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
s = input()
tab_temp_1 = [0]*s
tab_temp_2 = [0]*s
tab_temp_3 = [0]*s
tab_temp_4 = [0]*s
chess = ''
wynik = 999999999
pat = ''
pat_1 = ''
for x in range(0, 2*s, +1):
    for y in range(0, 2*s, +1):
        if x%2 == 0:
            if y%2 == 0:
                pat += '1'
                pat_1 += '0'
            else:
                pat += '0'
                pat_1 += '1'
        else:
            if y%2 == 0:
                pat += '0'
                pat_1 += '1'
            else:
                pat += '1'
                pat_1 += '0'
def hash(tab_1, tab_2, tab_3, tab_4, pat, pat_1):
    wyn = 0
    wyn_2 = 0
    chess_fun = ''
    for x in range(0, s, +1):
        chess_fun += tab_1[x]
        chess_fun += tab_2[x]
    for x in range(0, s, +1):
        chess_fun += tab_3[x]
        chess_fun += tab_4[x]
    for x in range(0, len(chess_fun), +1):
            if chess_fun[x] != pat[x]:
                wyn += 1
    for x in range(0, len(chess_fun), +1):
            if chess_fun[x] != pat_1[x]:
                wyn_2 += 1
    return min(wyn,wyn_2)
for x in range(0, s, +1):
    txt_in = str(raw_input())
    if txt_in != '':
        tab_temp_1[x] = txt_in
txt_in = raw_input()
for x in range(0, s, +1):
    txt_in = str(raw_input())
    if txt_in != '':
        tab_temp_2[x] = txt_in
txt_in = raw_input()
for x in range(0, s, +1):
    txt_in = str(raw_input())
    if txt_in != '':
        tab_temp_3[x] = txt_in
txt_in = raw_input()
for x in range(0, s, +1):
    txt_in = str(raw_input())
    if txt_in != '':
        tab_temp_4[x] = txt_in
wynik = min(wynik, hash(tab_temp_1, tab_temp_2, tab_temp_3, tab_temp_4, pat, pat_1))
wynik = min(wynik, hash(tab_temp_1, tab_temp_2, tab_temp_4, tab_temp_3, pat, pat_1))
wynik = min(wynik, hash(tab_temp_1, tab_temp_3, tab_temp_2, tab_temp_4, pat, pat_1))
wynik = min(wynik, hash(tab_temp_1, tab_temp_3, tab_temp_4, tab_temp_2, pat, pat_1))
wynik = min(wynik, hash(tab_temp_1, tab_temp_4, tab_temp_2, tab_temp_3, pat, pat_1))
wynik = min(wynik, hash(tab_temp_1, tab_temp_4, tab_temp_3, tab_temp_2, pat, pat_1))
wynik = min(wynik, hash(tab_temp_2, tab_temp_1, tab_temp_3, tab_temp_4, pat, pat_1))
wynik = min(wynik, hash(tab_temp_2, tab_temp_1, tab_temp_4, tab_temp_3, pat, pat_1))
wynik = min(wynik, hash(tab_temp_2, tab_temp_3, tab_temp_1, tab_temp_4, pat, pat_1))
wynik = min(wynik, hash(tab_temp_2, tab_temp_3, tab_temp_4, tab_temp_1, pat, pat_1))
wynik = min(wynik, hash(tab_temp_2, tab_temp_4, tab_temp_1, tab_temp_3, pat, pat_1))
wynik = min(wynik, hash(tab_temp_2, tab_temp_4, tab_temp_3, tab_temp_1, pat, pat_1))
wynik = min(wynik, hash(tab_temp_3, tab_temp_1, tab_temp_2, tab_temp_4, pat, pat_1))
wynik = min(wynik, hash(tab_temp_3, tab_temp_1, tab_temp_4, tab_temp_2, pat, pat_1))
wynik = min(wynik, hash(tab_temp_3, tab_temp_2, tab_temp_1, tab_temp_4, pat, pat_1))
wynik = min(wynik, hash(tab_temp_3, tab_temp_2, tab_temp_4, tab_temp_1, pat, pat_1))
wynik = min(wynik, hash(tab_temp_3, tab_temp_4, tab_temp_2, tab_temp_1, pat, pat_1))
wynik = min(wynik, hash(tab_temp_3, tab_temp_4, tab_temp_1, tab_temp_2, pat, pat_1))
wynik = min(wynik, hash(tab_temp_4, tab_temp_1, tab_temp_2, tab_temp_3, pat, pat_1))
wynik = min(wynik, hash(tab_temp_4, tab_temp_1, tab_temp_3, tab_temp_2, pat, pat_1))
wynik = min(wynik, hash(tab_temp_4, tab_temp_2, tab_temp_1, tab_temp_3, pat, pat_1))
wynik = min(wynik, hash(tab_temp_4, tab_temp_2, tab_temp_3, tab_temp_1, pat, pat_1))
wynik = min(wynik, hash(tab_temp_4, tab_temp_3, tab_temp_2, tab_temp_1, pat, pat_1))
wynik = min(wynik, hash(tab_temp_4, tab_temp_3, tab_temp_1, tab_temp_2, pat, pat_1))
print wynik