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.lang.*;
import java.io.*;


/* Name of the class has to be "Main" only if the class is public. */
public class Codechef
{
   
	
    static FastReader sc = new FastReader();
	public static void main (String[] args) throws java.lang.Exception
	{
	// your code goes here
		
		
		int t = sc.nextInt() ;
		
		while(t>0) {
		    int n=sc.nextInt();
		    String s1=sc.next();
		    String s2=sc.next();
		    char arr[]=s1.toCharArray();
		    char brr[]=s2.toCharArray();
		    int store=0;
		    int storezero=0;
		    int count=0;
		    for(int i=0;i<arr.length;i++)
		    {
		        if(arr[i]== '1' && brr[i]=='0')
		        {
		            count=count+2;
		            store=0;
		           if(storezero>0)
		           {
		               count++;
		               storezero=0;
		           }
		        }
		        else if(brr[i]=='1' && arr[i]=='0')
		        {
		            count+=2;
		            store=0;
		              if(storezero>0)
		           {
		               count++;
		               storezero=0;
		           }
		        }
		        else if(arr[i]=='0' && brr[i]=='0'){
		            if(store>0)
		            {
		                count+=2;
		                store=0;
		            }
		            else{
		            storezero++;}
		        }
		     
		        else{
		            if(storezero>0)
		            {
		                count+=2;
		                storezero=0;
		            }
		            else{
		           store++;}
		        }
		      //  System.out.println(count);
		    }
		    count=count+storezero;
		    System.out.println(count);
			t--;
		}
	}
	
	
	
	//	FAST I/O
	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;
        }
	}

public static boolean two(int n)//power of two
{
if((n&(n-1))==0)
{
return true;
}
else{
return false;
}
	
}	
}



// Vector<Integer>arr=new Vector<Integer>();
// HashMap<Integer,Integer>arr=new HashMap<Integer>();
// LinkedList<Integer>arr=new LinkedList<Integer>();
// int arr[]=new int[n];