class Solution {
    public int maxValue(int[][] grid) {
        int m = grid.length, n = grid[0].length;
        int[][] dp = new int[m][n];
        dp[0][0] = grid[0][0];
        for(int i = 1; i < m; i++) dp[i][0] = grid[i][0] + dp[i - 1][0];
        for(int i = 1; i < n; i++) dp[0][i] = grid[0][i] + dp[0][i - 1];

        for(int i = 1; i < m; i++){
            for(int j = 1; j < n; j++){
                dp[i][j] = grid[i][j] + Math.max(dp[i - 1][j], dp[i][j - 1]);
            }
        }

        return dp[m - 1][n - 1];
    }
}