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 

import java.util.*;


import java.io.*;
import java.math.*;
import java.sql.Array;
import java.sql.ResultSet;
import java.sql.SQLException;
import java.sql.SQLIntegrityConstraintViolationException;



public class Main {
	 private static class MyScanner {
	        private static final int BUF_SIZE = 2048;
	        BufferedReader br;
	 
	        private MyScanner() {
	            br = new BufferedReader(new InputStreamReader(System.in));
	        }
	 
	        private boolean isSpace(char c) {
	            return c == '\n' || c == '\r' || c == ' ';
	        }
	 
	        String next() {
	            try {
	                StringBuilder sb = new StringBuilder();
	                int r;
	                while ((r = br.read()) != -1 && isSpace((char)r));
	                if (r == -1) {
	                    return null;
	                }
	 
	                sb.append((char) r);
	                while ((r = br.read()) != -1 && !isSpace((char)r)) {
	                    sb.append((char)r);
	                }
	                return sb.toString();
	            } catch (IOException e) {
	                e.printStackTrace();
	            }
	            return null;
	        }
	 
	        int nextInt() {
	            return Integer.parseInt(next());
	        }
	 
	        long nextLong() {
	            return Long.parseLong(next());
	        }
	 
	        double nextDouble() {
	            return Double.parseDouble(next());
	        }
	    }
	  static class Reader{
		  
			BufferedReader br;
			StringTokenizer st;
			public Reader() {
				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; 
		    } 
		}
	 
	  static long mod = (long)(1e9 + 7);
	 
	static void sort(long[] arr ) {
		 ArrayList<Long> al = new ArrayList<>();
		 for(long e:arr) al.add(e);
		 Collections.sort(al);
		 for(int i = 0 ; i<al.size(); i++) arr[i] = al.get(i);
	 }
	static void sort(int[] arr ) {
		 ArrayList<Integer> al = new ArrayList<>();
		 for(int e:arr) al.add(e);
		 Collections.sort(al);
		 for(int i = 0 ; i<al.size(); i++) arr[i] = al.get(i);
	 }
	
	static void sort(char[] arr) {
		ArrayList<Character> al = new ArrayList<Character>();
		for(char cc:arr) al.add(cc);
		Collections.sort(al);
		for(int i = 0 ;i<arr.length ;i++) arr[i] = al.get(i);
	}

	static long mod_mul(  long... a) {
		long ans = a[0]%mod;
		for(int i = 1 ; i<a.length ; i++) {
			ans = (ans * (a[i]%mod))%mod;
		}
		
		return ans;
	}
	static long mod_sum( long... a) {
		long ans = 0;
		for(long e:a) {
			ans = (ans + e)%mod;
		}
		return ans;
	}
	 static long gcd(long a, long b)
	  {      
	     if (b == 0)
	        return a;
	     return gcd(b, a % b); 
	  }
	 static boolean[] prime(int num) {
			boolean[] bool = new boolean[num];
		     
		      for (int i = 0; i< bool.length; i++) {
		         bool[i] = true;
		      }
		      for (int i = 2; i< Math.sqrt(num); i++) {
		         if(bool[i] == true) {
		            for(int j = (i*i); j<num; j = j+i) {
		               bool[j] = false;
		            }
		         }
		      }
		      if(num >= 0) {
		    	  bool[0] = false;
		    	  bool[1] = false;
		      }
		      
		      return bool;
		}

	 static long modInverse(long a, long m)
	    {
	        long g = gcd(a, m);
	       
	          return   power(a, m - 2);
	        
	    }
	   static long lcm(long a , long b) {
		   return (a*b)/gcd(a, b);
	   }
	   static int lcm(int a , int b) {
		   return (int)((a*b)/gcd(a, b));
	   }
	 static long power(long x, long y){
		 if(y<0) return 0;
		 long m = mod;
	        if (y == 0) return 1; long p = power(x, y / 2) % m; p = (int)((p * (long)p) % m);
	        if (y % 2 == 0) return p; else return (int)((x * (long)p) % m); }
	   
     static class Combinations{
	    	 private long[] z;
	    	 private long[] z1;
	    	 private long[] z2;
	    	 private long mod;
	    	  public Combinations(long N , long mod) {
	    		  this.mod = mod;
				z = new long[(int)N+1];
				z1 = new long[(int)N+1];
				z[0] = 1;
				for(int i =1 ; i<=N ; i++) z[i] = (z[i-1]*i)%mod;
			     z2 = new long[(int)N+1];
				z2[0] = z2[1] = 1;
			    for (int i = 2; i <= N; i++)
			        z2[i] = z2[(int)(mod % i)] * (mod - mod / i) % mod;
			    
			    
			    z1[0] = z1[1] = 1;
			    
			    for (int i = 2; i <= N; i++)
			        z1[i] = (z2[i] * z1[i - 1]) % mod;
			}
	    	  long fac(long n) {
	    		  return z[(int)n];
	    	  }
	    	  long invrsNum(long n) {
	    		  return z2[(int)n];
	    	  }
	    	  long invrsFac(long n) {
	    		  return invrsFac((int)n);
	    	  }
	    	  long ncr(long N, long R)
	    	  {		if(R<0 || R>N ) return 0;
	    		    long ans = ((z[(int)N] * z1[(int)R])
	    		              % mod * z1[(int)(N - R)])
	    		             % mod;
	    		    return ans;
	    		}
	      }
	      static class DisjointUnionSets {
			    int[] rank, parent;
			    int n;
			  
			    public DisjointUnionSets(int n)
			    {
			        rank = new int[n];
			        parent = new int[n];
			        this.n = n;
			        makeSet();
			    }
			  
			    void makeSet()
			    {
			        for (int i = 0; i < n; i++) {
			          
			            parent[i] = i;
			        }
			    }
			  
			    int find(int x)
			    {
			        if (parent[x] != x) {
			        
			            parent[x] = find(parent[x]);
			  
			        }
			  
			        return parent[x];
			    }
			  
			    void union(int x, int y)
			    {
			        int xRoot = find(x), yRoot = find(y);
			  
			        if (xRoot == yRoot)
			            return;
			  
			        if (rank[xRoot] < rank[yRoot])
			  
			            parent[xRoot] = yRoot;
			  
			        else if (rank[yRoot] < rank[xRoot])
			  
			            parent[yRoot] = xRoot;
			  
			        else
			        {
			            parent[yRoot] = xRoot;
			  
			            rank[xRoot] = rank[xRoot] + 1;
			        }
			    }
			}
	      static int max(int... a ) {
	    	  int max = a[0];
	    	  for(int e:a) max = Math.max(max, e);
	    	  return max;
	      }
	      static long max(long... a ) {
	    	  long max = a[0];
	    	  for(long e:a) max = Math.max(max, e);
	    	  return max;
	      }
	      static int min(int... a ) {
	    	  int min = a[0];
	    	  for(int e:a) min = Math.min(e, min);
	    	  return min;
	      }
	      static long min(long... a ) {
	    	  long min = a[0];
	    	  for(long e:a) min = Math.min(e, min);
	    	  return min;
	      }
	      static int[] KMP(String str) {
	    	  int n = str.length();
	    	  int[] kmp = new int[n];
	    	  for(int i = 1 ; i<n ; i++) {
	    		  int j = kmp[i-1];
	    		  while(j>0 && str.charAt(i) != str.charAt(j)) {
	    			  j = kmp[j-1];
	    		  }
	    		  if(str.charAt(i) == str.charAt(j)) j++;
	    		  kmp[i] = j;
	    	  }
	    	  
	    	  return kmp;
	      }
	      
	      
/************************************************ Query **************************************************************************************/	  
	 
/***************************************** 		Sparse Table	********************************************************/
	      static class SparseTable{
	    		
	    		private long[][] st;
	    		
	    		SparseTable(long[] arr){
	    			int n = arr.length;
	    			st = new long[n][25];
	    			log = new int[n+2];
	    			build_log(n+1);
	    			build(arr);
	    		}
	    		
	    		private void build(long[] arr) {
	    			int n = arr.length;
	    			
	    			for(int i = n-1 ; i>=0 ; i--) {
	    				for(int j = 0 ; j<25 ; j++) {
	    					int r = i + (1<<j)-1;
	    					if(r>=n) break;
	    					if(j == 0 ) st[i][j] = arr[i];
	    					else st[i][j] = Math.min(st[i][j-1] , st[ i + ( 1 << (j-1) ) ][ j-1 ] );
	    				}
	    			}
	    		}
	    		public long gcd(long a  ,long b) {
	    			if(a == 0) return b;
	    			return gcd(b%a , a);
	    		}
	    		public long query(int l ,int r) {
	    			int w = r-l+1;
	    			int power = log[w];
	    			return Math.min(st[l][power],st[r - (1<<power) + 1][power]);
	    		}
	    		private int[] log;
	    		void build_log(int n) {
	    			log[1] = 0;
	    			for(int i = 2 ; i<=n ; i++) {
	    				log[i] = 1 + log[i/2];
	    			}
	    		}
	    	}
	      
	      
/********************************************************	Segement Tree	*****************************************************/
/**
	 	 static class SegmentTree{
			 long[] tree;
			 long[] arr;
			 int n;
			 SegmentTree(long[] arr){
				 this.n = arr.length;
				 tree = new long[4*n+1];
				 this.arr = arr;
				 buildTree(0, n-1, 1);
			 }
			 
			 
			  void buildTree(int s ,int e  ,int index ) {
					if(s == e) {
						tree[index] = arr[s];
						return;
					}
				
					int mid = (s+e)/2;
					
					buildTree( s,  mid, 2*index);
					buildTree( mid+1, e, 2*index+1);
					
					tree[index] = Math.min(tree[2*index] , tree[2*index+1]);
				}
			  
			 long query(int si ,int ei) {
				 return query(0 ,n-1 , si ,ei , 1   );
			 }
			 private long query( int ss ,int se ,int qs , int qe,int index) {
					
					if(ss>=qs && se<=qe) return tree[index];
					
					if(qe<ss || se<qs) return (long)(1e17);
					
					int mid = (ss + se)/2;
					long left = query( ss , mid , qs ,qe , 2*index);
					long right= query(mid + 1 , se , qs ,qe , 2*index+1);
					return Math.min(left, right);
				}
			 public void update(int index , int val) {
				 arr[index] = val;
				 for(long e:arr) System.out.print(e+" ");
				 update(index , 0 , n-1 , 1);
			 }
			 private void update(int id ,int si , int ei , int index) {
				 if(id < si || id>ei) return;
				 if(si == ei ) { 
					 tree[index] = arr[id];
					 return;
				 }
				 if(si > ei) return;
				 int mid = (ei + si)/2;
					
					update( id,  si, mid , 2*index);
					update( id , mid+1, ei , 2*index+1);
					
					tree[index] = Math.min(tree[2*index] ,tree[2*index+1]);
			 }
			  
		 }
		 */

/* ***************************************************************************************************************************************************/	 
	 
//	      static MyScanner sc = new MyScanner(); // only in case of less memory
	      static Reader sc = new Reader();
	 static StringBuilder sb = new StringBuilder();
	 public static void main(String args[]) throws IOException {

		 int tc = 1;
		 tc = sc.nextInt();

		 for(int i = 1 ; i<=tc ; i++) {

//			 sb.append("Case #" + i + ": "  );	// During KickStart && HackerCup
			 TEST_CASE();
			  
		 }
		 System.out.print(sb);
	 }
	 
	 static void TEST_CASE() {
		 int n = sc.nextInt();
		char[] arr1 = sc.next().toCharArray();
		char[] arr2 = sc.next().toCharArray();
		if(arr1.length!=arr2.length) {
			sb.append("NO\n");
			return;
		}
		long oz = 0 , zo = 0 , zz = 0 , oo = 0;
		for(int i =0 ; i <n ; i++) {
			if(arr1[i] == '1' && arr1[i] == arr2[i]) oo++;
			else if(arr1[i] == '0' && arr2[i] == arr1[i]) zz++;
			else if(arr1[i] == '1' && arr1[i] != arr2[i]) oz++;
			else zo++;
		}
		if(oo == 1 && oz == 0 && zz == 0) {
			sb.append(1+"\n");
			return;
		}
		if(oz != zo) {
			sb.append("-1\n");
			return;
		}
		long ans = min(oz*2  );
		if(oo-1 == zz) {
			ans = min(ans ,1+( zz)*2 );
		}
		sb.append(ans+"\n");
		
	 }
	 
	
	

}
  



/*******************************************************************************************************************************************************/

/**
  
 
 
 */

 

