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?

Input

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 $*a*_{*i*1}, *a*_{*i*2}, ..., *a*_{*im*}$ $(0 ≤ *a*_{*i*, *j*} ≤ 1)$ — the values in the cells of the $*i*$-th row.

Output

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