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.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;


public class d {

	public static void main(String[] args) throws Exception {
		in = new BufferedReader(new InputStreamReader(System.in));
		out = new PrintWriter(System.out);
		sc = new FastScanner(in);
		int t = 1;

		while (t-- > 0) {
			int n = sc.nextInt();
			ArrayList<Integer> arr = new ArrayList<Integer>();
			int[] dp = new int[n];
			String a = sc.nextToken();
			String b = sc.nextToken();
			int ans1 = 0 ;
			int ans2 =  0 ; 
			Stack<Character> st = new  Stack<>();
			for(int i = 0 ;i < n ;i++) {
				if(a.charAt(i)!=b.charAt(i)) {
				    if(st.isEmpty()) {
				    	st.add(a.charAt(i));
				    	if(a.charAt(i)=='0')
						ans1 = Math.max(ans1  , st.size());
				    	else
				    		ans2 = Math.max(ans2  , st.size());
				    	continue;
				    }
			
					if(!st.isEmpty() && st.peek()!=a.charAt(i)) {
						st.pop();
					}else {
						st.push(a.charAt(i));
					}
					if(!st.isEmpty()) {
					if( st.peek()=='0')
						ans1 = Math.max(ans1  , st.size());
				    else
				    	ans2 = Math.max(ans2  , st.size());}
				}
			}
//			while(arr.size()>0) {
//				int s = -1;
//				int ini = arr.size();
//				ans++;
//				int cou = 0 ;
//				ArrayList<Integer> temp = new ArrayList<Integer>();
//				for(int i : arr) {
//					if(s==-1 || s!=dp[i]) {
//						s= dp[i];
//						cou++;
//					}
//					else {
//						temp.add(i);
//					}
//				}
//				if(cou%2==1) {
//					temp.add(arr.remove(arr.size()-1));
//				}
//				if(ini==temp.size()) {
//					System.out.println(-1);
//					return;
//				}
//				arr =temp;
//			}
			if(st.size()>0)
				out.println(-1);
			else
			out.println(ans1+ans2);
		}

		out.flush();

	}

	static BufferedReader in;
	static FastScanner sc;
	static PrintWriter out;

	static class FastScanner {
		BufferedReader in;
		StringTokenizer st;

		public FastScanner(BufferedReader in) {
			this.in = in;
		}

		public String nextToken() throws Exception {
			while (st == null || !st.hasMoreTokens()) {
				st = new StringTokenizer(in.readLine());
			}
			return st.nextToken();
		}

		public int nextInt() throws Exception {
			return Integer.parseInt(nextToken());
		}

		public long nextLong() throws Exception {
			return Long.parseLong(nextToken());
		}

		public double nextDouble() throws Exception {
			return Double.parseDouble(nextToken());
		}
	}
}
