Sereja has an n×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×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≤n,m≤100;1≤k≤10). Next n lines describe the table a: the i-th of them contains m integers a_i1,a_i2,...,a_im (0≤a_i,j≤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.