int[][][]dp;
int max(int k, int x, int y){
    if(k == x){
       return 0;
    }
    if this state is visited {
       return dp[k][x][y];
    }
    int result = array[x][y];
    for(int i = y + 1; i < n; i++){
        result = max(result, array[x][y] + max(k + 1, y, i));
    }
    return dp[k][x][y] = result;

}