Vasya has recently started to learn English. Now he needs to remember how to write English letters. He isn't sure about some of them, so he decided to train a little.

He found a sheet of squared paper and began writing arbitrary English letters there. In the end Vasya wrote n lines containing m characters each. Thus, he got a rectangular n×m table, each cell of the table contained some English letter. Let's number the table rows from top to bottom with integers from 1 to n, and columns − from left to right with integers from 1 to m.

After that Vasya looked at the resulting rectangular table and wondered, how many subtables are there, that matches both following conditions:

• the subtable contains at most k cells with "a" letter;
• all letters, located in all four corner cells of the subtable, are equal.

Formally, a subtable's definition is as follows. It is defined by four integers x₁,y₁,x₂,y₂ such that 1≤x₁<x₂≤n, 1≤y₁<y₂≤m. Then the subtable contains all such cells (x,y) (x is the row number, y is the column number), for which the following inequality holds x₁≤x≤x₂,y₁≤y≤y₂. The corner cells of the table are cells (x₁,y₁), (x₁,y₂), (x₂,y₁), (x₂,y₂).

Vasya is already too tired after he's been writing letters to a piece of paper. That's why he asks you to count the value he is interested in.