There are n candles on a Hanukkah menorah, and some of its candles are initially lit. We can describe which candles are lit with a binary string s, where the i-th candle is lit if and only if s_i=1.

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Initially, the candle lights are described by a string a. In an operation, you select a candle that is currently lit. By doing so, the candle you selected will remain lit, and every other candle will change (if it was lit, it will become unlit and if it was unlit, it will become lit).

You would like to make the candles look the same as string b. Your task is to determine if it is possible, and if it is, find the minimum number of operations required.

Input

The first line contains an integer t (1≤ t≤ 10^4) — the number of test cases. Then t cases follow.

The first line of each test case contains a single integer n (1≤ n≤ 10^5) — the number of candles.

The second line contains a string a of length n consisting of symbols 0 and 1 — the initial pattern of lights.

The third line contains a string b of length n consisting of symbols 0 and 1 — the desired pattern of lights.

It is guaranteed that the sum of n does not exceed 10^5.

Output

For each test case, output the minimum number of operations required to transform a to b, or -1 if it's impossible.

Example

Input


5
5
11010
11010
2
01
11
3
000
101
9
100010111
101101100
9
001011011
011010101


Output


0
1
-1
3
4

Note

In the first test case, the two strings are already equal, so we don't have to perform any operations.

In the second test case, we can perform a single operation selecting the second candle to transform 01 into 11.

In the third test case, it's impossible to perform any operations because there are no lit candles to select.

In the fourth test case, we can perform the following operations to transform a into b: 

  1. Select the 7-th candle: 100010{\color{red}1}11→ 011101{\color{red} 1}00. 
  2. Select the 2-nd candle: 0{\color{red} 1}1101100→ 1{\color{red} 1}0010011. 
  3. Select the 1-st candle: {\color{red}1}10010011→ {\color{red}1}01101100. 



In the fifth test case, we can perform the following operations to transform a into b: 

  1. Select the 6-th candle: 00101{\color{red}1}011→ 11010{\color{red}1}100 
  2. Select the 2-nd candle: 1{\color{red}1}0101100→ 0{\color{red}1}1010011 
  3. Select the 8-th candle: 0110100{\color{red}1}1→ 1001011{\color{red}1}0 
  4. Select the 7-th candle: 100101{\color{red}1}10→ 011010{\color{red}1}01 
//package currentContest;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Random;
import java.util.StringTokenizer;


public class P1 {
	public static int karkamal(ArrayList<Integer> remaining) {
		int sum=0;
		return sum;
	}
	public static void main(String[] args) {
		// TODO Auto-generated method stub
		FastReader sc=new FastReader();
		int t=sc.nextInt();
		StringBuilder st=new StringBuilder();
		while(t--!=0){
			int n=sc.nextInt();
			String ci=sc.nextLine();
			String cf=sc.nextLine();
			int icount1=0;
			int fcount1=0;
			for(int i=0;i<n;i++) {
				icount1+=ci.charAt(i)-'0';
				fcount1+=cf.charAt(i)-'0';
			}
			int ans=-1;
			int cccc=0;
			int cccf=0;
			for(int i=0;i<n;i++) {
				if(ci.charAt(i)=='0'&&cf.charAt(i)=='1') cccc++;
				if(ci.charAt(i)=='1'&&cf.charAt(i)=='0') cccf++;
			}
			if(cccc-cccf==1||cccc-cccf==0) {
				ans=cccc+cccf;
			}
			if(ans==0) {
				st.append(ans+"\n");
				continue;
			}
			int ccc=0;
			int ccf=0;
			for(int i=0;i<n;i++) {
				if(ci.charAt(i)=='1'&&cf.charAt(i)=='1') ccc++;
				if(ci.charAt(i)=='0'&&cf.charAt(i)=='0') ccf++;
			}
			if(ccc-ccf==1||ccc-ccf==0) {
				if(ans==-1) {
					ans=ccc+ccf;
				}else {
					ans=Math.min(ccc+ccf, ans);
				}
			}
			st.append(ans+"\n");
			continue;
		}
		System.out.println(st);
	}
	
	static class DisjointUnionSets {
		int[] rank, parent;
		int n;
		
		// Constructor
		public DisjointUnionSets(int n)
		{
			rank = new int[n];
			parent = new int[n];
			this.n = n;
			makeSet();
		}
		
		// Creates n sets with single item in each
		void makeSet()
		{
			for (int i = 0; i < n; i++) {
				// Initially, all elements are in
				// their own set.
				parent[i] = i;
			}
		}
		
		// Returns representative of x's set
		int find(int x)
		{
			// Finds the representative of the set
			// that x is an element of
			if (parent[x] != x) {
				// if x is not the parent of itself
				// Then x is not the representative of
				// his set,
				parent[x] = find(parent[x]);
				
				// so we recursively call Find on its parent
				// and move i's node directly under the
				// representative of this set
			}
			
			return parent[x];
		}
		
		// Unites the set that includes x and the set
		// that includes x
		void union(int x, int y)
		{
			// Find representatives of two sets
			int xRoot = find(x), yRoot = find(y);
			
			// Elements are in the same set, no need
			// to unite anything.
			if (xRoot == yRoot)
				return;
			
			// If x's rank is less than y's rank
			if (rank[xRoot] < rank[yRoot])
				
				// Then move x under y  so that depth
				// of tree remains less
				parent[xRoot] = yRoot;
			
			// Else if y's rank is less than x's rank
			else if (rank[yRoot] < rank[xRoot])
				
				// Then move y under x so that depth of
				// tree remains less
				parent[yRoot] = xRoot;
			
			else // if ranks are the same
			{
				// Then move y under x (doesn't matter
				// which one goes where)
				parent[yRoot] = xRoot;
				
				// And increment the result tree's
				// rank by 1
				rank[xRoot] = rank[xRoot] + 1;
			}
		}
	}

	static FastReader sc = new FastReader();

	public static void solvegraph() {
		int n = sc.nextInt();

		int edge[][] = new int[n - 1][2];
		for (int i = 0; i < n - 1; i++) {
			edge[i][0] = sc.nextInt() - 1;
			edge[i][1] = sc.nextInt() - 1;
		}
		ArrayList<ArrayList<Integer>> ad = new ArrayList<>();
		for (int i = 0; i < n; i++) {
			ad.add(new ArrayList<Integer>());
		}
		for (int i = 0; i < n - 1; i++) {
			ad.get(edge[i][0]).add(edge[i][1]);
			ad.get(edge[i][1]).add(edge[i][0]);
		}
		int parent[] = new int[n];
		Arrays.fill(parent, -1);
		parent[0] = n;
		ArrayDeque<Integer> queue = new ArrayDeque<>();
		queue.add(0);
		int child[] = new int[n];
		Arrays.fill(child, 0);
		ArrayList<Integer> lv = new ArrayList<Integer>();
		while (!queue.isEmpty()) {
			int toget = queue.getFirst();
			queue.removeFirst();
			child[toget] = ad.get(toget).size() - 1;
			for (int i = 0; i < ad.get(toget).size(); i++) {
				if (parent[ad.get(toget).get(i)] == -1) {
					parent[ad.get(toget).get(i)] = toget;
					queue.addLast(ad.get(toget).get(i));
				}
			}
			lv.add(toget);
		}

		child[0]++;
	}

	static void sort(int[] A) {
		int n = A.length;
		Random rnd = new Random();
		for (int i = 0; i < n; ++i) {
			int tmp = A[i];
			int randomPos = i + rnd.nextInt(n - i);
			A[i] = A[randomPos];
			A[randomPos] = tmp;
		}
		Arrays.sort(A);
	}
	static void sort(char[] A) {
		int n = A.length;
		Random rnd = new Random();
		for (int i = 0; i < n; ++i) {
			char tmp = A[i];
			int randomPos = i + rnd.nextInt(n - i);
			A[i] = A[randomPos];
			A[randomPos] = tmp;
		}
		Arrays.sort(A);
	}

	static void sort(long[] A) {
		int n = A.length;
		Random rnd = new Random();
		for (int i = 0; i < n; ++i) {
			long tmp = A[i];
			int randomPos = i + rnd.nextInt(n - i);
			A[i] = A[randomPos];
			A[randomPos] = tmp;
		}
		Arrays.sort(A);
	}

	static String sort(String s) {
		Character ch[] = new Character[s.length()];
		for (int i = 0; i < s.length(); i++) {
			ch[i] = s.charAt(i);
		}
		Arrays.sort(ch);
		StringBuffer st = new StringBuffer("");
		for (int i = 0; i < s.length(); i++) {
			st.append(ch[i]);
		}
		return st.toString();
	}

	public static long gcd(long a, long b) {
		if (a == 0) {
			return b;
		}
		return gcd(b % a, a);
	}

	static class FastReader {
		BufferedReader br;
		StringTokenizer st;

		public FastReader() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		String next() {
			while (st == null || !st.hasMoreElements()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

		int nextInt() {
			return Integer.parseInt(next());
		}

		long nextLong() {
			return Long.parseLong(next());
		}

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

		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return str;
		}
	}
}
