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 

import java.io.*;
import java.util.*;
import java.lang.*;
import java.util.function.Supplier;

import static java.lang.Math.*;

// Sachin_2961 submission //
public class Codeforces {

    static long[][]cnt;
    static void solve() {

        int n = fs.nInt();
        char[]a = fs.n().toCharArray();
        char[]b = fs.n().toCharArray();
        int _00=0,_01=0,_10=0,_11=0;
        for(int i=0;i<n;i++){
            if(a[i]=='0'){
                if(b[i]=='0')_00++;
                else _01++;
            }else{
                if(b[i]=='0')_10++;
                else _11++;
            }
        }
        int ans = Integer.MAX_VALUE/2;
        if(_01==_10){
            ans = _01*2;
        }
        if(_11!=0){
            if((_00+1)==_11){
                ans = min(ans,1+_00*2);
            }
        }
        if(ans != Integer.MAX_VALUE/2){
            out.println(ans);
        }else{
            out.println(-1);
        }
    }

    static class PairI{
        int f,s,w;
        PairI(int f,int s,int w){
            this.f = f;
            this.s = s;
            this.w = w;
        }

    }
    static class Pair{
        int f,s;
        Pair(int f,int s) {
            this.f = f;
            this.s = s;
        }
    }
    static boolean multipleTestCase = true;
    static FastScanner fs;
    static PrintWriter out;
    public static void main(String[]args){
        try{
            out = new PrintWriter(System.out);
            fs = new FastScanner();
            int tc = multipleTestCase?fs.nInt():1;
            while (tc-->0)solve();
            out.flush();
            out.close();
        }catch (Exception e){
            e.printStackTrace();
        }
    }
    static class FastScanner {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st=new StringTokenizer("");
        String n() {
            while (!st.hasMoreTokens())
                try {
                    st=new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            return st.nextToken();
        }
        String Line()
        {
            String str = "";
            try
            {
                str = br.readLine();
            }catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
        int nInt() {return Integer.parseInt(n()); }
        long nLong() {return Long.parseLong(n());}
        double nDouble(){return Double.parseDouble(n());}
        int[]aI(int n){
            int[]ar = new int[n];
            for(int i=0;i<n;i++)
                ar[i] = nInt();
            return ar;
        }
    }
    public static void sort(int[] arr){
        ArrayList<Integer> ls = new ArrayList<>();
        for(int x: arr)
            ls.add(x);
        Collections.sort(ls);
        for(int i=0; i < arr.length; i++)
            arr[i] = ls.get(i);
    }
    public static void sort(long[] arr){
        ArrayList<Long> ls = new ArrayList<>();
        for(long x: arr)
            ls.add(x);
        Collections.sort(ls);
        for(int i=0; i < arr.length; i++)
            arr[i] = ls.get(i);
    }
}