As for a 01-matrix(whose entries are all either 0 or 1, similarly hereinafter) of size , an index set of the matrix is considered good if following two conditions are satisfied:

1. , for all
2.  For each entry , there exists an index satisfying the following two conditions at the same time:

Moreover, the value of a 01-matrix is the minimum size among all of its good index sets.

Now given a 012-matrix, you should replace all the 2 entries to 0 or 1, and determine the minimum possible value among all replacing schemes. As can be seen, there are totally replacing schemes, where denotes the number of 2 entries in the given matrix.

The first line contains two integers , denoting the size of given 012-matrix.

Following  lines each contains one 012-string of length , where the -th character in the -th line among the  lines denotes entry .

Output one line containing one integer, denoting the minimum possible value after replacing.

3 7
0001101
0201020
0001101

3

One possible replacing scheme is:

One possible good set of the minimum size is