Ramps

You are given an $N \times N$ map. Each cell holds the height of the ground there.

You want to count how many roads on this map can be crossed. A road is one whole row or one whole column, and crossing it means going from one end to the other end. There are $2N$ roads in total.

Look at this map with $N = 6$.

Its $2N$ roads are drawn below.

A road can be crossed when every cell on it has the same height. Otherwise you can lay ramps to build a road you can cross. A ramp always has height 1 and length $L$, and you never run out of ramps. A ramp connects a lower cell to a higher cell and must satisfy the following conditions.

• A ramp is laid on the lower side, and its bottom must touch $L$ consecutive cells along their whole length.
• The height difference between the lower cell and the higher cell must be 1.
• The $L$ cells under a ramp must be consecutive and must all have the same height.

A ramp cannot be laid in the following cases.

• Laying a ramp on a cell that another ramp already covers.
• The height difference between the lower cell and the higher cell is not 1.
• The cells on the lower side do not all have the same height, or $L$ of them are not consecutive.
• The ramp runs outside the map.

The picture below shows where a ramp can be laid when $L = 2$.

The next picture shows cases where a ramp cannot be laid.

Number those four cases 1 to 4 from the left. Case 1 fails because the height difference is not 1, case 2 because the bottom of the ramp does not touch the cells, case 3 because the ramps overlap, and case 4 because the ramp is laid at a slant.

For the $N = 6$ map shown at the top with $L = 2$, the roads that can be crossed are drawn in blue and the roads that cannot are drawn in red.

Given the map, write a program that counts the roads that can be crossed.

The first line contains $N$ ($2 \le N \le 100$) and $L$ ($1 \le L \le N$). Each of the next $N$ lines contains $N$ numbers describing the map. The height of a cell is a natural number not greater than 10.

Print the number of roads that can be crossed on the first line.