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 itertools
n = int(input())
t1 = [[] for i in range(n)]
t2 = [[] for i in range(n)]
t3 = [[] for i in range(n)]
t4 = [[] for i in range(n)]

for i in range(n):
    a = list(input())
    t1[i] = a
w = input()

for i in range(n):
    a = list(input())
    t2[i] = a
w = input()

for i in range(n):
    a = list(input())
    t3[i] = a
w = input()

for i in range(n):
    a = list(input())
    t4[i] = a

rec1, rec2 = [0, 0, 0, 0], [0, 0, 0, 0]
for i in range(n):
    if i % 2 == 0:
        p = 1
    else:
        p = 0
    for j in range(n):
        if int(t1[i][j]) != p:
            rec1[0] += 1
        else:
            rec2[0] += 1
        p ^= 1

for i in range(n):
    if i % 2 == 0:
        p = 1
    else:
        p = 0
    for j in range(n):
        if int(t2[i][j]) != p:
            rec1[1] += 1
        else:
            rec2[1] += 1
        p ^= 1

for i in range(n):
    if i % 2 == 0:
        p = 1
    else:
        p = 0
    for j in range(n):
        if int(t3[i][j]) != p:
            rec1[2] += 1
        else:
            rec2[2] += 1
        p ^= 1

for i in range(n):
    if i % 2 == 0:
        p = 1
    else:
        p = 0
    for j in range(n):
        if int(t4[i][j]) != p:
            rec1[3] += 1
        else:
            rec2[3] += 1
        p ^= 1

R = [0, 1, 2, 3]
num = float("inf")
for a, b, c, d in itertools.permutations(R, 4):
    num = min(num, rec1[a] + rec1[b] + rec2[c] + rec2[d])

print(num)