K. Knockout Spell
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

John is an enthusiast of online role-playing games. This afternoon, he started playing a new game where he can choose from different types of fantastic characters. As usual, John always chooses a wizard. Like in most role-playing games, John's character starts at level 1, and as he progresses in the game and defeats enemies, his level increases. At the maximum level, a wizard has the ability to cast the knockout spell.

The knockout spell is a skill that is cast over a square area measuring $$$K$$$ cells on each side, as long as the corners of that area have the same type of terrain. Since this spell is obtained at the maximum level, it is the most powerful and it knocks out all enemies within the invoked area.

John has acquired a digital map of the game, which is represented by a square matrix measuring $$$N$$$ rows and $$$N$$$ columns. Each cell in the matrix contains a number between 0 and 9, representing the type of terrain on the map. Since John has already leveled up his wizard to the maximum level, he wants to know the number of different areas over which he can cast the knockout spell. The map is too large to count the areas manually so he asked for your help: Given the map of the game and the size $$$K$$$ of the squares in which a wizard can cast the knockout spell, you need to determine in how many different areas John can cast the knockout spell.

Input

The first line of input contains two integer numbers separated by a space $$$N$$$ ($$$2 \leq N \leq 1000$$$) and $$$K$$$ ($$$2 \leq K \leq N$$$), representing the size of the map, and the size of the square where the knockout spell can be casted.

Each of the next $$$N$$$ lines contains $$$N$$$ an integer number between $$$0$$$ and $$$9$$$, representing, the type of terrain on each cell of the map.

Output

Print a line with an integer number, the number of different areas where John can cast the knockout spell on the game.

Examples
Input
2 2
0 0
0 0
Output
1
Input
2 2
1 2
1 1
Output
0
Input
5 3
1 5 1 6 1
1 7 8 9 5
1 1 1 1 1
1 2 3 4 1
1 1 1 1 1
Output
5