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*<sub class="lower-index">*i*1</sub>, *a*<sub class="lower-index">*i*2</sub>, ..., *a*<sub class="lower-index">*im*</sub> (0 ≤ *a*<sub class="lower-index">*i*, *j*</sub> ≤ 1) — the values in the cells of the *i*-th row.
print("_RANDOM_GUESS_1691392811.1827707")# 1691392811.1827881