**Description**

Character recognition is the conversion of images into text. For now we consider each

character in the picture is a N*M matrix with only zeros and ones, and we need to

recognize K characters. You are to write a program to find minimal number of pixels so

that we can recognize each character.

For example, we have only two characters ‘T’ and ‘L’, and the matrix size is 3*3, we

can think ‘T’ and ‘L’ are

**Input**

The first line of input is three integers N, M, K (1 <= N, M <= 10, 2 <= K <= 6).

Which represents the size of matrix and number of characters. Then is following K

blocks, which represents the matrix. Notice that each block starts with a blank

line.

Output

You should output the minimum number of pixels, which is the answer.

**Sample test case**

**Input**

2 3 2

111

010

100

100

**output**

1