Sereja has an n \times m rectangular table a, each cell of the table contains a zero or a number one. Sereja wants his table to meet the following requirement: each connected component of the same values forms a rectangle with sides parallel to the sides of the table. Rectangles should be filled with cells, that is, if a component form a rectangle of size h \times w, then the component must contain exactly hw cells.

A connected component of the same values is a set of cells of the table that meet the following conditions:
every two cells of the set have the same value; the cells of the set form a connected region on the table (two cells are connected if they are adjacent in some row or some column of the table); it is impossible to add any cell to the set unless we violate the two previous conditions.
Can Sereja change the values of at most k cells of the table so that the table met the described requirement? What minimum number of table cells should he change in this case?

The first line contains integers n, m and k (1 \le n,m \le 100;1 \le k \le 10). Next n lines describe the table a: the i-th of them contains m integers ai1,ai2,...,aim (0 \le ai,j \le 1) - the values in the cells of the i-th row.

Print -1, if it is impossible to meet the requirement. Otherwise, print the minimum number of cells which should be changed.