There is a chessboard of size n by n. The square in the i-th row from top and j-th column from the left is labelled (i,j).

Currently, Gregor has some pawns in the n-th row. There are also enemy pawns in the 1-st row. On one turn, Gregor moves one of his pawns. A pawn can move one square up (from (i,j) to (i-1,j)) if there is no pawn in the destination square. Additionally, a pawn can move one square diagonally up (from (i,j) to either (i-1,j-1) or (i-1,j+1)) if and only if there is an enemy pawn in that square. The enemy pawn is also removed.

Gregor wants to know what is the maximum number of his pawns that can reach row 1?

Note that only Gregor takes turns in this game, and the enemy pawns never move. Also, when Gregor's pawn reaches row 1, it is stuck and cannot make any further moves.

Input

The first line of the input contains one integer t (1≤ t≤ 2⋅ 10^4) — the number of test cases. Then t test cases follow.

Each test case consists of three lines. The first line contains a single integer n (2≤ n≤ 2⋅{10}^{5}) — the size of the chessboard.

The second line consists of a string of binary digits of length n, where a 1 in the i-th position corresponds to an enemy pawn in the i-th cell from the left, and 0 corresponds to an empty cell.

The third line consists of a string of binary digits of length n, where a 1 in the i-th position corresponds to a Gregor's pawn in the i-th cell from the left, and 0 corresponds to an empty cell.

It is guaranteed that the sum of n across all test cases is less than 2⋅{10}^{5}.

Output

For each test case, print one integer: the maximum number of Gregor's pawns which can reach the 1-st row.

Example

Input


4
3
000
111
4
1111
1111
3
010
010
5
11001
00000


Output


3
4
0
0

Note

In the first example, Gregor can simply advance all 3 of his pawns forward. Thus, the answer is 3.

In the second example, Gregor can guarantee that all 4 of his pawns reach the enemy row, by following the colored paths as demonstrated in the diagram below. Remember, only Gregor takes turns in this "game"!

<image>

In the third example, Gregor's only pawn is stuck behind the enemy pawn, and cannot reach the end.

In the fourth example, Gregor has no pawns, so the answer is clearly 0.
1
20
01001100111111000100
00101100011010001110

8

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.Deque;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.List;
import java.util.Map;
import java.util.Map.Entry;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Random;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;

public class hacker49 {

	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; 
        } 
    }
	static long[] x= {1,1,1,0,0,0,-1,-1,-1};
	static long[] y= {1,-1,0,-1,0,1,1,-1,0};
	public static void main(String[] args) {
		OutputStream outputStream =System.out;
	    PrintWriter out =new PrintWriter(outputStream);
		FastReader s=new FastReader();
		int t=s.nextInt();
	while(t>0) {
		int n=s.nextInt();
		String str1=s.next();
		String str2=s.next();
		char[] a=str1.toCharArray();
		char[] b=str2.toCharArray();
		int c=0;
		for(int i=0;i<n;i++) {
			if(str2.charAt(i)=='1') {
			if(i==0) {
				if(a[0]=='0') {
					c++;
				}else if(a[1]=='1') {
					c++;
					a[1]='2';
				}
			}else if(i==n-1) {
				if(a[n-1]=='0') {
					c++;
				}else if(a[n-2]=='1') {
					c++;
					a[n-2]='2';
				}
			}else {
				if(a[i]=='0') {
					c++;
				}else if(a[i-1]=='1') {
					c++;
					a[i-1]='2';
				}else if(a[i+1]=='1') {
					c++;
					a[i+1]='2';
				}
			}
		}
			}
		out.println(c);
		t--;
	}
			out.close();
	}
	public static int[] KMP( String str) {
		int[] a=new int[str.length()];
		int j;
		int i;
     for(i=1,j=0;i<str.length();) {
    	 if(str.charAt(i)==str.charAt(j)) {
    		 a[i]=j+1;
    		 j++;
    		 i++;
    	 }else {
    		 if(j!=0) {
    			 j=a[j-1];
    		  }else {
    			 a[j]=0;
    			 i++;
    		 }
    	 }
     }
		return a;
	}
	public static void CS(long[] arr,long[] segtree,int low,int high,int pos,int c,int n) {
		if(low==high) {
			segtree[pos]=arr[low];
//			c=0;
			return;
		}
		int mid=(low+high)/2;
		CS(arr,segtree,low,mid,2*pos+1,c+1,n);
		CS(arr,segtree,mid+1,high,2*pos+2,c+1,n);
		if((n-c)%2!=0) {
		segtree[pos]=(segtree[2*pos+1]|segtree[2*pos+2]);
	}else {
		segtree[pos]=(segtree[2*pos+1]^segtree[2*pos+2]);
	}
		}
	public static void US(long[] segtree,int low,int high,int pos ,long new_val,int index,long prev_val,int c,int n) {
//		if(index>high || index<low) {
//			return ;
//		}
		if(low==high) {
			segtree[pos]=new_val;
			return;
		}
//		segtree[pos]+=diff;
//		 segtree[pos] = (segtree[pos] ^ prev_val) ^ new_val;
		if(high!=low) {
			int mid=(high+low)/2;
			if(index<=mid) {
			US(segtree,low,mid,2*pos+1,new_val,index,prev_val,c+1,n);}else {
			US(segtree,mid+1,high,2*pos+2,new_val,index,prev_val,c+1,n);}
			if((n-c)%2!=0) {
				segtree[pos]=(segtree[2*pos+1]|segtree[2*pos+2]);
			}else {
				segtree[pos]=(segtree[2*pos+1]^segtree[2*pos+2]);
			}
		}
	}
	public static long RS(long[] segtree,int qlow,int qhigh,int low,int high,int pos) {
		if(low>=qlow && high<=qhigh) {
			return segtree[pos];
		}
		if(qhigh<low || qlow>high) {
			return 0;
		}
		int mid=(low+high)/2;
	return RS(segtree,qlow,qhigh,low,mid,2*pos+1)^RS(segtree,qlow,qhigh,mid+1,high,2*pos+2);
	}
	static int nextPowerOf2(int n) 
	{ 
	    n--; 
	    n |= n >> 1; 
	    n |= n >> 2; 
	    n |= n >> 4; 
	    n |= n >> 8; 
	    n |= n >> 16; 
	    n++; 
	      
	    return n; 
	} 

	public static int longest_Repeating_Subsequence(String str,int n) {
		int[][] dp=new int[n+1][n+1];
		
		for(int i=1;i<=n;i++) {
			for(int j=1;j<=n;j++) {
				if(str.charAt(i-1)==str.charAt(j-1) &&  i!=j) {
					dp[i][j]=1+dp[i-1][j-1];
				}else {
					dp[i][j]=Math.max(dp[i][j-1], dp[i-1][j]);
				}
			}
		}	
		return dp[n][n];
	}
	public static int d1(ArrayList<Integer> e,int n,int i) {
		int l=-1;
		int r=n;
				;
		while(r>l+1) {
			int mid=(l+r)/2;
//			long h=mid^n;
//			System.out.println(e.get(mid)+" "+mid);
			if(e.get(mid)>i) {
				r=mid;
			}else {
				l=mid;
			}
		}
		return r;
				
	}
	public static int upper_bound(long[] a ,long x,int n) {
		int l=-1;
		int r=n;
		while(r>l+1) {
			int mid=(l+r)/2;
			if(a[mid]>x) {
				r=mid;
			}else {
				l=mid;
			}
		}
		return r;
				
	}
	public static int lower_bound(long[] a ,long x,int n) {
		int l=-1;
		int r=n;
		while(r>l+1) {
			int mid=(l+r)/2;
			if(a[mid]<=x) {
				l=mid;
			}else {
				r=mid;
			}
		}
		return l;
				
	}
	static long get=0;
	static int[] ans=new int[200001];
//	static int[] dx= {2,2,-2,-2,-1,-1,1,1};
//	static int[] dy= {1,-1,-1,1,-2,2,-2,2};
//	static int[][] vis1=new int[101][101];
//	static boolean valid(int x,int y,int n) {
//		if(x>=1 && x<=n && y>=1 && y<=n) {
//			return true;
//		}
//		return false;
//	}
//	static void dfs(int x,int y,char[][] a,int n,char t) {
//		a[x][y]=t;
//		vis1[x][y]=1;
//		for(int i=0;i<8;i++) {
//			if(valid(x+dx[i],y+dy[i],n) && vis1[x+dx[i]][y+dy[i]]==0) {
//				dfs(x+dx[i],y+dy[i],a,n,(t=='W')?'B':'W');
//			}
//		}
//	}

	static int[] h=new int[200001];
	static int[] subtree=new int[200001];
	static int[] vis=new int[200001];
	static HashMap<Integer,pair> e=new HashMap<>();
	static ArrayList<Integer>[] f1=new ArrayList[200001];	
	static PriorityQueue<pair> q=new PriorityQueue<>();	
	static ArrayList<pair>[] f=new ArrayList[200001];   
//	static void bfs() {
//		Queue<node> q=new LinkedList<>();
//		q.add(new node(1,0));
//		h[1]=0;
//		vis[1]=1;
//		while(!q.isEmpty()) {
//			node p=q.poll();
////			h[p.a]=p.b;
//			for(int i=0;i<f1[p.a].size();i++) {
//				if(vis[f1[p.a].get(i)]==0) {
//					q.add(new node(f1[p.a].get(i),p.b+1));
//					h[f1[p.a].get(i)]=p.b+1;
//					vis[f1[p.a].get(i)]=1;
//				}
//			}
//		}
//	}
	static int dfs(int node) {
		int c=1;
		vis[node]=1;
		for(int i=0;i<f1[node].size();i++) {
			if(vis[f1[node].get(i)]==0) {
				c+=dfs(f1[node].get(i));
			}
		}
		subtree[node]=c;
		return c;
	}
	static void dfs2(int node,int v) {
		vis[node]=1;
		if(ans[node]==1) {
			get+=v;
		}
		for(int i=0;i<f1[node].size();i++) {
			if(vis[f1[node].get(i)]==0) {
				dfs2(f1[node].get(i),v+((ans[node]==0)?1:0));
			}
		}
	}
static long m=-1;
static void sf(long[] min){
        int n = min.length;
        Random rnd = new Random();
        for(int i=0; i<n; ++i){
            long tmp = min[i];
            int randomPos = i + rnd.nextInt(n-i);
            min[i] = min[randomPos];
            min[randomPos] = tmp;
        }   
}

	static class pair implements Comparable<pair>{
		private long a;
		private long b;
		private long c;
		
		pair(long a,long b,long c){
			this.a=a;
//			this.f=f;
			this.b=b;
			this.c=c;
//			this.d=d;
//			this.e=e;
		}
		public int compareTo(pair o) {
			if(o.c!=this.c) {
//			return Integer.compare(o.c, this.c);}
//		else {
				return Long.compare(this.c,o.c);
			}else {
				return Long.compare(this.a*this.b,o.a*o.b);
			}
		}
//		
		
	}
	static class node implements Comparable<node>{
		private long a;
		private long b;
		private long c;
		node(long a,long b,long c){
			this.a=a;
			this.b=b;
			this.c=c;
		}
		public int compareTo(node o) {
//			return Long.compare(arg0, arg1)
			if(this.c!=o.c) {
				return Long.compare(o.c, this.c);
			}else {
				return Long.compare(this.b, o.b);
			}
		}
	}

//	public static int upper_bound(long[] a ,long x,int n) {
//		int l=-1;
//		int r=n;
//		while(r>l+1) {
//			int mid=(l+r)/2;
//			if(a[mid]<x) {
//				l=mid;
//			}else {
//				r=mid;
//			}
//		}
//		return r;
//				
//	}
//	public static int lower_bound(long[] a ,long x,int m) {
//		int l=0;
//		int r=m+1;
//		while(r>l+1) {
//			int mid=(l+r)/2;
//			if(a[mid]>=x) {
//				r=mid;
//			}else {
//				l=mid;
//			}
//		}
//		return r;
//				
//	}
	public static long lb(int n,long[] pre,long k,long a,long b,long x,long y) {
		long l=0;
		long r=n+1;
		while(l<r) {
			long mid=(l+r)/2;
			long sum=0;
			long gcd=GCD(a,b);
			long g=mid/(a*b/gcd);
			long a1=mid/a;
			long b1=mid/b;
			sum+=(pre[(int) g]*(x+y))/100;
			if(x>=y) {
				sum+=((pre[(int) a1]-pre[(int) g])*x)/100;
				sum+=(((pre[(int)(a1+b1-g)]-pre[(int)(a1)])*y))/100;
			}else {
				sum+=((pre[(int) b1]-pre[(int) g])*y)/100;
				sum+=(((pre[(int)(a1+b1-g)]-pre[(int)(b1)])*x))/100;
			}
			if(sum>=k) {
				r=mid;
			}else {
				l=mid+1;
			}
//			System.out.println(mid+" "+h);
		}
		
		return r;
				
	}
	
	
	
	public static long[] merge_sort(long[] A, int start, int end) {
		if (end > start) {
			int mid = (end + start) / 2;
			long[] v = merge_sort(A, start, mid);
			long[] o = merge_sort(A, mid + 1, end);
			return (merge(v, o));
		} else {
			long[] y = new long[1];
			y[0] = A[start];
			return y;
		}
	}
	public static long[] merge(long a[], long b[]) {
		
		long[] temp = new long[a.length + b.length];
		int m = a.length;
		int n = b.length;
		int i = 0;
		int j = 0;
		int c = 0;
		while (i < m && j < n) {
			if (a[i] < b[j]) {
				temp[c++] = a[i++];
			
			} else {
				temp[c++] = b[j++];
			}
		}
		while (i < m) {
			temp[c++] = a[i++];
		}
		while (j < n) {
			temp[c++] = b[j++];
		}
		return temp;
	}	
	public static int[] Create(int[] a,int n) {
		int[] b=new int[n+1];
		for(int i=1;i<=n;i++) {
			int j=i;
			int h=a[i];
			while(i<=n) {
				b[i]+=h;
				i=get_next(i);
			}
			i=j;
		}
		return b;
	}
public static int get_next(int a) {
	return a+(a&-a);
}
public static int get_parent(int a) {
	return a-(a&-a);
}
public static int query_1(int[] b,int index) {
	int sum=0;
	if(index<=0) {
		return 0;
	}
	while(index>0) {
		sum+=b[index];
		index=get_parent(index);
	}
	return sum;
}
public static int query(int[] b,int n,int l,int r) {
	int sum=0;
	sum+=query_1(b,r);
	sum-=query_1(b,l-1);
	return sum;
}
public static void update(int[] a,int[] b,int n,int index,int val) {
	int diff=val-a[index];
	a[index]+=diff;
	while(index<=n) {
		b[index]+=diff;
		index=get_next(index);
	}	
}
	
//	public static void Create(int[] a,pair[] segtree,int low,int high,int pos) {
//		if(low>high) {
//			return;
//		}
//		if(low==high) {
//			segtree[pos].b.add(a[low]);
//			return ;
//		}
//		int mid=(low+high)/2;
//		Create(a,segtree,low,mid,2*pos);
//		Create(a,segtree,mid+1,high,2*pos+1);
//		segtree[pos].b.addAll(segtree[2*pos].b);
//		segtree[pos].b.addAll(segtree[2*pos+1].b);
//	}
//	public static void update(pair[] segtree,int low,int high,int index,int pos,int val,int prev) {
//		if(index>high || index<low) {
//			return ;
//		}
//		if(low==high && low==index) {
//			segtree[pos].b.remove(prev);
//			segtree[pos].b.add(val);
//			return;
//		}
//			int mid=(high+low)/2;
//			 update(segtree,low,mid,index,2*pos,val,prev);
//			 update(segtree,mid+1,high,index,2*pos+1,val,prev);
//			 segtree[pos].b.clear();
//			  segtree[pos].b.addAll(segtree[2*pos].b);
//			  segtree[pos].b.addAll(segtree[2*pos+1].b);
//			  
//	}
//	public static pair query(pair[] segtree,int low,int high,int qlow,int qhigh ,int pos) {
//		if(low>=qlow && high<=qhigh) {
//			return segtree[pos];
//		}
//		if(qhigh<low || qlow>high) {
//			return new pair();
//		}
//		int mid=(low+high)/2;
//	  pair a1=query(segtree,low,mid,qlow,qhigh,2*pos);
//	  pair a2=query(segtree,mid+1,high,qlow,qhigh,2*pos+1);
//	  pair a3=new pair();
//	  a3.b.addAll(a1.b);
//	  a3.b.addAll(a2.b);
//	  return a3;
//	  
//	}
//	
//	public static int nextPowerOf2(int n) 
//	{ 
//	    n--; 
//	    n |= n >> 1; 
//	    n |= n >> 2; 
//	    n |= n >> 4; 
//	    n |= n >> 8; 
//	    n |= n >> 16; 
//	    n++;     
//	    return n; 
//	} 
//	
////	static class pair implements Comparable<pair>{
////		private int a;
////		private long b;
//////		private long c;
////		pair(int a,long b){
////			this.a=a;
////			this.b=b;
//////			this.c=c;
////		}
////		public int compareTo(pair o) {
//////		if(this.a!=o.a) {
//////			return Long.compare(this.a, o.a);
//////		}else {
////			return Long.compare(o.b,this.b);
//////		}
////		}
////	}
//	static class pair implements Comparable<pair>{
//		private int a;
//		private int b;
//		pair(int a,int b){
////			this.b=new HashSet<>();
//			this.a=a;
//			this.b=b;
//		}
//		public int compareTo(pair o) {
//			return Integer.compare(this.b, o.b);
//		}
//	}
	public static int lower_bound(ArrayList<Long> a ,int n,long x) {
		int l=0;
		int r=n;
		while(r>l+1) {
			int mid=(l+r)/2;
			if(a.get(mid)<=x) {
				l=mid;
			}else {
				r=mid;
			}
		}
		return l;		
	}
	public static int[] is_prime=new int[1000001];
	public static ArrayList<Long> primes=new ArrayList<>();
 	public static void sieve() {
		long maxN=1000000;
		for(long i=1;i<=maxN;i++) {
			is_prime[(int) i]=1;
		}
		is_prime[0]=0;
		is_prime[1]=0;
		for(long i=2;i*i<=maxN;i++) {
			if(is_prime[(int) i]==1) {
//				primes.add((int) i);
				for(long j=i*i;j<=maxN;j+=i) {
					is_prime[(int) j]=0;
				}
			}
		}
		for(long i=0;i<=maxN;i++) {
			if(is_prime[(int) i]==1) {
				primes.add(i);
			}
		}		
	}
//	public static pair[] merge_sort(pair[] A, int start, int end) {
//		if (end > start) {
//			int mid = (end + start) / 2;
//			pair[] v = merge_sort(A, start, mid);
//			pair[] o = merge_sort(A, mid + 1, end);
//			return (merge(v, o));
//		} else {
//			pair[] y = new pair[1];
//			y[0] = A[start];
//			return y;
//		}
//	}
//	public static pair[] merge(pair a[], pair b[]) {
//		pair[] temp = new pair[a.length + b.length];
//		int m = a.length;
//		int n = b.length;
//		int i = 0;
//		int j = 0;
//		int c = 0;
//		while (i < m && j < n) {
//			if (a[i].b >= b[j].b) {
//				temp[c++] = a[i++];
//			
//			} else {
//				temp[c++] = b[j++];
//			}
//		}
//		while (i < m) {
//			temp[c++] = a[i++];
//		}
//		while (j < n) {
//			temp[c++] = b[j++];
//		}
//		return temp;
//	}
	public static long im(long a) {
		return binary_exponentiation_1(a,mod-2)%mod;
	}
	public static long binary_exponentiation_1(long a,long n) {
		long res=1;
		while(n>0) {
			if(n%2!=0) {
				res=((res)%(mod) * (a)%(mod))%(mod);
				n--;
			}else {
				a=((a)%(mod) *(a)%(mod))%(mod);
				n/=2;
			}
		}
		return (res)%(mod);
		
	}
	public static long b1(long a,long n) {
		long res=1;
		while(n>0) {
			if(n%2!=0) {
				res=((res)%(mod) * (a)%(mod))%(mod);
				n--;
			}else {
				a=((a)%(mod) *(a)%(mod))%(mod);
				n/=2;
			}
		}
		return (res)%(mod);
		
	}

	public static double bn1(double a,double n) {
		double res=1;
		while(n>0) {
			if(n%2!=0) {
//				res=((res)%(1000000007) * (a)%(1000000007))%(1000000007);
				res=(res*a);
				n--;
			}else {
//				a=((a)%(1000000007) *(a)%(1000000007))%(1000000007);
				a=(a*a);
				n/=2;
			}
		}
		return (res);	
	}
	public static long bn(long a,long n) {
		long res=1;
		while(n>0) {
			if(n%2!=0) {
				res=res*a;
				n--;
			}else {
				a*=a;
				n/=2;
			}
		}
		return res;
		
	}
public static long[] fac=new long[300001];
public static void ff() {
		fac[0]=(long)1;
		fac[1]=(long)1;
		for(long i=2;i<=300000;i++) {
			fac[(int) i]=(fac[(int) (i-1)]*i)%(m);
		}
	}	
public static long mod=1000000007;
public static long GCD(long a,long b) {
		if(b==(long)0) {
			return a;
		}
		return GCD(b , a%b);
	}
public static long c=0;	
}