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
import heapq
import random
import collections

# available on Google, not available on Codeforces
# import numpy as np
# import scipy


def maxSubArraySum(arr): 
       
    max_so_far = 0
    max_ending_here = 0
       
    for a in arr: 
        max_ending_here = max_ending_here + a 
        if (max_so_far < max_ending_here): 
            max_so_far = max_ending_here 
  
        if max_ending_here < 0: 
            max_ending_here = 0   
    return max_so_far 


def solve(arr, brr):  # fix inputs here
    console("----- solving ------")

    ar = []
    br = []

    if collections.Counter(arr)["0"] != collections.Counter(brr)["0"]:
        return -1

    for a,b in zip(arr,brr):
        if a == b:
            continue
        ar.append(2*int(a)-1)
        br.append(2*int(b)-1)
        # ar.append(int(a))
        # br.append(int(b))

    return max(maxSubArraySum(ar), maxSubArraySum(br))
        

def console(*args):  # the judge will not read these print statement
    print('\033[36m', *args, '\033[0m', file=sys.stderr)
    return


# for case_num in range(int(input())):
# read line as a string
# strr = input()

# read line as an integer
_ = int(input())
arr = input()
brr = input()

# read one line and parse each word as a string
# lst = input().split()

# read one line and parse each word as an integer
# lst = list(map(int,input().split()))

# read matrix and parse as integers (after reading read nrows)
# lst = list(map(int,input().split()))
# nrows = lst[0]  # index containing information, please change
# grid = []
# for _ in range(nrows):
#     grid.append(list(map(int,input().split())))

res = solve(arr, brr)  # please change

assert res == solve(brr, arr)

# Google - case number required
# print("Case #{}: {}".format(case_num+1, res))

# Codeforces - no case number required
print(res)
