Problem hidden
This problem was hidden by Editorial Board member probably because it has incorrect language version or invalid test data, or description of the problem is not clear.
Problem hidden

MOON3 - Moon Safari

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.

Input

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')

Output

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

Example

Input:
4 3 3
CED
CEB
CBC
DDA


Output:
12


Added by:Francky
Date:2014-06-07
Time limit:1s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ASM64
© Spoj.com. All Rights Reserved. Spoj uses Sphere Engine™ © by Sphere Research Labs.