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 java.util.*;

public class E{
	
		
	public static void main(String[] args){
		Scanner in = new Scanner(System.in);
		StringBuilder str = new StringBuilder();
		int n = in.nextInt();
		String a = in.next();
		String b = in.next();
		int res = 0;
		int counta = 0;
		int countb = 0;
		int count01 = 0;
		int count10 = 0;
		int equal = 0;
		for(int i = 0;i<n;++i){
			int digita = a.charAt(i) -'0';
			int digitb = b.charAt(i) -'0';
			counta += digita;
			countb += digitb;
			equal += digita==digitb ? 1 : 0;
			if(digita != digitb){
				if(digita == 1){
					count10++;
					if(count01 > 0)
						count01--;
				} else{
					count01++;
					if(count10 > 0)
						count10--;
				}
			}
		}
		res = count01 + count10;
		if(counta != countb){
			res = -1;
		}
		System.out.println(res);
	}
}

			