// 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;