Container Yard Triple Silhouette Area

A rectangular container yard is laid out as an n x n grid of stacking slots. Slot (i, j) currently holds a stack of h[i][j] unit-sized shipping containers (a value of 0 means the slot is empty). A drone photographs the yard from three vantage points: straight overhead, from the front along one side of the yard, and from the side along the perpendicular direction. Each photograph shows a silhouette: overhead, a slot contributes to the silhouette only if it holds at least one container; from the front, an entire row's silhouette height equals the tallest stack anywhere in that row; from the side, an entire column's silhouette height equals the tallest stack anywhere in that column. Compute the combined area: the overhead area, plus the sum of front-silhouette heights over all rows, plus the sum of side-silhouette heights over all columns.

Input format

• Line 1: a single integer n.
• Each of the next n lines contains n space-separated integers, the j-th integer on the i-th of these lines being h[i][j].

Output format

Print a single integer: the total combined silhouette area.

Constraints

• 1 <= n <= 50
• 0 <= h[i][j] <= 100

2
1 2
3 4

17

1
2

5