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 heapq


def doxor(a, b):
    cnt = 0
    for i in range(len(a)):
        for j in range(len(a[0])):
            cnt += a[i][j] ^ b[i][j]
    return cnt


n = int(input())

a, b = [], []
for i in range(n):
    ai, bi = [], []
    for j in range(n):
        if i % 2 == 0:
            ai.append(j % 2)
            bi.append((j % 2) ^ 1)
        else:
            ai.append((j % 2) ^ 1)
            bi.append(j % 2)
    a.append(ai)
    b.append(bi)

board = []
board.append([list(map(int, list(input()))) for _ in range(n)])
input()
board.append([list(map(int, list(input()))) for _ in range(n)])
input()
board.append([list(map(int, list(input()))) for _ in range(n)])
input()
board.append([list(map(int, list(input()))) for _ in range(n)])

a_cnts = []
b_cnts = []
for b0 in board:
    heapq.heappush(a_cnts, doxor(b0, a))
    heapq.heappush(b_cnts, doxor(b0, b))

print(heapq.heappop(a_cnts) + heapq.heappop(a_cnts) +
      heapq.heappop(b_cnts) + heapq.heappop(b_cnts))
