SP4329 KRECT - Counting K-Rectangle

[English](/problems/KRECT/en/) [Vietnamese](/problems/KRECT/vn/) Given a M\*N square board. Each square contains a letter of the English alphabet ('A' .. 'Z'). A K-rectangle of the board is a rectangle whose sides are parallel to the sides of the board, and contains exactly K different types of letter. For example, with this 4\*3 board: ``` CED CEB CBC DDA ``` The rectangle \[(1,1), (2,2)\] is a 2-rectangle of the board because it contains 2 different letters: C and E. Given M, N, K and the M\*N board. Determine how many K-rectangles there are in the board.

The first line contains 3 integers M, N and K. (1 ≤ M, N ≤ 100, 1 ≤ K ≤ 26) The following M lines, each contains N letters of the English alphabet ('A' .. 'Z')

Write one integer - the number of K-rectangles in the given board.