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.

<image>

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 
// हर हर महादेव
import java.util.*;
import java.lang.*;
import java.io.*;
import java.math.BigInteger;
import java.text.DecimalFormat;

public final class Solution {

    static int inf = Integer.MAX_VALUE;
    static long mod = 1000000000 + 7;
    
 static void ne(Scanner sc, BufferedWriter op) throws Exception {
            int n=sc.nextInt();
     String one=sc.next();
     String two=sc.next();
     int _10=0;
     int _00=0;
     int _11=0;
     int _01=0;
   for(int i=0;i<n;i++){
       int c1=one.charAt(i)-'0';
       int c2=two.charAt(i)-'0';
       if(c1==0 && c2==0){
           _00++;
       }
       if(c1==1 && c2==0){
           _10++;
       }
       if(c1==1 && c2==1){
           _11++;
       }
       if(c1==0 && c2==1){
           _01++;
       }
   }
   int same=_00+_11;
   int diff=_01+_10;
   if(same==n){
      op.write("0\n");
      return;
   }
   if(same==1 && _11==1){
       op.write("1\n");
       return;
   }
//    if(diff==n){
//        if(diff%2==0){
//            op.write(n+"\n");
 
//        }else{
//            op.write("-1\n");
//        }
//        return;
//    }
   int ans=inf;
    
    if(_11-_00==1 && _00!=0 && _11!=0){
        // print("here");
        ans=Math.min(ans,same);
     }
     if(_10 ==_01 && _10!=0 && _01!=0){
        ans=Math.min(ans,diff);
     }
    
    if(ans==inf){
        op.write("-1\n");
    }else{
        op.write(ans+"\n");
    }

 }
 public static boolean ok(int n, int k)
    {
        if ((n & (1 << (k - 1))) > 0)
           return true;
        else
            return false;
    }
  
  static int gcd(int a, int b)
    {
        if (a == 0)
            return b; 
        return gcd(b % a, a); 
    }
  

    public static void main(String[] args) throws Exception {
        BufferedWriter op = new BufferedWriter(new OutputStreamWriter(System.out));
        // Reader sc = new Reader();
        Scanner sc= new Scanner(System.in);
        int t = sc.nextInt();
        while (t-->0){ ne(sc, op); }
        
        // ne(sc,op);
           
                   
        op.flush();
    }

    static void print(Object o) {
        System.out.println(String.valueOf(o));
    }
    static int[] toIntArr(String s){
        int[] val= new int[s.length()];
        for(int i=0;i<s.length();i++){
            val[i]=s.charAt(i)-'a';
        }
        return val;
    }

    static void  sort(int[] arr){
        ArrayList<Integer> list= new ArrayList<>();
        for(int i=0;i<arr.length;i++){
            list.add(arr[i]);

        }
        Collections.sort(list);
        for(int i=0;i<arr.length;i++){
            arr[i]=list.get(i);
        }
    }
       static void  sort(long[] arr){
        ArrayList<Long> list= new ArrayList<>();
        for(int i=0;i<arr.length;i++){
            list.add(arr[i]);

        }
        Collections.sort(list);
        for(int i=0;i<arr.length;i++){
            arr[i]=list.get(i);
        }
    }

}



// return -1 to put no ahed in array
class pair {
    int  xx;
    int yy;
    pair(int xx, int yy ) {
        this.xx = xx;
        this.yy = yy;
    }
}


class sortY implements Comparator<pair> {
    public int compare(pair p1, pair p2) {
        if (p1.yy > p2.yy) {
            return 1;
        } else if (p1.yy == p2.yy) {
            if (p1.xx > p2.xx) {
                return 1;
            } else if (p1.xx < p2.xx) {
                return -1;
            }
            return 0;

        }
        return -1;
    }
}

class sortX implements Comparator<pair> {
    public int compare(pair p1, pair p2) {
        if (p1.xx > p2.xx) {
            return 1;
        } else if (p1.xx == p2.xx) {
            if (p1.yy > p2.yy) {
                return 1;
            } else if (p1.yy < p2.yy) {
                return -1;
            }
            return 0;

        }
        return -1;
    }
}

class debug {

    static void print1d(long[] arr) {
        System.out.println();
        for (int i = 0; i < arr.length; i++) {
            System.out.print(arr[i] + " ");
        }

    }

    static void print1d(int[] arr) {
        System.out.println();
        for (int i = 0; i < arr.length; i++) {
            System.out.println(i+" = "+arr[i]);
        }

    }

    static void print1d(boolean[] arr) {
        System.out.println();
        for (int i = 0; i < arr.length; i++) {
            System.out.println(i + "= " + arr[i]);
        }

    }

    static void print2d(int[][] arr) {
        System.out.println();
        int n = arr.length;
        int n2 = arr[0].length;
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n2; j++) {
                System.out.print(arr[i][j] + " ");
            }
            System.out.println();
        }

    }
       static void print2d(boolean[][] arr) {
        System.out.println();
        int n = arr.length;
        int n2 = arr[0].length;
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n2; j++) {
                System.out.print(arr[i][j] + " ");
            }
            System.out.println();
        }

    }

    static void print2d(long[][] arr) {
        System.out.println();
        int n = arr.length;
        int n2 = arr[0].length;
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n2; j++) {
                System.out.print(arr[i][j] + " ");
            }
            System.out.println();
        }

    }
     static void printPair(ArrayList<pair> list) {
        if(list.size()==0){
            System.out.println("empty list");
            return;
        }
       System.out.println();
       for(int i=0;i<list.size();i++){
          System.out.println(list.get(i).xx+"-"+list.get(i).yy);
       }
    }

}

class Reader {
    final private int BUFFER_SIZE = 1 << 16;
    private DataInputStream din;
    private byte[] buffer;
    private int bufferPointer, bytesRead;

    public Reader() {
        din = new DataInputStream(System.in);
        buffer = new byte[BUFFER_SIZE];
        bufferPointer = bytesRead = 0;
    }

    public Reader(String file_name) throws IOException {
        din = new DataInputStream(new FileInputStream(file_name));
        buffer = new byte[BUFFER_SIZE];
        bufferPointer = bytesRead = 0;
    }

    public String readLine() throws IOException {
        byte[] buf = new byte[64]; // line length
        int cnt = 0, c;
        while ((c = read()) != -1) {
            if (c == '\n') {
                if (cnt != 0) {
                    break;
                } else {
                    continue;
                }
            }
            buf[cnt++] = (byte) c;
        }
        return new String(buf, 0, cnt);
    }

    public int nextInt() throws IOException {
        int ret = 0;
        byte c = read();
        while (c <= ' ') {
            c = read();
        }
        boolean neg = (c == '-');
        if (neg)
            c = read();
        do {
            ret = ret * 10 + c - '0';
        } while ((c = read()) >= '0' && c <= '9');

        if (neg)
            return -ret;
        return ret;
    }

    public long nextLong() throws IOException {
        long ret = 0;
        byte c = read();
        while (c <= ' ')
            c = read();
        boolean neg = (c == '-');
        if (neg)
            c = read();
        do {
            ret = ret * 10 + c - '0';
        } while ((c = read()) >= '0' && c <= '9');
        if (neg)
            return -ret;
        return ret;
    }

    public double nextDouble() throws IOException {
        double ret = 0, div = 1;
        byte c = read();
        while (c <= ' ')
            c = read();
        boolean neg = (c == '-');
        if (neg)
            c = read();

        do {
            ret = ret * 10 + c - '0';
        } while ((c = read()) >= '0' && c <= '9');

        if (c == '.') {
            while ((c = read()) >= '0' && c <= '9') {
                ret += (c - '0') / (div *= 10);
            }
        }

        if (neg)
            return -ret;
        return ret;
    }

    private void fillBuffer() throws IOException {
        bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
        if (bytesRead == -1)
            buffer[0] = -1;
    }

    private byte read() throws IOException {
        if (bufferPointer == bytesRead)
            fillBuffer();
        return buffer[bufferPointer++];
    }

    public void close() throws IOException {
        if (din == null)
            return;
        din.close();
    }
}
 class MultiTreeSet<E> {
	TreeMap<E, Integer> freqTreeMap = new TreeMap<E, Integer>();
	int size;
 
	public MultiTreeSet() {}
 
	public MultiTreeSet(Collection<? extends E> c) {
		for(E element : c)
			add(element);
	}
 
	public int size() {
		return size;
	}
 
	public void add(E element) {
		Integer freq = freqTreeMap.get(element);
		if(freq==null)
			freqTreeMap.put(element, 1);
		else
			freqTreeMap.put(element,freq+1);
		++size;
	}
 
	public void remove(E element) {
		Integer freq = freqTreeMap.get(element);
		if(freq!=null) {
			if(freq==1)
				freqTreeMap.remove(element);
			else
				freqTreeMap.put(element, freq-1);
			--size;
		}
	}
 
	public int get(E element) {
		Integer freq = freqTreeMap.get(element);
		if(freq==null)
			return 0;
		return freq;
	}
 
	public boolean contains(E element) {
		return get(element)>0;
	}
 
	public boolean isEmpty() {
		return size==0;
	}
 
	public E first() {
		return freqTreeMap.firstKey();
	}
 
	public E last() {
		return freqTreeMap.lastKey();
	}
 
	public E ceiling(E element) {
		return freqTreeMap.ceilingKey(element);
	}
 
	public E floor(E element) {
		return freqTreeMap.floorKey(element);
	}
 
	public E higher(E element) {
		return freqTreeMap.higherKey(element);
	}
 
	public E lower(E element) {
		return freqTreeMap.lowerKey(element);
	}
}
 