sgu262：Symbol Recognition(状压DP)

题目大意：

给出k个n∗ m的01矩阵Si，求出一个1尽量少的n∗ m的01矩阵P，满足k个矩阵与该矩阵的交互不相同，也就是说通过该矩阵能表示出给出的k个矩阵。-262. Symbol Recognition



time limit per test: 0.25 sec.

memory limit per test: 65536 KB

input: standard

output: standard







Consider a monochrome computer monitor with N x M pixels resolution. It can display K symbols. Symbol is a non-empty set of black pixels on the screen. You are to write a program, that computes minimal possible amount of pixels, that are enough to recognize a symbol.



Input

First line of input contains integers N, M, K (1 <= N, M <= 10, 2 <= K <= 6). K blocks follow, separated by empty lines. Each block consists of N rows of M characters. It s a symbols representation on the N x M screen. `1　denotes black pixel, `0　denotes white pixel. You may assume that symbols are unique.



Output

Print on the first line of output the minimal possible amount of pixels that enough to recognize symbol. I.e. you have to find set of pixels that has different color in each pair of symbols. If there are several sets with equal amount of pixels, output any