Naman has two binary strings s and t of length n (a binary string is a string which only consists of the characters "0" and "1"). He wants to convert s into t using the following operation as few times as possible.

In one operation, he can choose any subsequence of s and rotate it clockwise once.

For example, if s = 1110100, he can choose a subsequence corresponding to indices (1-based) \{2, 6, 7 \} and rotate them clockwise. The resulting string would then be s = 1010110.

A string a is said to be a subsequence of string b if a can be obtained from b by deleting some characters without changing the ordering of the remaining characters.

To perform a clockwise rotation on a sequence c of size k is to perform an operation which sets c_1:=c_k, c_2:=c_1, c_3:=c_2, …, c_k:=c_{k-1} simultaneously.

Determine the minimum number of operations Naman has to perform to convert s into t or say that it is impossible. 

Input

The first line contains a single integer n (1 ≤ n ≤ 10^6) — the length of the strings.

The second line contains the binary string s of length n.

The third line contains the binary string t of length n.

Output

If it is impossible to convert s to t after any number of operations, print -1.

Otherwise, print the minimum number of operations required.

Examples

Input


6
010000
000001


Output


1

Input


10
1111100000
0000011111


Output


5

Input


8
10101010
01010101


Output


1

Input


10
1111100000
1111100001


Output


-1

Note

In the first test, Naman can choose the subsequence corresponding to indices \{2, 6\} and rotate it once to convert s into t.

In the second test, he can rotate the subsequence corresponding to all indices 5 times. It can be proved, that it is the minimum required number of operations.

In the last test, it is impossible to convert s into t.
from sys import stdin, stdout

# 6
# 010000
# 000001
#  1   0
#
# 101000
# 101  1
# 010110
#
# 1010100
# 0100011
# 101 100
#
# 10
# 1111100000
# 0000011111
# 1111100000
#
# if count(s0) == count(t0), count(s1) == count(t1)
#   res <= count(dif bit) // 2
if __name__ == '__main__':
    n = int(stdin.readline())
    s = stdin.readline().strip()
    t = stdin.readline().strip()


    def binary_subsequence_rotation(n, s, t):
        scnt0 = 0
        scnt1 = 0
        tcnt0 = 0
        tcnt1 = 0

        for i in range(n):
            if s[i] == '0':
                scnt0 += 1
            else:
                scnt1 += 1

            if t[i] == '0':
                tcnt0 += 1
            else:
                tcnt1 += 1

        if scnt0 != tcnt0 or scnt1 != tcnt1:
            return -1

        tl0 = 0
        tl1 = 0
        for i in range(n):
            if s[i] == t[i]:
                continue

            if s[i] == '1':
                if tl0 == 0:
                    tl1 += 1
                else:
                    tl0 -= 1
                    tl1 += 1
            else:
                if tl1 == 0:
                    tl0 += 1
                else:
                    tl1 -= 1
                    tl0 += 1

        return tl0 + tl1


    print(str(binary_subsequence_rotation(n, s, t)))
