The Do-Barareh military area is like an 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 , 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.
输入格式
The first line of input contains two space-separated integers and (). Each of the next lines contains space-separated integers showing the cell heights. It is guaranteed cell heights are distinct numbers between and (inclusive).
输出格式
Print the number of valid sub-areas to be used as an ammunition storage.
