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.io.*;
import java.util.*;


import java.math.*;
import java.math.BigInteger;


public final class A
{    
	static PrintWriter out = new PrintWriter(System.out); 
	static StringBuilder ans=new StringBuilder();
	static FastReader in=new FastReader();
	static ArrayList<Integer> g[];
	static long mod=(long)998244353,INF=Long.MAX_VALUE;
	//	static boolean set[]; 
	static int par[],partial[];
	static int Days[],P[][];
	static int sum=0,size[];
	static int col[];
	//	static ArrayList<Long> A;
	static char X[][];
	static boolean set[][];
	static int D[],min[],A[];
	static long dp[][],seg[];
	//	static HashSet<Integer> visited,imposters;
	//	static HashSet<Integer> set;
	//	static node1 seg[];
	//static pair moves[]= {new pair(-1,0),new pair(1,0), new pair(0,-1), new pair(0,1)};
	public static void main(String args[])throws IOException
	{	
		/*
		 * star,rope,TPST
		 * BS,LST,MS,MQ
		 */	
		int max=(int)(2e5+5);


		int T=i();
		outer:while(T-->0)
		{
			int N=i();
			char X[]=in.next().toCharArray();
			char Y[]=in.next().toCharArray();
			int a=0,b=0,c=0,d=0;
			for(int i=0; i<N; i++)
			{
				if(X[i]=='1')
				{
					if(Y[i]=='0')c++;
					else a++;
				}
				else 
				{
					if(Y[i]=='0')b++;
					else d++;
				}
			}
			//type one
			int copy_a=a,copy_b=b,copy_c=c,copy_d=d;
			if(c==0 && d==0)
			{
				ans.append("0\n");
				continue ;
			}
			int mina=Integer.MAX_VALUE,minb=Integer.MAX_VALUE;
			boolean f=true;
			for(int i=1; i>=0; i++)
			{
				int a1=0,b1=0,c1=0,d1=0;
				if(f)
				{
					if(a<=0)break;
                    a1=d1+1;
                    d1=a-1;
                    b1=c;
                    c1=b;
                    
				}
				else
				{
					if(c<=0)break;
					a1=d;
					d1=a;
					c1=b+1;
					b1=c-1;
				}
				a=a1;
                b=b1;
                c=c1;
                d=d1;
				if(c==0 && d==0)
				{
					mina=i;
				}
				f^=true;
			}
			f=false;
			a=copy_a;
			b=copy_b;
			c=copy_c;
			d=copy_d;
			for(int i=1; i>=0; i++)
			{
				int a1=0,b1=0,c1=0,d1=0;
				if(f)
				{
					if(a<=0)break;
                    a1=d1+1;
                    d1=a-1;
                    b1=c;
                    c1=b;
                    
				}
				else
				{
					if(c<=0)break;
					a1=d;
					d1=a;
					c1=b+1;
					b1=c-1;
				}
				a=a1;
                b=b1;
                c=c1;
                d=d1;
				if(c==0 && d==0)
				{
					minb=i;
				}
				f^=true;
			}
			

			if(mina==Integer.MAX_VALUE && minb==Integer.MAX_VALUE)ans.append("-1\n");
			else
			{
				ans.append(Math.min(mina, minb)+"\n");
			}
		}
		out.println(ans);
		out.close();
	}


	static String reverse (String X)
	{
		StringBuilder sb=new StringBuilder(X);
		return sb.reverse().toString();
	}
	static String binary(long x)
	{
		String str="";
		long p=1L;
		while(p<=x)
		{
			if((p&x)!=0)str="1"+str;
			else str="0"+str;
			p<<=1;
		}
		return str;
	}

	static boolean can_loose(Trie root,boolean t)
	{
		if(root==null)return true; //never hits
		int cnt=0;
		for(Trie x:root.A)
		{
			if(x!=null)
			{
				cnt++;
				if(!can_loose(x,t^true)) 
				{
					//System.out.println("TRUE FOR--> "+x.ch+" "+t);
					return true;
				}
			}
		}
		if(cnt==0)return true;
		return false;
	}
	static boolean f(Trie root)
	{
		if(root==null)return false;		
		//		int cnt=0;
		for(Trie x:root.A)
		{
			if(x!=null)
			{
				//				cnt++;
				if(!f(x))
				{

					return true;
				}
			}
		}	
		return false;
	}
	static void insert(String X,Trie head)
	{
		Trie root=head;
		for(char x:X.toCharArray())
		{
			int a=x-'a';
			if(root.A[a]==null)root.A[a]=new Trie();
			root=root.A[a];
			root.ch=x;
		}
		root.ends=true;        
	}
	static boolean search(String X,Trie head)
	{
		Trie root=head;
		for(char x:X.toCharArray()) {
			int a=x-'a';
			if(root.A[a]==null)return false;
			root=root.A[a];
		}
		return root.ends;

	}
	static boolean starts_with(String X,Trie head)
	{
		Trie root=head;
		for(char x:X.toCharArray()) {
			int a=x-'a';
			if(root.A[a]==null)return false;
			root=root.A[a];
		}
		return true;
	}
	static int lower(ArrayList<Integer>A,int i)
	{
		int l=-1,r=A.size();
		while(r-l>1)
		{
			int m=(l+r)/2;
			if(A.get(m)>i)r=m;
			else l=m;
		}		
		return r;
	}
	static int upper(ArrayList<Integer>A,int i)
	{
		int l=-1,r=A.size();
		while(r-l>1)
		{
			int m=(l+r)/2;
			if(A.get(m)<i)l=m;
			else l=m;
		}		
		return l;
	}
	static String f()
	{
		StringBuilder X=new StringBuilder(i()+"");int p=i();
		while(p-->0)X.append("0");
		return X.toString();
	}
	static long f(int i,int g,int x,int left)
	{
		if(x<=1)return left;
		if(i<0 || g==1)return left;
		//		System.out.println(i+" "+g);
		if(dp[i][g]==0)
		{
			int next=min[i];
			int new_gcd=(int)GCD(g,x);
			//System.out.println(" factor--> "+x+" gcd--> "+g+" new-->  "+new_gcd);
			long s=0;
			int c=0;
			for(int j=next+1; j<=i; j++)
			{
				if(A[i]%new_gcd==0)
				{
					s+=new_gcd;
					c--;
				}
			}
			long a=0,b=0;
			a=f(i,g,x-1,left);
			b=s+f(next,new_gcd,x-1,left-c);
			dp[i][g]=Math.max(a, b);
		}
		return dp[i][g];
	}
	static boolean f(int A[],int B[],int x)
	{
		int c=0;
		int N=A.length;
		int l=0,r=x-1;
		for(int i=0; i<N; i++)
		{
			if(A[i]>=r && B[i]>=l)
			{
				r--;
				l++;
				c++;				
			}
			if(c>=x)return true;
		}
		return false;
	}
	static boolean isPalindrome(int A[])
	{
		int i=0,j=A.length-1;
		while(i<j)
		{
			if(A[i]!=A[j])return false;
			i++;
			j--;
		}
		return true;
	}
	static boolean isPalindrome(int A[],int x)
	{
		int i=0,j=A.length-1;
		while(i<j)
		{
			if(A[i]!=A[j])
			{
				if(A[i]==x)i++;
				else if(A[j]==x)j--;
				else return false;
			}
			else
			{
				i++;
				j--;
			}
		}
		return true;
	}
	static long fact[];
	static double nCr(int a,int b)
	{
		double x=fact[a], y=fact[b]*fact[a-b];
		return x/y;
	}
	static int f(ArrayList<Integer> A,int x)
	{
		int l=-1,r=A.size();
		while(r-l>1)
		{
			int m=(l+r)/2;
			if(A.get(m)<x)l=m;
			else r=m;
		}
		return r;
	}
	static boolean f(long a,long b,long x)
	{
		if(b==0)
		{
			return (x==a || x==b);
		}
		if(a<x)return false;
		else
		{
			if(a%b==x%b)return true;
			return f(b,a%b,x);
		}
	}

	static void dfs(int n,int p)
	{
		if(p!=-1)D[n]=D[p]+1;
		for(int c:g[n])
		{
			if(c!=p)
				dfs(c,n);
		}
	}
	static long f(long a,long A[])
	{
		int l=-1,r=A.length;
		while(r-l>1)
		{
			int m=(l+r)/2;
			if(A[m]<=a)l=m;
			else r=m;
		}
		return A[l];
	}
	static void build(int v,int tl,int tr,long A[])
	{
		if(tl==tr)
		{
			seg[v]=A[tl];
			return;
		}
		int tm=(tl+tr)/2;
		build(v*2,tl,tm,A);
		build(v*2+1,tm+1,tr,A);
		seg[v]=GCD(seg[v*2],seg[v*2+1]);
	}
	static void update(int v,int tl,int tr,int index,int x)
	{
		if(tl==tr && tl==index)
		{
			seg[v]=x;
			return;
		}		
		int tm=(tl+tr)/2;
		if(index<=tm)update(v*2,tl,tm,index,x);
		else update(v*2+1,tm+1,tr,index,x);
		seg[v]=Math.min(seg[v*2], seg[v*2+1]);
	}
	static long ask(int v,int tl,int tr,int l,int r)
	{
		if(l>r)return 0L;
		if(tl==l && tr==r)return seg[v];
		int tm=(tl+tr)/2;
		long a=ask(v*2,tl,tm,l,Math.min(tm, r));
		long b=ask(v*2+1,tm+1,tr,Math.max(l, tm+1),r);
		return GCD(a, b);
	}
	static int find(int a)
	{
		if(par[a]<0)return a;
		return par[a]=find(par[a]);
	}
	static void union(int a,int b)
	{
		a=find(a);
		b=find(b);
		if(a!=b)
		{
			par[a]+=par[b];
			par[b]=a;
		}
	}
	static int ask(int a,int b)
	{
		System.out.println("? "+a+" "+b);
		return i();
	}




	static long and(int i,int j)
	{
		System.out.println("and "+i+" "+j);
		return l();
	}
	static long or(int i,int j)
	{
		System.out.println("or "+i+" "+j);
		return l();
	}
	static boolean is_Sorted(int A[])
	{
		int N=A.length;
		for(int i=1; i<=N; i++)if(A[i-1]!=i)return false;
		return true;
	}
	static boolean f(StringBuilder sb,String Y,String order)
	{
		StringBuilder res=new StringBuilder(sb.toString());
		HashSet<Character> set=new HashSet<>();
		for(char ch:order.toCharArray())
		{
			set.add(ch);
			for(int i=0; i<sb.length(); i++)
			{
				char x=sb.charAt(i);
				if(set.contains(x))continue;
				res.append(x);
			}
		}

		String str=res.toString();
		return str.equals(Y);
	}
	static boolean all_Zero(int f[])
	{
		for(int a:f)if(a!=0)return false;
		return true;
	}
	static long form(int a,int l)
	{
		long x=0;
		while(l-->0)
		{
			x*=10;
			x+=a;
		}
		return x;
	}
	static int count(String X)
	{
		HashSet<Integer> set=new HashSet<>();
		for(char x:X.toCharArray())set.add(x-'0');
		return set.size();
	}


	//	static void build(int v,int tl,int tr,long A[])
	//	{
	//		if(tl==tr)
	//		{
	//			seg[v]=A[tl];
	//		}
	//		else
	//		{
	//			int tm=(tl+tr)/2;
	//			build(v*2,tl,tm,A);
	//			build(v*2+1,tm+1,tr,A);
	//			seg[v]=Math.min(seg[v*2], seg[v*2+1]);
	//		}
	//	}

	static int [] sub(int A[],int B[])
	{
		int N=A.length;
		int f[]=new int[N];
		for(int i=N-1; i>=0; i--)
		{
			if(B[i]<A[i])
			{
				B[i]+=26;
				B[i-1]-=1;
			}
			f[i]=B[i]-A[i];
		}
		for(int i=0; i<N; i++)
		{
			if(f[i]%2!=0)f[i+1]+=26;
			f[i]/=2;
		}
		return f;
	}





	static int max(int a ,int b,int c,int d)
	{
		a=Math.max(a, b);
		c=Math.max(c,d);
		return Math.max(a, c);
	}
	static int min(int a ,int b,int c,int d)
	{
		a=Math.min(a, b);
		c=Math.min(c,d);
		return Math.min(a, c);
	}



	static HashMap<Integer,Integer> Hash(int A[])
	{
		HashMap<Integer,Integer> mp=new HashMap<>();
		for(int a:A)
		{
			int f=mp.getOrDefault(a,0)+1;
			mp.put(a, f);
		}
		return mp;
	}
	static long mul(long a, long b)
	{
		return ( a %mod * 1L * b%mod )%mod;
	}
	static void swap(int A[],int a,int b)
	{
		int t=A[a];
		A[a]=A[b];
		A[b]=t;
	}



	static boolean isSorted(int A[])
	{
		for(int i=1; i<A.length; i++)
		{
			if(A[i]<A[i-1])return false;
		}
		return true;
	}

	static boolean isDivisible(StringBuilder X,int i,long num)
	{
		long r=0;
		for(; i<X.length(); i++)
		{
			r=r*10+(X.charAt(i)-'0');
			r=r%num;
		}
		return r==0;
	}    



	static int lower_Bound(int A[],int low,int high, int x) 
	{ 
		if (low > high) 
			if (x >= A[high]) 
				return A[high]; 

		int mid = (low + high) / 2; 

		if (A[mid] == x) 
			return A[mid]; 

		if (mid > 0 && A[mid - 1] <= x && x < A[mid]) 
			return A[mid - 1]; 

		if (x < A[mid]) 
			return lower_Bound( A, low, mid - 1, x); 

		return lower_Bound(A, mid + 1, high, x); 
	} 

	static String f(String A)
	{
		String X="";
		for(int i=A.length()-1; i>=0; i--)
		{
			int c=A.charAt(i)-'0';
			X+=(c+1)%2;
		}
		return X;
	}

	static void sort(long[] a) //check for long
	{
		ArrayList<Long> l=new ArrayList<>();
		for (long i:a) l.add(i);
		Collections.sort(l);
		for (int i=0; i<a.length; i++) a[i]=l.get(i);
	}

	static String swap(String X,int i,int j)
	{
		char ch[]=X.toCharArray();
		char a=ch[i];
		ch[i]=ch[j];
		ch[j]=a;
		return new String(ch);
	}

	static int sD(long n)  
	{  

		if (n % 2 == 0 )  
			return 2;  

		for (int i = 3; i * i <= n; i += 2) {  
			if (n % i == 0 )  
				return i;  
		}  

		return (int)n;  
	}  

	static void setGraph(int N)
	{
		//		tot=new int[N+1];
		partial=new int[N+1];
		Days=new int[N+1];
		P=new int[N+1][(int)(Math.log(N)+10)];
		//		set=new boolean[N+1];
		g=new ArrayList[N+1];
		D=new int[N+1];
		for(int i=0; i<=N; i++)
		{

			g[i]=new ArrayList<>();		
			Days[i]=-1;
			D[i]=Integer.MAX_VALUE;
			//D2[i]=INF;
		}
	}



	static  long pow(long a,long b)
	{
		long pow=1;
		long x=a;
		while(b!=0)
		{
			if((b&1)!=0)pow=(pow*x)%mod;
			x=(x*x)%mod;
			b/=2;
		}
		return pow;
	}

	static long toggleBits(long x)//one's complement || Toggle bits
	{
		int n=(int)(Math.floor(Math.log(x)/Math.log(2)))+1;

		return ((1<<n)-1)^x;
	}

	static int countBits(long a)
	{
		return (int)(Math.log(a)/Math.log(2)+1);
	}

	static long fact(long N)
	{ 
		long n=2; 
		if(N<=1)return 1;
		else
		{
			for(int i=3; i<=N; i++)n=(n*i)%mod;
		}
		return n;
	}

	static int kadane(int A[])
	{
		int lsum=A[0],gsum=A[0];
		for(int i=1; i<A.length; i++)
		{
			lsum=Math.max(lsum+A[i],A[i]);
			gsum=Math.max(gsum,lsum);
		}
		return gsum;
	}

	static void sort(int[] a) {
		ArrayList<Integer> l=new ArrayList<>();
		for (int i:a) l.add(i);
		Collections.sort(l);
		for (int i=0; i<a.length; i++) a[i]=l.get(i);
	}

	static boolean isPrime(long N)
	{
		if (N<=1)  return false; 
		if (N<=3)  return true; 
		if (N%2 == 0 || N%3 == 0) return false; 
		for (int i=5; i*i<=N; i=i+6) 
			if (N%i == 0 || N%(i+2) == 0) 
				return false; 
		return true; 
	}
	static void print(char A[])
	{
		for(char c:A)System.out.print(c+" ");
		System.out.println();
	}
	static void print(boolean A[])
	{
		for(boolean c:A)System.out.print(c+" ");
		System.out.println();
	}
	static void print(int A[])
	{
		for(int a:A)System.out.print(a+" ");
		System.out.println();	
	}
	static void print(long A[])
	{
		for(long i:A)System.out.print(i+ " ");
		System.out.println();

	}
	static void print(boolean A[][])
	{
		for(boolean a[]:A)print(a);
	}
	static void print(long A[][])
	{
		for(long a[]:A)print(a);
	}
	static void print(int A[][])
	{
		for(int a[]:A)print(a);
	}
	static void print(ArrayList<Integer> A)
	{
		for(int a:A)System.out.print(a+" ");
		System.out.println();
	}

	static int i()
	{
		return in.nextInt();
	}

	static long l()
	{
		return in.nextLong();
	}

	static int[] input(int N){
		int A[]=new int[N];
		for(int i=0; i<N; i++)
		{
			A[i]=in.nextInt();
		}
		return A;
	}

	static long[] inputLong(int N)     {
		long A[]=new long[N];
		for(int i=0; i<A.length; i++)A[i]=in.nextLong();
		return A;
	}

	static long GCD(long a,long b) 
	{
		if(b==0)
		{
			return a;
		}
		else return GCD(b,a%b);
	}

}
class Trie
{
	char ch;
	Trie A[];
	boolean ends;
	Trie()
	{
		ch='*';
		A=new Trie[26];
		ends=false;
	}
}


//Code For FastReader
//Code For FastReader
//Code For FastReader
//Code For FastReader
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;
	}

}