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
input=lambda : stdin.readline().strip()
from math import ceil,sqrt,gcd
from collections import deque
n=int(input())
s=list(input())
t=list(input())
o=0
z=0
x=[]
for i in range(n):
	if s[i]=='1':
		o+=1
	else:
		z+=1
	if t[i]=='1':
		o-=1
	else:
		z-=1
if z==0 and o==0:
	st1=[]
	st2=[]
	for i in range(n):
		if s[i]=='1' and t[i]=='0':
			if len(st1)==0:
				x.append([i])
				st2.append(len(x)-1)
			else:
				ne=st1.pop()
				x[ne].append(i)
				st2.append(ne)
		elif s[i]=='0' and t[i]=='1':
			if len(st2)==0:
				x.append([i])
				st1.append(len(x)-1)
			else:
				ne=st2.pop()
				x[ne].append(i)
				st1.append(ne)
	print(len(x))
	# print(x)
else:
	print(-1)