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.InputStreamReader;
public class HelloWorld{
     public static void main(String []args) throws java.io.IOException{
        BufferedReader scan = new BufferedReader(new InputStreamReader(System.in));
        int t = Integer.parseInt(scan.readLine());
        for(int i=0; i<t; i++) {
            int n = Integer.parseInt(scan.readLine());
            String row1 = scan.readLine();
            String row2 = scan.readLine();
            int sum = 0;
            char prev = ' ';
            for(int j=0; j<n; j++) {
                if(row1.charAt(j) != row2.charAt(j)) {
                    sum += 2;
                    prev = ' ';
                }
                else {
                    if(row1.charAt(j) == '0') {
                        if(prev == '1') {
                            sum += 2;
                            prev = ' ';
                        }
                        else if(prev == '0') {
                            sum += 1;
                            prev = row1.charAt(j);
                        }
                        else {
                            sum += 1;
                            prev = row1.charAt(j);
                        }
                    }
                    else {
                        if(prev == '0') {
                            sum += 1;
                            prev = ' ';
                        }
                        else  {
                            prev = row1.charAt(j);
                        }
                    }
                }
            }
            System.out.println(sum);
        }
     }
}