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


/**
 * @author Naitik
 * 
 */
public class Main

{ 
	 static FastReader sc=new FastReader(); 
	 static long dp[][];
	 static int mod=1000000007;
	 static int mod1=998244353;
	 static int max;
	 static long bit[];
	 static long seg[];
	 static long fact[];

	   static PrintWriter out=new PrintWriter(System.out);
	  public static void main(String[] args)
{
		    //CHECK FOR N=1
	       	//CHECK FOR N=1
		   //StringBuffer sb=new StringBuffer("");
		  int ttt=1;
		      ttt =i();
	        outer :while (ttt-- > 0) 
			{
	        	int n=i();
	        	char A[]=s().toCharArray();
	        	char B[]=s().toCharArray();
	        	int ans=0;
	        	for(int i=0;i<n;i++) {
	        		if(A[i]=='0') {
	        			if(B[i]=='1') {
	        				ans++;
	        				B[i]='0';
	        			}
	        		}
	        	}
	        	for(int i=0;i<n;i++) {
	        		if(A[i]=='1') {
	        			if(i-1>=0 && B[i-1]=='1') {
	        				ans++;
	        				B[i-1]='0';
	        				continue;
	        			}
	        			if(i+1<n && B[i+1]=='1') {
	        				ans++;
	        				B[i+1]='0';
	        			}
	        		}
	        	}
	        	System.out.println(ans);
	        	
	        	
	        	
	        }
	        //System.out.println(sb.toString());
		     out.close();
	     
	     
	    //CHECK FOR N=1                    //CHECK FOR M=0
        //CHECK FOR N=1                    //CHECK FOR M=0
       	//CHECK FOR N=1
       	
		        
		     
    }


static class Pair implements Comparable<Pair>
     {
    	 int x;
    	 int y;
    	 Pair(int x,int y){
    		 this.x=x;
    		 this.y=y;
    		 
    	 }
		@Override
		public int compareTo(Pair o) {
			if(this.x>o.x)
				return -1;
			else if(this.x<o.x)
				return +1;
			else {
				if(this.y>o.y)
					return -1;
				else if(this.y<o.y)
					return +1;
				else
					return 0;
			}
		}
//		public int hashCode() 
//		{ 
//			final int temp = 14; 
//			int ans = 1; 
//			ans =x*31+y*13; 
//			return ans; 
//		} 
//		@Override
//		public boolean equals(Object o) 
//		{ 
//			if (this == o) { 
//				return true; 
//			} 
//			if (o == null) { 
//				return false; 
//			} 
//			if (this.getClass() != o.getClass()) { 
//				return false; 
//			} 
//			Pair other = (Pair)o; 
//			if (this.x != other.x || this.y!=other.y) { 
//				return false; 
//			} 
//			return true; 
//		} 	
//		
		/* FOR TREE MAP PAIR USE */
		
//		public int compareTo(Pair o) {
// 			if (x > o.x) {
// 				return 1;
// 			}
// 			if (x < o.x) {
// 				return -1;
// 			}
// 			if (y > o.y) {
// 				return 1;
// 			}
// 			if (y < o.y) {
// 				return -1;
// 			}
// 			return 0;
// 		}
		
     }
//FENWICK TREE
static void update(int i, int x){
	for(; i < bit.length; i += (i&-i))
		bit[i] += x;
}

static int sum(int i){
	int ans = 0;
	for(; i > 0; i -= (i&-i))
		ans += bit[i];
	return ans;
}
//END
//static void add(int v) {
//	if(!map.containsKey(v)) {
//		map.put(v, 1);
//	}
//	else {
//		map.put(v, map.get(v)+1);
//	}
//}
//static void remove(int v) {
//	if(map.containsKey(v)) {
//		map.put(v, map.get(v)-1);
//		if(map.get(v)==0)
//			map.remove(v);
//	}
//}
public static int upper(int A[],int k,int si,int ei)
{
	int l=si;
	int u=ei;
	int ans=-1;
	while(l<=u) {
		int mid=(l+u)/2;
		if(A[mid]<=k) {
			ans=mid;
			l=mid+1;
		}
		else {
			u=mid-1;
		}
	}
	return ans;
}
public static int lower(int A[],int k,int si,int ei)
{
	int l=si;
	int u=ei;
	int ans=-1;
	while(l<=u) {
		int mid=(l+u)/2;
		if(A[mid]<=k) {
			l=mid+1;
		}
		else {
			ans=mid;
			u=mid-1;
		}
	}
	return ans;
	
    
}
static int[] copy(int A[]) {
	int B[]=new int[A.length];
	for(int i=0;i<A.length;i++) {
		B[i]=A[i];
	}
	return B;
}
static long[] copy(long A[]) {
	long B[]=new long[A.length];
	for(int i=0;i<A.length;i++) {
		B[i]=A[i];
	}
	return B;
}
static int[] input(int n) {
	int A[]=new int[n];
	   for(int i=0;i<n;i++) {
		   A[i]=sc.nextInt();
	   }
	   return A;
   }
static long[] inputL(int n) {
	long A[]=new long[n];
	   for(int i=0;i<n;i++) {
		   A[i]=sc.nextLong();
	   }
	   return A;
   }
static String[] inputS(int n) {
	String A[]=new String[n];
	   for(int i=0;i<n;i++) {
		   A[i]=sc.next();
	   }
	   return A;
   }
static long sum(int A[]) {
	long sum=0;
	for(int i : A) {
		sum+=i;
	}
	return sum;
}
static long sum(long A[]) {
	long sum=0;
	for(long i : A) {
		sum+=i;
	}
	return sum;
}
static void reverse(long A[]) {
	int n=A.length;
	long B[]=new long[n];
	for(int i=0;i<n;i++) {
		B[i]=A[n-i-1];
	}
	for(int i=0;i<n;i++)
		A[i]=B[i];
	
}
static void reverse(int A[]) {
	int n=A.length;
	int B[]=new int[n];
	for(int i=0;i<n;i++) {
		B[i]=A[n-i-1];
	}
	for(int i=0;i<n;i++)
		A[i]=B[i];
	
}
static void input(int A[],int B[]) {
	   for(int i=0;i<A.length;i++) {
		   A[i]=sc.nextInt();
		   B[i]=sc.nextInt();
	   }
}
static int[][] input(int n,int m){
	int A[][]=new int[n][m];
	for(int i=0;i<n;i++) {
		for(int j=0;j<m;j++) {
			A[i][j]=i();
		}
	}
	return A;
}
static char[][] charinput(int n,int m){
	char A[][]=new char[n][m];
	for(int i=0;i<n;i++) {
		String s=s();
		for(int j=0;j<m;j++) {
			A[i][j]=s.charAt(j);
		}
	}
	return A;
}
static int find(int A[],int a) {
	  if(A[a]==a)
		  return a;
	  return A[a]=find(A, A[a]);
}
static int max(int A[]) {
	int max=Integer.MIN_VALUE;
	for(int i=0;i<A.length;i++) {
		max=Math.max(max, A[i]);
	}
	return max;
}
static int min(int A[]) {
	int min=Integer.MAX_VALUE;
	for(int i=0;i<A.length;i++) {
		min=Math.min(min, A[i]);
	}
	return min;
}
static long max(long A[]) {
	long max=Long.MIN_VALUE;
	for(int i=0;i<A.length;i++) {
		max=Math.max(max, A[i]);
	}
	return max;
}
static long min(long A[]) {
	long min=Long.MAX_VALUE;
	for(int i=0;i<A.length;i++) {
		min=Math.min(min, A[i]);
	}
	return min;
}
static long [] prefix(long A[]) {
	long p[]=new long[A.length];
	p[0]=A[0];
	for(int i=1;i<A.length;i++)
		p[i]=p[i-1]+A[i];
	return p;
}
static long [] prefix(int A[]) {
	long p[]=new long[A.length];
	p[0]=A[0];
	for(int i=1;i<A.length;i++)
		p[i]=p[i-1]+A[i];
	return p;
}
static long [] suffix(long A[]) {
	long p[]=new long[A.length];
	p[A.length-1]=A[A.length-1];
	for(int i=A.length-2;i>=0;i--)
		p[i]=p[i+1]+A[i];
	return p;
}
static long [] suffix(int A[]) {
	long p[]=new long[A.length];
	p[A.length-1]=A[A.length-1];
	for(int i=A.length-2;i>=0;i--)
		p[i]=p[i+1]+A[i];
	return p;
}
static void fill(int dp[]) {
	Arrays.fill(dp, -1);
}
static void fill(int dp[][]) {
	for(int i=0;i<dp.length;i++)
	Arrays.fill(dp[i], -1);
}
static void fill(int dp[][][]) {
	for(int i=0;i<dp.length;i++) {
		for(int j=0;j<dp[0].length;j++) {
			Arrays.fill(dp[i][j],-1);
		}
	}
}
static void fill(int dp[][][][]) {
	for(int i=0;i<dp.length;i++) {
		for(int j=0;j<dp[0].length;j++) {
			for(int k=0;k<dp[0][0].length;k++) {
			Arrays.fill(dp[i][j][k],-1);
			}
		}
	}
}
static void fill(long dp[]) {
	Arrays.fill(dp, -1);
}
static void fill(long dp[][]) {
	for(int i=0;i<dp.length;i++)
	Arrays.fill(dp[i], -1);
}
static void fill(long dp[][][]) {
	for(int i=0;i<dp.length;i++) {
		for(int j=0;j<dp[0].length;j++) {
			Arrays.fill(dp[i][j],-1);
		}
	}
}
static void fill(long dp[][][][]) {
	for(int i=0;i<dp.length;i++) {
		for(int j=0;j<dp[0].length;j++) {
			for(int k=0;k<dp[0][0].length;k++) {
			Arrays.fill(dp[i][j][k],-1);
			}
		}
	}
}
static int min(int a,int b) {
	return Math.min(a, b);
}
static int min(int a,int b,int c) {
	return Math.min(a, Math.min(b, c));
}
static int min(int a,int b,int c,int d) {
	return Math.min(a, Math.min(b, Math.min(c, d)));
}
static int max(int a,int b) {
	return Math.max(a, b);
}
static int max(int a,int b,int c) {
	return Math.max(a, Math.max(b, c));
}
static int max(int a,int b,int c,int d) {
	return Math.max(a, Math.max(b, Math.max(c, d)));
}
static long min(long a,long b) {
	return Math.min(a, b);
}
static long min(long a,long b,long c) {
	return Math.min(a, Math.min(b, c));
}
static long min(long a,long b,long c,long d) {
	return Math.min(a, Math.min(b, Math.min(c, d)));
}
static long max(long a,long b) {
	return Math.max(a, b);
}
static long max(long a,long b,long c) {
	return Math.max(a, Math.max(b, c));
}
static long max(long a,long b,long c,long d) {
	return Math.max(a, Math.max(b, Math.max(c, d)));
}

static long power(long x, long y, long p)
{

	if(y==0)
		return 1;
	if(x==0)
		return 0;
    long res = 1;
    x = x % p;

    while (y > 0) {

        if (y % 2 == 1)
            res = (res * x) % p;

        y = y >> 1; 
        x = (x * x) % p;
    }

    return res;
}
static void print(int A[]) {
	for(int i : A) {
		System.out.print(i+" ");
	}
	System.out.println();
}
static void print(long A[]) {
	for(long i : A) {
		System.out.print(i+" ");
	}
	System.out.println();
}
static long mod(long x) {
	  return ((x%mod + mod)%mod);
}
static String reverse(String s) {
	StringBuffer p=new StringBuffer(s);
	p.reverse();
	return p.toString();
}

     static int i() {
    	 return sc.nextInt();
     }
     static String s() {
    	 return sc.next();
     }
     static long l() {
    	 return sc.nextLong();
     }  
     static void sort(int[] A){
        int n = A.length;
        Random rnd = new Random();
        for(int i=0; i<n; ++i){
            int tmp = A[i];
            int randomPos = i + rnd.nextInt(n-i);
            A[i] = A[randomPos];
            A[randomPos] = tmp;
        }
        Arrays.sort(A);
     }
     static void sort(long[] A){
	        int n = A.length;
	        Random rnd = new Random();
	        for(int i=0; i<n; ++i){
	            long tmp = A[i];
	            int randomPos = i + rnd.nextInt(n-i);
	            A[i] = A[randomPos];
	            A[randomPos] = tmp;
	        }
	        Arrays.sort(A);
	     }
  static String sort(String s) {
 	 Character ch[]=new Character[s.length()];
 	 for(int i=0;i<s.length();i++) {
 		 ch[i]=s.charAt(i);
 	 }
 	 Arrays.sort(ch);
 	 StringBuffer st=new StringBuffer("");
 	 for(int i=0;i<s.length();i++) {
 		 st.append(ch[i]);
 	 }
 	 return st.toString();
  }
  static HashMap<Integer,Integer> hash(int A[]){
	  HashMap<Integer,Integer> map=new HashMap<Integer, Integer>();
	  for(int i : A) {
		  if(map.containsKey(i)) {
			  map.put(i, map.get(i)+1);
		  }
		  else {
			  map.put(i, 1);
		  }
	  }
	  return map;
  }
  static TreeMap<Integer,Integer> tree(int A[]){
	  TreeMap<Integer,Integer> map=new TreeMap<Integer, Integer>();
	  for(int i : A) {
		  if(map.containsKey(i)) {
			  map.put(i, map.get(i)+1);
		  }
		  else {
			  map.put(i, 1);
		  }
	  }
	  return map;
  }
     static boolean prime(int n) 
	    { 
	        if (n <= 1) 
	            return false; 
	        if (n <= 3) 
	            return true; 
	        if (n % 2 == 0 || n % 3 == 0) 
	            return false; 
	        double sq=Math.sqrt(n);
	  
	        for (int i = 5; i <= sq; i = i + 6) 
	            if (n % i == 0 || n % (i + 2) == 0) 
	                return false; 
	        return true; 
	    } 
     static boolean prime(long n) 
	    { 
	        if (n <= 1) 
	            return false; 
	        if (n <= 3) 
	            return true; 
	        if (n % 2 == 0 || n % 3 == 0) 
	            return false; 
	        double sq=Math.sqrt(n);
	  
	        for (int i = 5; i <= sq; i = i + 6) 
	            if (n % i == 0 || n % (i + 2) == 0) 
	                return false; 
	        return true; 
	    } 
     static int gcd(int a, int b) 
     { 
         if (a == 0) 
             return b; 
         return gcd(b % a, a); 
     } 
     static long gcd(long a, long b) 
     { 
         if (a == 0) 
             return b; 
         return gcd(b % a, a); 
     } 
     
        
    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; 
        } 
    } 
} 



