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
n = int(input())
s1 = []
for i in range(n):
    s1.append(list(map(int,input())))
input()
s2 = []
for i in range(n):
    s2.append(list(map(int,input())))
input()
s3 = []
for i in range(n):
    s3.append(list(map(int,input())))
input()
s4 = []
for i in range(n):
    s4.append(list(map(int,input())))
a = [s1,s2,s3,s4]
b = [0,1,2,3]
m = float('inf')
for i in range(4):
    b = [0,1,2,3]
    f = []
    f.append(b[i])
    b.pop(i)
    
    for j in range(3):
        d= b[:]
        f.append(d[j])
        d.pop(j)
        for k in range(2):
            e= d[:]
            #print(e)
            f.append(e[k])
            e.pop(k)
            f.append(e[0])


            se = []
            for v in f:se.append(a[v])
            fa = 0
            if n%2==0:
                for seg in se:
                    for ii in range(n):
                        for jj in range(n):
                            if (ii+jj)%2 != seg[ii][jj]:
                                fa += 1
                m = min(m,fa,4*n*n-fa)
                #print(fa)
            else:
                for seg in se[:2]:
                    for ii in range(n):
                        for jj in range(n):
                            if (ii+jj)%2 != seg[ii][jj]:
                                fa += 1
                for seg in se[2:]:
                    for ii in range(n):
                        for jj in range(n):
                            if (ii+jj)%2 == seg[ii][jj]:
                                fa += 1
             #   print(fa)
                m = min(m,fa,4*n*n-fa)
            #print(m,f)
            f.pop()
            f.pop()
        f.pop()
    f.pop()
print(m)
