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.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.Scanner;
import java.util.StringTokenizer;

public class Main {
	
	static FastScanner fs = new FastScanner();

	public static void main(String[] args) {
		
		
		int t = fs.nextInt();
		while(t-->0) {
			
			int n = fs.nextInt();
			String s1 = fs.next(), s2 = fs.next();
			StringBuffer ss = new StringBuffer();
			for(int i=0 ; i<n ; i++) {
				if(s1.charAt(i)=='1' && s2.charAt(i)=='0' || s1.charAt(i)=='0' && s2.charAt(i)=='1') ss.append("2");
				else if(s1.charAt(i)=='1' && s2.charAt(i)=='1') ss.append("0");
				else ss.append("1");
			}
			
			
			int cnt=0;
			char[] s = ss.toString().toCharArray();
			for(int i=0 ; i<n ; i++) {
				if(s[i]=='2') cnt += 2;
				else if(s[i]=='0' && i+1<n && s[i+1]=='1') {
					cnt+=2;
					i++;
				}
				else if(s[i]=='1'){
					if(i+1<n && s[i+1]=='0') {
						cnt += 2;
						i++;
					}else cnt += 1;
				}
			}
//			System.out.println(ss.toString());
			System.out.println(cnt);
		}	
	}
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	public static int[] readArray(int n){
		int[] a = new int[n];
		for(int i=0 ; i<n ; i++) {
			a[i] = fs.nextInt();
		}
        return a;
    }
	
	public static void printArray(int[] n){
        for(int e:n) {
        	System.out.print(e + " ");
        }
        System.out.println();
    }
	
	static int[] sort(int[] a) {
		ArrayList<Integer> l=new ArrayList<>();
		for (int i:a) l.add(i);
		Collections.sort(l);
		for (int i=0; i<a.length; i++) a[i]=l.get(i);
		return a;
	}
	
	static class FastScanner {
		BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st=new StringTokenizer("");
		String next() {
			while (!st.hasMoreTokens())
				try {
					st=new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			return st.nextToken();
		}
		
		int nextInt() {
			return Integer.parseInt(next());
		}
		int[] readArray(int n) {
			int[] a=new int[n];
			for (int i=0; i<n; i++) a[i]=nextInt();
			return a;
		}
		String[] readStringArray(int n) {
			String[] a=new String[n];
			for (int i=0; i<n; i++) a[i]=next();
			return a;
		}
		long nextLong() {
			return Long.parseLong(next());
		}
	}
	
//	BufferedWriter output = new BufferedWriter(
//            new OutputStreamWriter(System.out));
// 
//        for (int i = 0; i < gfg.length; i++) {
//            output.write(gfg[i] + "\n");
//        }
// 
//        output.flush();
	

}
