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.
import sys
from fractions import gcd
from math import ceil,sqrt,sin,pi,tan
from collections import defaultdict
read=sys.stdin.buffer.readline
import heapq
mi=lambda:map(int,read().split())
li=lambda:list(mi())
cin=lambda:int(read())

def sol():
    pass

def isp(n):
    i=2
    while i*i<=n:
        if n%i==0:
            return False
        i+=1
    return True

for _t in range(1):
    n=int(input())
    a=input()
    b=input()
    s=''
    e0,e1=0,0
    nz,no=0,0
    for i in range(n):
        if a[i]!=b[i]:
            if b[i]=='1':
                no+=1
                if e0>0:
                    e0-=1
                e1+=1
            else:
                nz+=1
                if e1>0:
                    e1-=1
                e0+=1
    if nz!=no:
        print(-1)
    else:
        print(e0+e1)