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.
//package com.company;

import java.io.FileInputStream;
import java.io.InputStream;
import java.util.*;



public class Main {

    public static void main(String[] args) {
        // write your code here

        try {
            //InputStream is = new FileInputStream("/Users/francescarnero/Downloads/traffic_control_input.txt");

            Scanner scanner = new Scanner(System.in);
            int t = scanner.nextInt();

            while (t-- > 0) {

                int n = scanner.nextInt();
                String s = scanner.next();
                String s1 = scanner.next();


                StringBuilder sb = new StringBuilder();
                for(int i=0; i < n;i++)
                {
                    if(s.charAt(i)==s1.charAt(i))
                    {
                        if(s.charAt(i)=='0')
                            sb.append('1');
                        else
                            sb.append('0');
                    }else{
                        sb.append('2');
                    }
                }
                int i =0;
                long sol =0;
                while(i<sb.length())
                {
                    if(sb.charAt(i)=='2')
                        sol +=2;
                    else if(sb.charAt(i)=='0')
                    {
                        if(i>0&&sb.charAt(i-1)=='1')
                        {
                           sol += 2;
                           sb.setCharAt(i,'3');
                           if(i==1) sol--;

                        }
                    }else{
                        if(i>0&&sb.charAt(i-1)=='0')
                        {
                            sol += 2;
                            sb.setCharAt(i,'3');

                        }else
                            sol+= 1;
                    }
                    i++;
                }
                System.out.println(sol);





            }

        }catch (Exception e){

        }
    }










}