dp[0][j - 1] + grid[0][j]

        # Step 4: Iterate over the grid to populate the rest of the dp array.
        for i in range(1, m):
            for j in range(1, n):
                dp[i][j] = grid[i][j] + min(dp[i - 1][j], dp[i][j - 1])

        # Step 5: Return the value in the bottom-right corner.
        return dp[-1][-1]