CF961C Chessboard

Magnus decided to play a classic chess game. Though what he saw in his locker shocked him! His favourite chessboard got broken into $ 4 $ pieces, each of size $ n $ by $ n $ , $ n $ is always odd. And what's even worse, some squares were of wrong color. $ j $ -th square of the $ i $ -th row of $ k $ -th piece of the board has color $ a_{k,i,j} $ ; $ 1 $ being black and $ 0 $ being white. Now Magnus wants to change color of some squares in such a way that he recolors minimum number of squares and obtained pieces form a valid chessboard. Every square has its color different to each of the neightbouring by side squares in a valid board. Its size should be $ 2n $ by $ 2n $ . You are allowed to move pieces but not allowed to rotate or flip them.

The first line contains odd integer $ n $ $ (1

Print one number — minimum number of squares Magnus should recolor to be able to obtain a valid chessboard.