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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Collections;
import java.util.StringTokenizer;
import java.util.TreeSet;

public class E {

	public static void main(String[] args) {
		FastScanner fs=new FastScanner();
		int n=fs.nextInt();
		char[] line1=fs.next().toCharArray();
		char[] line2=fs.next().toCharArray();
		TreeSet<Integer> pluses=new TreeSet<>(), minuses=new TreeSet<>();
		for (int i=0; i<n; i++) {
			if (line1[i]==line2[i]) continue;
			if (line1[i]=='0') pluses.add(i);
			else minuses.add(i);
		}
		
		if (pluses.size()!=minuses.size()) {
			System.out.println(-1);
			return;
		}
		int turns=0;
		while (!pluses.isEmpty()) {
			TreeSet<Integer> a=null, b=null;
			if (pluses.first()<minuses.first()) {
				a=pluses;
				b=minuses;
			}
			else {
				a=minuses;
				b=pluses;
			}
			int pos=-1;
			while (true) {
				Integer higher=a.higher(pos);
				if (higher==null) break;
				Integer bHigher=b.higher(higher);
				if (bHigher==null) break;
				a.remove(higher);
				b.remove(bHigher);
				pos=bHigher;
			}
			turns++;
		}
		System.out.println(turns);
	}

	static void sort(int[] a) {
		ArrayList<Integer> l=new ArrayList<>();
		for (int i:a) l.add(i);
		Collections.sort(l);
		for (int i=0; i<a.length; i++) a[i]=l.get(i);
	}
	
	static class FastScanner {
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st=new StringTokenizer("");
		String next() {
			while (!st.hasMoreTokens())
				try {
					st=new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			return st.nextToken();
		}
		
		int nextInt() {
			return Integer.parseInt(next());
		}
		int[] readArray(int n) {
			int[] a=new int[n];
			for (int i=0; i<n; i++) a[i]=nextInt();
			return a;
		}
		long nextLong() {
			return Long.parseLong(next());
		}
	}

	
}
