A binary string is a string that consists of characters 0 and 1. A bi-table is a table that has exactly two rows of equal length, each being a binary string.

Let \operatorname{MEX} of a bi-table be the smallest digit among 0, 1, or 2 that does not occur in the bi-table. For example, \operatorname{MEX} for \begin{bmatrix} 0011\\\ 1010 \end{bmatrix} is 2, because 0 and 1 occur in the bi-table at least once. \operatorname{MEX} for \begin{bmatrix} 111\\\ 111 \end{bmatrix} is 0, because 0 and 2 do not occur in the bi-table, and 0 < 2.

You are given a bi-table with n columns. You should cut it into any number of bi-tables (each consisting of consecutive columns) so that each column is in exactly one bi-table. It is possible to cut the bi-table into a single bi-table — the whole bi-table.

What is the maximal sum of \operatorname{MEX} of all resulting bi-tables can be?

Input

The input consists of multiple test cases. The first line contains a single integer t (1 ≤ t ≤ 10^4) — the number of test cases. Description of the test cases follows.

The first line of the description of each test case contains a single integer n (1 ≤ n ≤ 10^5) — the number of columns in the bi-table.

Each of the next two lines contains a binary string of length n — the rows of the bi-table.

It's guaranteed that the sum of n over all test cases does not exceed 10^5.

Output

For each test case print a single integer — the maximal sum of \operatorname{MEX} of all bi-tables that it is possible to get by cutting the given bi-table optimally.

Example

Input


4
7
0101000
1101100
5
01100
10101
2
01
01
6
000000
111111


Output


8
8
2
12

Note

In the first test case you can cut the bi-table as follows:

  * \begin{bmatrix} 0\\\ 1 \end{bmatrix}, its \operatorname{MEX} is 2.
  * \begin{bmatrix} 10\\\ 10 \end{bmatrix}, its \operatorname{MEX} is 2.
  * \begin{bmatrix} 1\\\ 1 \end{bmatrix}, its \operatorname{MEX} is 0.
  * \begin{bmatrix} 0\\\ 1 \end{bmatrix}, its \operatorname{MEX} is 2.
  * \begin{bmatrix} 0\\\ 0 \end{bmatrix}, its \operatorname{MEX} is 1.
  * \begin{bmatrix} 0\\\ 0 \end{bmatrix}, its \operatorname{MEX} is 1.



The sum of \operatorname{MEX} is 8.
import java.util.*;
import java.io.*;
import java.lang.*;

public class Main {
    //input
    static out op = new out();
    static inp ip = new inp();
    static FastReader sc = new FastReader();
    static BufferedWriter output = new BufferedWriter( 
        new OutputStreamWriter(System.out));
    static long inf = (long)1e9+7;
   
   static long mod = (long)1e18+7;
   static long z = 0;

   static void sol() throws Exception{
      
      int n = ip.in();
      char[] s1 = ip.cain();
      char[] s2 = ip.cain();
      
      int[] arr = new int[n];
      for(int i=0;i<n;i++)
         arr[i] = Integer.parseInt(s1[i]+"")*10+Integer.parseInt(s2[i]+"");
      
      int sum = 0;
      boolean shared[] = new boolean[n];
      for(int i=0;i<n;i++){
         if(arr[i] == 1)sum += 2;
         if(arr[i] == 10)sum += 2;
         
         if(arr[i] == 0){
            if(i+1<n && arr[i+1] == 11){
               if(!shared[i]){
                  sum ++;
                  shared[i+1] = true;
               }
            }
            sum += 1;
         }
         
         if(arr[i] == 11){
            if(i+1<n && arr[i+1] == 0){
               if(!shared[i]){
                  sum++;
                  shared[i+1] = true;
               }
            }
         }
      }
      
      op.sbln(sum);
      
   }
   
   
   static long gcd(long a,long b){
     if(b==0)
     return a;
     return gcd(b,a%b);
   }
   
   public static void main(String[] args) throws Exception { 
       
      int t = ip.in();
      while(t-- > 0){
         sol();
      }
      op.output.flush();
    }
   //  static class Node implements Comparable<Node>{
   //     int data;
   //     int ind;
   //    //  Node left,right;
   //    //  Node(){
   //    //       left = null;
   //    //       right = null;
   //    //  }
   //     Node(int ind,int data){
   //          this.data = data;
   //          this.ind = ind;
   //     }
    
   //       @Override
   //       public int compareTo(Node o) {
   //           if(this.data == o.data)
   //           return this.ind - o.ind;
   //           // TODO Auto-generated method stub
   //           return this.data - o.data;
   //       }
   //  }
}


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; 
    }

}
class inp{
    FastReader sc = new FastReader();
    int in(){
        int a = sc.nextInt();
        return a;
    }
    long lin(){
        long a = sc.nextLong();
        return a;
    }
    char cin(){
        char c = sc.next().charAt(0);
        return c;
    }
    char[] cain(){
        char[] a = sc.nextLine().toCharArray();
        return a;
    }
    int[] arrin(int n){
        int [] arr = new int[n];
        for(int i=0;i<n;i++)
            arr[i] = in();

        return arr;
    }
    int[] mm_arr(int[] arr){
        int max = Integer.MIN_VALUE;
        int min = Integer.MAX_VALUE;
        for(int i=0;i<arr.length;i++){
            max = Math.max(max,arr[i]);
            min = Math.min(min,arr[i]);
        }
        int ans[] = {max,min};
        return ans;
    }
    int[] srt(int[] arr){
        Arrays.sort(arr);
        return arr;
    }
    long pow(long a,long b){
        if(b == 0)return 1;
        long res = pow(a,b/2);
        //System.out.println(res + " " + b + " " + (b&1));
        if((b&1) == 0)return res*res;
        return a*res*res; 
    }

   //  boolean[] prime(){
   //     boolean prime[] = new boolean[100000001];
   //     Arrays.fill(prime,true);
   //     for (int p = 2; p * p <= 10000000; p++)
   //     {
   //          // If prime[p] is not changed,
   //          // then it is a prime
   //          if (prime[p] == true)
   //          {
   //              // Update all multiples
   //              // of p greater than or
   //              // equal to the square of it
   //              // numbers which are multiple
   //              // of p and are less than p^2
   //              // are already been marked.
   //              for (int i = p * p; i <= 10000000; i += p)
   //                 prime[i] = false;
   //          }
   //     }
   //     return prime;
   //  }
}
class out{
    BufferedWriter output = new BufferedWriter( 
        new OutputStreamWriter(System.out)); 

    void sb(String s) throws IOException {
        output.write(s);
    }
    void sbln(Object s) throws IOException {
        output.write(s+"\n");
    }
    void yes() throws IOException{
        output.write("YES\n");
    }
    void no() throws IOException{
        output.write("NO\n");
    }
}