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
#in
import math

n = int(input())

parts = []
for i in range(0, 4):
    part = []
    for j in range(0, n):
        part.append(int(input(),2))
    if(i < 3):
        input()    
    parts.append(part)    

#proc
mask = 0
for i in range(0, int((n+1)/2)):
    mask += int(math.pow(2,2*i))
    
def onesCount(num):
    counter = 0
    while num != 0:
        if((num & 1) == 1):
            counter+=1
        num = num>>1    
    return counter        
    
difs = []
for part in parts:
    dif = 0
    for i in range(0, n):
        if i % 2 == 0:
            dif += onesCount(part[i]^mask)
        else:
            dif += n - onesCount(part[i]^mask)
    difs.append(dif)    
    
difs.sort()    

min = difs[0] + difs[1] + (n * n - difs[2]) + (n * n - difs[3])
 
#out
print(min)



