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.*;
import java.util.*;
public class Sol{
	final public static long MOD = 998244353;
	public static void main(String[] args) throws IOException{
		PrintWriter out = new PrintWriter(System.out);
		FastIO sc = new FastIO(System.in);
		int n = sc.nextInt();
		String str = sc.next();
		int s[] = new int[n];
		int ones = 0;
		int onet = 0;
		for(int i=0; i <n; ++i) {
			s[i] = str.charAt(i)-'0';
			if(s[i]==0) ones++;
		}
		str = sc.next();
		int t[] = new int[n];
		for(int i=0; i<n; ++i) {
			t[i] = str.charAt(i)-'0';
			if(t[i]==0)onet++;
		}
		if(ones!=onet) {
			System.out.println(-1);
			System.exit(0);
		}
		ArrayList<Integer> diff = new ArrayList<>();
		for(int i=0; i<n; ++i) {
			if(s[i]!=t[i]) {
				diff.add(t[i]);
			}
 		}
		int ans =0;
		int curr =0;
		int num = 0;
		for(int i=0; i<diff.size(); ++i) {
			if(diff.get(i)==num)curr++;
			else curr--;
			ans = Math.max(ans, curr);
		}	
		int best = 0;
		num = 1;
		curr = 0;
		for(int i=0; i<diff.size(); ++i) {
			if(diff.get(i)==num)curr++;
			else curr--;
			best = Math.max(best, curr);
		}
		System.out.println(ans+best);
		out.close();
	}
	static class FastIO {
		InputStream dis;
		byte[] buffer = new byte[1 << 17];
		int pointer = 0;
		public FastIO(String fileName) throws IOException {
			dis = new FileInputStream(fileName);
		}
		public FastIO(InputStream is) throws IOException {
			dis = is;
		}
		int nextInt() throws IOException {
			int ret = 0;
 
			byte b;
			do {
				b = nextByte();
			} while (b <= ' ');
			boolean negative = false;
			if (b == '-') {
				negative = true;
				b = nextByte();
			}
			while (b >= '0' && b <= '9') {
				ret = 10 * ret + b - '0';
				b = nextByte();
			}
 
			return (negative) ? -ret : ret;
		}
		long nextLong() throws IOException {
			long ret = 0;
 
			byte b;
			do {
				b = nextByte();
			} while (b <= ' ');
			boolean negative = false;
			if (b == '-') {
				negative = true;
				b = nextByte();
			}
			while (b >= '0' && b <= '9') {
				ret = 10 * ret + b - '0';
				b = nextByte();
			}
			return (negative) ? -ret : ret;
		}
		byte nextByte() throws IOException {
			if (pointer == buffer.length) {
				dis.read(buffer, 0, buffer.length);
				pointer = 0;
			}
			return buffer[pointer++];
		}
		String next() throws IOException {
			StringBuffer ret = new StringBuffer();
 
			byte b;
			do {
				b = nextByte();
			} while (b <= ' ');
			while (b > ' ') {
				ret.appendCodePoint(b);
				b = nextByte();
			}
 
			return ret.toString();
		}
	}
}