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 morph(desk, cur):
    k = 0
    for i in range(len(desk)):
        for j in range(len(desk)):
            if desk[i][j] != cur:
                k += 1
            cur = 1 - cur

    return k

n = int(input())

mf = []
m1 = []
m2 = []
m3 = []
m4 = []
for i in range(n):
    m = []
    s = input()
    for j in s:
        m.append(int(j))
    m1.append(m)

s = input()

for i in range(n):
    m = []
    s = input()
    for j in s:
        m.append(int(j))
    m2.append(m)

s = input()

for i in range(n):
    m = []
    s = input()
    for j in s:
        m.append(int(j))
    m3.append(m)

s = input()

for i in range(n):
    m = []
    s = input()
    for j in s:
        m.append(int(j))
    m4.append(m)

mf.append(m1)

mf.append(m2)

mf.append(m3)

mf.append(m4)
min = 4 * n * n + 1
for i in range(4):
    for j in range(i+1, 4):
        cur = 0
        cur += morph(mf[i], 1)
        cur += morph(mf[j], 1)
        for k in range(4):
            if k != i and k != j:
                cur += morph(mf[k], 0)

        if cur < min:
            min = cur
print(min)