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B. Sereja and Table

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputSereja 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*_{i1}, *a*_{i2}, ..., *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.

Examples

Input

5 5 2

1 1 1 1 1

1 1 1 1 1

1 1 0 1 1

1 1 1 1 1

1 1 1 1 1

Output

1

Input

3 4 1

1 0 0 0

0 1 1 1

1 1 1 0

Output

-1

Input

3 4 1

1 0 0 1

0 1 1 0

1 0 0 1

Output

0

Codeforces (c) Copyright 2010-2017 Mike Mirzayanov

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