// stores the sums, in order
std::set<int> hourglass_sums;
 
/*
A core is the middle point of the glasshour
a b c 
  d 
e f g
 in the above, the core is d */

// finds the sum of the three neighbors above the core
int sumOfUpperNeighbors(int core_y, int core_x, vector<vector<int>> arr) { 
    int left_most_cordinate = core_x - 1; 
    int right_most_cordinate = core_x + 1; 
    int upper_coordinate = core_y - 1; 
    
    int sum =0; 
    sum += arr[upper_coordinate][left_most_cordinate];
    sum += arr[upper_coordinate][core_x];
    sum += arr[upper_coordinate][right_most_cordinate];
    return sum;
}

// finds the sum of the three neighbors above the core
int sumOfLowerNeighbors(int core_y, int core_x, vector<vector<int>> arr) { 
    int left_most_cordinate = core_x - 1; 
    int right_most_cordinate = core_x + 1; 
    int lower_coordinate = core_y + 1; 
    
    int sum =0; 
    sum += arr[lower_coordinate][left_most_cordinate];
    sum += arr[lower_coordinate][core_x];
    sum += arr[lower_coordinate][right_most_cordinate];
    return sum;
}

int hourglassSum(vector<vector<int>> arr) {    
    int total_sum = 0;
    for(int i = 1; i < 5; i++){
        for(int j = 1; j < 5; j++){
            total_sum += arr[i][j]; 
            total_sum += sumOfUpperNeighbors(i,j,arr);
            total_sum += sumOfLowerNeighbors(i,j,arr);
            hourglass_sums.insert(total_sum);
            total_sum = 0;

    public static int hourglassSum(List<List<Integer>> arr) {
        int biggest = Integer.MIN_VALUE;
        for(int i = 0; i < arr.size() - 2; i++){
            for(int j = 0; j < arr.get(i).size() - 2; j++){
                int count = 0;
                count += arr.get(i).get(j);
                count += arr.get(i).get(j + 1);
                count += arr.get(i).get(j + 2);
                count += arr.get(i + 1).get(j + 1);
                count += arr.get(i + 2).get(j);
                count += arr.get(i + 2).get(j + 1);
                count += arr.get(i + 2).get(j + 2);
                biggest = count >= biggest ? count : biggest;
            }
        }
        return biggest;
    }

public static int hourglassSum(List<List<Integer>> arr) {
    // Write your code here
        int maxInteger = Integer.MIN_VALUE;
        for (int row = 0; row < arr.size() - 2; row++) {
            for (int col = 0; col < arr.get(row).size() - 2; col++) {
                int topRow = arr.get(row).get(col) + arr.get(row).get(col + 1) + arr.get(row).get(col + 2);
                int bottomRow = arr.get(row + 2).get(col) + arr.get(row + 2).get(col + 1) + arr.get(row + 2).get(col + 2);
                int middleRow = arr.get(row + 1).get(col + 1);
                maxInteger = Math.max(maxInteger, topRow + bottomRow + middleRow);
            }
        }
        return maxInteger;
    }