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 E implements Runnable {
	boolean oj = false;
	Reader scn;
	PrintWriter out;
	String INPUT = "";

	void solve() {
		int n = scn.nextInt(), q = 0;
		String s = scn.next(), t = scn.next();
		for (int i = 0; i < n; i++) {
			q += s.charAt(i) - '0';
			q -= t.charAt(i) - '0';
		}

		if (q != 0) {
			out.println(-1);
			return;
		}
		
		if(s.equals(t)) {
			out.println(0);
			return;
		}

		TreeSet<Integer> s1 = new TreeSet<Integer>();
		TreeSet<Integer> s2 = new TreeSet<Integer>();

		for (int i = 0; i < n; i++) {
			if (s.charAt(i) != t.charAt(i)) {
				if (s.charAt(i) == '0') {
					s1.add(i);
				} else {
					s2.add(i);
				}
			}
		}
		
		if(s1.first() > s2.first()) {
			TreeSet<Integer> temp = s1;
			s1 = s2;
			s2 = temp;
		}
		
		int ans = 0;
		while(true) {
			ans++;
			ArrayList<Integer> rem = new ArrayList<Integer>();
			
			int x = s1.first(), y = s2.first();
			while(true) {
				rem.add(x);
				rem.add(y);
				if(s1.higher(y) != null) {
					int a = s1.higher(y);
					if(s2.higher(a) != null) {
						int b = s2.higher(a);
						x = a;
						y = b;
					} else {
						break;
					}
				} else {
					break;
				}
			}
			for(int r : rem) {
				s1.remove(r);
				s2.remove(r);
			}
			if(s1.isEmpty()) {
				break;
			}
			if(s1.first() > s2.first()) {
				TreeSet<Integer> temp = s1;
				s1 = s2;
				s2 = temp;
			}
		}
		out.println(ans);
	}

	public void run() {
		long time = System.currentTimeMillis();
		boolean judge = System.getProperty("ONLINE_JUDGE") != null || oj;
		out = new PrintWriter(System.out);
		scn = new Reader(judge);
		solve();
		out.flush();
		if (!judge) {
			System.out.println(Arrays.deepToString(new Object[] { System.currentTimeMillis() - time + " ms" }));
		}
	}

	public static void main(String[] args) {
		new Thread(null, new E(), "Main", 1 << 28).start();
	}

	class Reader {
		InputStream is;

		public Reader(boolean oj) {
			is = oj ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		}

		byte[] inbuf = new byte[1024];
		public int lenbuf = 0, ptrbuf = 0;

		int readByte() {
			if (lenbuf == -1)
				throw new InputMismatchException();
			if (ptrbuf >= lenbuf) {
				ptrbuf = 0;
				try {
					lenbuf = is.read(inbuf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (lenbuf <= 0)
					return -1;
			}
			return inbuf[ptrbuf++];
		}

		boolean isSpaceChar(int c) {
			return !(c >= 33 && c <= 126);
		}

		int skip() {
			int b;
			while ((b = readByte()) != -1 && isSpaceChar(b))
				;
			return b;
		}

		String next() {
			int b = skip();
			StringBuilder stringB = new StringBuilder();
			while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != ' ')
				stringB.appendCodePoint(b);
				b = readByte();
			}
			return stringB.toString();
		}

		String nextLine() {
			int b = skip();
			StringBuilder stringB = new StringBuilder();
			while ((!isSpaceChar(b) || b == ' ')) { // when nextLine, (isSpaceChar(b) && b != ' ')
				stringB.appendCodePoint(b);
				b = readByte();
			}
			return stringB.toString();
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}

		char nextChar() {
			return (char) skip();
		}

		char[] next(int n) {
			char[] buff = new char[n];
			int b = skip(), p = 0;
			while (p < n && !(isSpaceChar(b))) {
				buff[p++] = (char) b;
				b = readByte();
			}
			return n == p ? buff : Arrays.copyOf(buff, p);
		}

		int nextInt() {
			int num = 0, b;
			boolean minus = false;
			while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
				;
			if (b == '-') {
				minus = true;
				b = readByte();
			}

			while (true) {
				if (b >= '0' && b <= '9') {
					num = num * 10 + (b - '0');
				} else {
					return minus ? -num : num;
				}
				b = readByte();
			}
		}

		long nextLong() {
			long num = 0;
			int b;
			boolean minus = false;
			while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
				;
			if (b == '-') {
				minus = true;
				b = readByte();
			}

			while (true) {
				if (b >= '0' && b <= '9') {
					num = num * 10 + (b - '0');
				} else {
					return minus ? -num : num;
				}
				b = readByte();
			}
		}

		long[] nextLongArr(int n) {
			long[] a = new long[n];
			for (int i = 0; i < n; i++)
				a[i] = nextLong();
			return a;
		}

		int[] nextIntArr(int n) {
			int[] a = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = nextInt();
			return a;
		}

		char[][] nextMat(int n, int m) {
			char[][] map = new char[n][];
			for (int i = 0; i < n; i++)
				map[i] = next(m);
			return map;
		}

		long[][] next2Long(int n, int m) {
			long[][] arr = new long[n][];
			for (int i = 0; i < n; i++) {
				arr[i] = nextLongArr(m);
			}
			return arr;
		}

		int[][] next2Int(int n, int m) {
			int[][] arr = new int[n][];
			for (int i = 0; i < n; i++) {
				arr[i] = nextIntArr(m);
			}
			return arr;
		}

		long[] shuffle(long[] arr) {
			Random r = new Random();
			for (int i = 1, j; i < arr.length; i++) {
				j = r.nextInt(i);
				arr[i] = arr[i] ^ arr[j];
				arr[j] = arr[i] ^ arr[j];
				arr[i] = arr[i] ^ arr[j];
			}
			return arr;
		}

		int[] shuffle(int[] arr) {
			Random r = new Random();
			for (int i = 1, j; i < arr.length; i++) {
				j = r.nextInt(i);
				arr[i] = arr[i] ^ arr[j];
				arr[j] = arr[i] ^ arr[j];
				arr[i] = arr[i] ^ arr[j];
			}
			return arr;
		}

		long[] uniq(long[] arr) {
			arr = scn.shuffle(arr);
			Arrays.parallelSort(arr);
			long[] rv = new long[arr.length];
			int pos = 0;
			rv[pos++] = arr[0];
			for (int i = 1; i < arr.length; i++) {
				if (arr[i] != arr[i - 1]) {
					rv[pos++] = arr[i];
				}
			}
			return Arrays.copyOf(rv, pos);
		}

		int[] uniq(int[] arr) {
			arr = scn.shuffle(arr);
			Arrays.parallelSort(arr);
			int[] rv = new int[arr.length];
			int pos = 0;
			rv[pos++] = arr[0];
			for (int i = 1; i < arr.length; i++) {
				if (arr[i] != arr[i - 1]) {
					rv[pos++] = arr[i];
				}
			}
			return Arrays.copyOf(rv, pos);
		}

		long[] reverse(long[] arr) {
			int i = 0, j = arr.length - 1;
			while (i < j) {
				arr[i] = arr[i] ^ arr[j];
				arr[j] = arr[i] ^ arr[j];
				arr[i] = arr[i] ^ arr[j];
				i++;
				j--;
			}
			return arr;
		}

		int[] reverse(int[] arr) {
			int i = 0, j = arr.length - 1;
			while (i < j) {
				arr[i] = arr[i] ^ arr[j];
				arr[j] = arr[i] ^ arr[j];
				arr[i] = arr[i] ^ arr[j];
				i++;
				j--;
			}
			return arr;
		}

		long[] compres(long[] arr) {
			int n = arr.length;
			long[] rv = Arrays.copyOf(arr, n);
			rv = uniq(rv);
			for (int i = 0; i < n; i++) {
				arr[i] = Arrays.binarySearch(rv, arr[i]);
			}
			return arr;
		}

		int[] compres(int[] arr) {
			int n = arr.length;
			int[] rv = Arrays.copyOf(arr, n);
			rv = uniq(rv);
			for (int i = 0; i < n; i++) {
				arr[i] = Arrays.binarySearch(rv, arr[i]);
			}
			return arr;
		}

		void deepFillLong(Object array, long val) {
			if (!array.getClass().isArray()) {
				throw new IllegalArgumentException();
			}
			if (array instanceof long[]) {
				long[] intArray = (long[]) array;
				Arrays.fill(intArray, val);
			} else {
				Object[] objArray = (Object[]) array;
				for (Object obj : objArray) {
					deepFillLong(obj, val);
				}
			}
		}

		void deepFillInt(Object array, int val) {
			if (!array.getClass().isArray()) {
				throw new IllegalArgumentException();
			}
			if (array instanceof int[]) {
				int[] intArray = (int[]) array;
				Arrays.fill(intArray, val);
			} else {
				Object[] objArray = (Object[]) array;
				for (Object obj : objArray) {
					deepFillInt(obj, val);
				}
			}
		}

		void tr(Object... o) {
			if (!oj)
				System.out.println(Arrays.deepToString(o));
		}
	}
}