F. Ammunition Storage
time limit per test
2 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

The Do-Barareh military area is like an $$$n\times m$$$ grid, each cell of which has a specific height. The commander of this military area is looking for a rectangular sub-area of this area, with width and height least $$$2$$$, whose its four corner cells are higher than the rest of its cells. He plans to install watchtowers in the corners of this sub-area to monitor the entire sub-area and use it for ammunition storage. Your job is to help the commander to find out how many valid sub-areas there are to choose as the ammunition storage. You can assume cell heights are distinct.

Input

The first line of input contains two space-separated integers $$$n$$$ and $$$m$$$ ($$$2 \leq n, m \leq 750$$$). Each of the next $$$n$$$ lines contains $$$m$$$ space-separated integers showing the cell heights. It is guaranteed cell heights are distinct numbers between $$$1$$$ and $$$nm$$$ (inclusive).

Output

Print the number of valid sub-areas to be used as an ammunition storage.

Example
Input
3 3
9 4 8
2 1 3
7 5 6
Output
7