def hourglassSum(arr):
    # determine a value outside of the smallest possible
    # hourglass sum and use as the starting max_sum
    min_arr_val = -9
    max_sum = (min_arr_val - 1) * 7
    
    max_hourglass_starting_index = 4
    
    for i in range(max_hourglass_starting_index):
        # get sum of initial hourglass for row i
        # top row sum, bottom row sum, center value
        curr_sum = sum(arr[i][:3]) + sum(arr[i + 2][:3]) + arr[i + 1][1]
        max_sum = max(max_sum, curr_sum)
        
        for j in range(1, max_hourglass_starting_index):
            # sliding window through columns 0-3
            # top row sum
            curr_sum -= arr[i][j - 1]
            curr_sum += arr[i][j + 2]
            
            # bottom row sum
            curr_sum -= arr[i + 2][j - 1]
            curr_sum += arr[i + 2][j + 2]
            
            # center value
            curr_sum -= arr[i + 1][j]
            curr_sum += arr[i + 1][j + 1]
            
            max_sum = max(max_sum, curr_sum) 
            
    return max_sum