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.
/*
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Don't let that studying and grades consume you
Just live life young
******************************
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1st on Billboard, what do you think of it
Next is a Grammy, what do you think of it
However you think, I’m sorry, but shit, I have no fcking interest
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I'm standing on top of my Monopoly board
That means I'm on top of my game and it don't stop
til my hip don't hop anymore
https://www.a2oj.com/Ladder16.html
*******************************
300IQ as writer = Sad!
*/
import java.util.*;
import java.io.*;
import java.math.*;

   public class E
   {
      public static void main(String hi[]) throws Exception
      {
         BufferedReader infile = new BufferedReader(new InputStreamReader(System.in));  
         StringTokenizer st = new StringTokenizer(infile.readLine());
         int N = Integer.parseInt(st.nextToken());
         char[] input = infile.readLine().toCharArray();
         char[] target = infile.readLine().toCharArray();
         int[] arr = new int[N]; int[] brr = new int[N];
         for(int i=0; i < N; i++)
         {
            if(input[i] == '1')
               arr[i] = 1;
            if(target[i] == '1')
               brr[i] = 1;
         }
         ArrayList<Integer> ls = new ArrayList<Integer>();
         for(int i=0; i < N; i++)
            if(arr[i] != brr[i])
               ls.add(arr[i]-brr[i]);
         int sum = 0;
         for(int x: ls) sum += x;
         int res = kd(ls, 1);
         res = Math.max(res, kd(ls, -1));
         if(sum != 0)
            res = -1;
         System.out.println(res);
      }
      public static int kd(ArrayList<Integer> ls, int mult)
      {
         int res = 0;
         int curr = 0;
         for(int x: ls)
         {
            curr += x*mult;
            res = Math.max(res, curr);
            curr = Math.max(curr, 0);
         }
         return res;
      }
   }