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 collections import defaultdict as dd
from collections import Counter as cc
from queue import Queue
import math
import itertools
try:
	sys.stdin = open('input.txt', 'r') 
	sys.stdout = open('output.txt', 'w')
except:
	pass
# input = lambda: sys.stdin.buffer.readline().rstrip()


q=int(input())
w=input()
e=input()
r=[]
if w.count('1')!=e.count('1'):
	print(-1)
	exit()
if w.count('1')==q or w.count('1')==0:
	print(0)
	exit()
for i in range(q):
	if w[i]!=e[i]:
		r.append(e[i])
k=0
l=[]
for i in r:
	if i=='1':
		k+=1
	else:
		k-=1
	l.append(k)
print(max(l)-min(l))