A9377 | Sereja and Table

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.