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())
import copy
a={0:[],1:[],2:[],3:[]}
for i in range(4):
    for j in range(n):
        a[i].append([int(k) for k in input()])
    if i != 3:
        f = input()
a1 = copy.deepcopy(a[0])
a2 = copy.deepcopy(a[0])
c1 = 1
c2 = 0
def chkdif(l1,l2):
    co = 0
    for i in range(len(l1)):
        for j in range(len(l1[i])):
            if l1[i][j] != l2[i][j]:
                co+=1
    return co
for i in range(n):
    for j in range(n):
        a1[i][j] = c1%2
        c1 += 1
an =[[0,0] for i in range(4)]
for i in range(n):
    for j in range(n):
        a2[i][j] = 1-a1[i][j]
'''for i in a1:
    print('a1')
    print(i)
print()
for i in a2:
    print(i)
print()
for i in a:
    for j in a[i]:
        print(j)
    print()'''
for i in a:
    an[i][0] = chkdif(a1,a[i])
    an[i][1] = chkdif(a2,a[i])
pa = []
pa.append(an[0][0]+an[1][0]+an[2][1]+an[3][1])
pa.append(an[0][0]+an[1][1]+an[2][0]+an[3][1])
pa.append(an[0][0]+an[1][1]+an[2][1]+an[3][0])
pa.append(an[0][1]+an[1][0]+an[2][0]+an[3][1])
pa.append(an[0][1]+an[1][1]+an[2][0]+an[3][0])
pa.append(an[0][1]+an[1][0]+an[2][1]+an[3][0])
print(min(pa))
