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C. Chessboard

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputMagnus 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 2*n* by 2*n*. You are allowed to move pieces but not allowed to rotate or flip them.

Input

The first line contains odd integer *n* (1 ≤ *n* ≤ 100) — the size of all pieces of the board.

Then 4 segments follow, each describes one piece of the board. Each consists of *n* lines of *n* characters; *j*-th one of *i*-th line is equal to 1 if the square is black initially and 0 otherwise. Segments are separated by an empty line.

Output

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

Examples

Input

1

0

0

1

0

Output

1

Input

3

101

010

101

101

000

101

010

101

011

010

101

010

Output

2

Codeforces (c) Copyright 2010-2022 Mike Mirzayanov

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