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.io.BufferedReader;

import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;


public class Solve {
	static FastReader in=new FastReader();
    static final Random random=new Random();
    static long mod=1000000007L;
    static HashMap<Integer,Integer>map=new HashMap<>();
    static void ruffleSort(long[] a) {
        int n=a.length;
        for (int i=0; i<n; i++) {
            int oi=random.nextInt();
			long temp=a[oi];
            a[oi]=a[i]; a[i]=temp;
        }
        Arrays.sort(a);
    }
    public static int upper_bound(ArrayList<Integer> arr, int ele) {
    	int si = 0;
    	int ei = arr.size()-1;
    	int ans = -1;
    	while(si<=ei) {
    		int mid = (si + ei)/2;
    		if(arr.get(mid)<ele) {
    			si = mid +1;
    		}else {
    			ans = mid;
    			ei = mid -1;
    			
    		}
    	}
    	return ans;
    	
    }
    public static int lower_bound(ArrayList<Integer> arr, int ele) {
    	int si = 0;
    	int ei = arr.size()-1;
    	int ans = -1;
    	while(si<=ei) {
    		int mid = (si + ei)/2;
    		if(arr.get(mid)<=ele) {
    			ans = mid;
    			si = mid +1;
    		}
    		
    		else {
    			ei = mid -1;
    			
    			
    		}
    	}
    	return ans;
    	
    }
    
    
    
    
	
	public static void main(String[]args) {
FastReader res = new FastReader();
		
		int t = res.nextInt();
		
		
		while(t>0) {
			int n = res.nextInt();
			String s1 = res.nextLine();
			String s2 = res.nextLine();
			int ans = 0;
			int i =0; 
			while(i<n) {
				if(s1.charAt(i)=='1' && s2.charAt(i)=='1') {
					if(i+1<n && (s1.charAt(i+1)=='0' || s2.charAt(i+1)=='0')) {
						i = i+2;
						ans = ans +2;
						
					}else {
						i = i+1;
					}
				}else if(s1.charAt(i)=='0' && s2.charAt(i)=='0') {
					if(i+1<n && (s1.charAt(i+1)=='1' || s2.charAt(i+1)=='1')) {
						i = i+2;
						ans = ans +2;
						
					}else {
						ans = ans+1;
						i = i+1;
					}
				}else {
					
					ans = ans +2;
					i++;
				}
			}
			System.out.println(ans);
			
			
			
        		
        	
        	
        	
        	
        	
        	
        	

			
			t--;
			
			
			
			
			
			
	        
			
			
			
		}
	}
	static int max(int a, int b)
    {
        if(a<b)
        	return b;
        return a;
    }
 
 
    static void ruffleSort(int[] a) {
        int n=a.length;
        for (int i=0; i<n; i++) {
            int oi=random.nextInt(n), temp=a[oi];
            a[oi]=a[i]; a[i]=temp;
        }
        Arrays.sort(a);
    }
 
    static < E > void print(E res)
    {
        System.out.println(res);
    }
 
 
    static  int gcd(int a,int b)
    {
        if(b==0)
        {
            return a;
        }
        return gcd(b,a%b);
    }
 
    static int lcm(int a, int b)
    {
        return (a / gcd(a, b)) * b;
    }
 
 
    static int abs(int a)
    {
        if(a<0)
            return -1*a;
        return 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;
	        }
	 
	        int [] readintarray(int n) {
	            int res [] = new int [n];
	            for(int i = 0; i<n; i++)res[i] = nextInt();
	            return res;
	        }
	        long [] readlongarray(int n) {
	            long res [] = new long [n];
	            for(int i = 0; i<n; i++)res[i] = nextLong();
	            return res;
	        }
	    }
	 
	}
class pair{
	int x;
	int y;
}
