Swimming Pool

A long time ago, swimming pools were built as follows. First, a rectangular area $m$ meters long and $n$ meters wide is marked out. This area is divided into $1 \times 1$ meter square cells, giving $m \times n$ cells in total. Then, in each cell, either a single perfectly cut granite cube with side length 1 or a tower made by stacking such cubes is placed.

The cubes are made so precisely that it is enough for the edges of two cubes to touch for the joint to be hermetically sealed, so that water cannot flow through.

When water is poured in, such a stack of cubes can hold only a limited amount of water.

Write a program that determines the maximum possible volume of water, in cubic meters, that can be collected in this pool.

The first line contains two positive integers $m$ and $n$, the side lengths of the rectangular area in meters ($0 < m, n \le 100$).

Each of the next $m$ lines contains $n$ natural numbers.

The $j$-th number on the $(i+1)$-th line is the height of the cube tower in the $i$-th row and $j$-th column (that is, the number of cubes stacked there). Every cell contains at least one cube, and no tower is taller than 10000.

Print a single integer on one line: the maximum volume of water, in cubic meters, that can be stored in the given pool.

The pictures below show a top-down view of an empty pool and of a filled pool.