public class Solution {
    private int[,] PrepareDP(int[][] grid) {
        int[,] dp = new int[grid.Length, grid.Length];

        var y = grid.Length - 1;
        for (var x = 0; x < grid.Length; ++x) {
            dp[y, x] = grid[y][x];
        }

        return dp;
    }

    private void Compute(int[][] grid, int[,] dp, int y, int x0) {
        var minimum = int.MaxValue;

        for (var x = 0; x < grid.Length; ++x) {
            // need to continue with different column
            if (x == x0) {
                continue;
            }

            minimum = Math.Min(minimum, dp[y + 1, x]);
        }

        dp[y, x0] = grid[y][x0] + minimum;
    }

    public int MinFallingPathSum(int[][] grid) {
        var dp = PrepareDP(grid);

        for (var y = grid.Length - 2; y >= 0; --y) {
            for (var x = 0; x < grid.Length; ++x) {
                Compute(grid, dp, y, x);
            }
        }

        int minFallingPath = int.MaxValue;
        for (var x = 0; x < grid.Length; ++x) {
            minFallingPath = Math.Min(minFallingPath, dp[0, x]);
        }

        return minFallingPath;
    }
}