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
#Bhargey Mehta (Junior)
#DA-IICT, Gandhinagar
import sys, math, queue, bisect
from itertools import permutations
#sys.stdin = open('input.txt', 'r')
MOD = 998244353
sys.setrecursionlimit(1000000)

def cost(p, r, s, n):
    c = 0
    for i in range(n):
        for j in range(n):
            if p[i][j] != r[s][j]:
                c += 1
        s = s^1
    return c

n = int(input())
p = [[], [], [], []]
for i in range(4):
    for j in range(n):
        p[i].append(input())
    if i < 3: input()
c = [[], []]
for i in range(n):
    c[(i&1)].append('0')
    c[(i&1)^1].append('1')
c[0] = ''.join(c[0])
c[1] = ''.join(c[1])

ans = 5*n*n
for perm in permutations(range(4)):
    u, v, w, x = perm
    pc = 0
    pc += cost(p[u], c, 0, n)
    pc += cost(p[v], c, 1, n)
    pc += cost(p[w], c, 1, n)
    pc += cost(p[x], c, 0, n)
    ans = min(ans, pc)
print(ans)