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
def s1(a,b):
    su = 0
    for i in range(len(a)):
        for j in range(len(a)):
            if (a[i][j]!=b[i][j]):
                su+=1
    return su
def s2(a,b):
    su = 0
    for i in range(len(a)):
        for j in range(len(a)):
            if (a[i][j]==b[i][j]):
                su+=1
    return su 
n = int(input())
ideal1,ideal2 = [],[]
for i in range(n):
    ideal1.append([])
    ideal2.append([])
    for j in range(n):
        if ((i+j)%2==0):
            ideal1[i].append(0)
            ideal2[i].append(1)
        else:
            ideal1[i].append(1)
            ideal2[i].append(0)
            
b = [[],[],[],[]]
for i in range(n):
    s = input()
    b[0].append([])
    for j in range(len(s)):
        if (s[j]=='0'):
            b[0][i].append(0)
        else:
            b[0][i].append(1)
s = input()            
for i in range(n):
    s = input()
    b[1].append([])
    for j in range(len(s)):
        if (s[j]=='0'):
            b[1][i].append(0)
        else:
            b[1][i].append(1)
s = input()            
for i in range(n):
    s = input()
    b[2].append([])
    for j in range(len(s)):
        if (s[j]=='0'):
            b[2][i].append(0)
        else:
            b[2][i].append(1)
s = input()            
for i in range(n):
    s = input()
    b[3].append([])
    for j in range(len(s)):
        if (s[j]=='0'):
            b[3][i].append(0)
        else:
            b[3][i].append(1)
l = []            
for i in range(4):
    for j in range(4):
        if (i!=j):
            c1 = s1(b[i],ideal1)+s1(b[j],ideal1)
            c2 = s1(b[i],ideal2)+s1(b[j],ideal2)
            su1 = c1
            su2 = c2
            for k in range(4):
                if ((k!=i) and (k!=j)):
                    su1+=s2(b[k],ideal1)
                    su2+=s2(b[k],ideal2)
            l.append(min(su1,su2))        
print(min(l))                     
            
            


