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 ak, 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.

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
import atexit
import io
import sys

# Buffering IO
_INPUT_LINES = sys.stdin.read().splitlines()
input = iter(_INPUT_LINES).__next__
_OUTPUT_BUFFER = io.StringIO()
sys.stdout = _OUTPUT_BUFFER

@atexit.register
def write():
    sys.__stdout__.write(_OUTPUT_BUFFER.getvalue())
    

def main():
    n = int(input())
    s = []
    for i in range(4):
        df = 0
        for k in range(n):
            l = input()
            for j in range(n):
                if int(l[j]) == (k + j) % 2:
                    df += 1
        if i <3 :
            input()
        s.append(df)
    
    print( min(s[0] + s[1] + n*n-s[2] + n*n-s[3],
        s[0] + s[2] + n*n-s[1] + n*n-s[3],
        s[0] + s[3] + n*n-s[1] + n*n-s[2],
        s[1] + s[2] + n*n-s[0] + n*n-s[3],
        s[1] + s[3] + n*n-s[0] + n*n-s[2],
        s[2] + s[3] + n*n-s[0] + n*n-s[1]))
        
        
    
    
    

    
if __name__ == '__main__':
    main()
        