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.Random;
import java.util.StringTokenizer;
public class C{
// author: Tarun Verma
	static FastScanner sc = new FastScanner();
	static int inf = Integer.MAX_VALUE;
	static long mod = 1000000007;
	
	/* Common Mistakes By Me
	 * make sure to read the bottom part of question
	 * special cases (n=1?)
	 * In Game Theory Check your solution and consider all the solutions
	 * Always initialise value to the declare array in local scope
	 * don't use debugs in interactive problems
	 * Always Reset vis,adj array upto n+1 otherwise can cause TLE
	 */
	public static void solve() {
		int n = sc.nextInt();
		char arr[][] = new char[2][n];
		String s = sc.next();
		for(int i =0;i<n;i++) {
			arr[0][i] = s.charAt(i);
		}
		s = sc.next();
		for(int i =0;i<n;i++) {
			arr[1][i] = s.charAt(i);
		}
		long ans = 0;
		for(int i =0;i<n;i++) {
//			System.out.println("i: " + i);
			if((arr[0][i] == '0' && arr[1][i] == '1') || (arr[0][i] == '1' && arr[1][i] == '0')) {
				ans += 2;
				continue;
			}
			if(arr[0][i] == '0' && arr[1][i] == '0') {
				if( i+1 < n &&   arr[0][i+1] == '1' && arr[1][i+1] == '1') {
					ans += 2;
					i+=1;
					continue;
				}
				ans ++;
				continue;
			}
			if(arr[0][i] == '1' && arr[1][i] == '1') {
				if(i+1 < n &&   arr[0][i+1] == '0' && arr[1][i+1] == '0') {
					ans += 2;
					i+=1;
					continue;
				}
			}
		}
		System.out.println(ans);
	}
	
	public static void main(String[] args) {
		int t = 1;
		t = sc.nextInt();
		outer: for (int tt = 0; tt < t; tt++) {
			solve();
		}
	}
	
////////////////////////////////////////////////////////////////////////////////////
////////////////////DO NOT BELOW BEFORE THIS LINE //////////////////////////////////
////////////////////////////////////////////////////////////////////////////////////
	
	static boolean isPalindrom(char[] arr, int i, int j) {
		boolean ok = true;
		while (i <= j) {
			if (arr[i] != arr[j]) {
				ok = false;
				break;
			}
			i++;
			j--;
		}
		return ok;
	}
	
	static int max(int a, int b) {
		return Math.max(a, b);
	}
	
	static int min(int a, int b) {
		return Math.min(a, b);
	}
	
	static long max(long a, long b) {
		return Math.max(a, b);
	}
	
	static long min(long a, long b) {
		return Math.min(a, b);
	}
	
	static int abs(int a) {
		return Math.abs(a);
	}
	
	static long abs(long a) {
		return Math.abs(a);
	}
	
	static void swap(long arr[], int i, int j) {
		long temp = arr[i];
		arr[i] = arr[j];
		arr[j] = temp;
	}
	
	static void swap(int arr[], int i, int j) {
		int temp = arr[i];
		arr[i] = arr[j];
		arr[j] = temp;
	}
	
	static int maxArr(int arr[]) {
		int maxi = Integer.MIN_VALUE;
		for (int x : arr)
			maxi = max(maxi, x);
		return maxi;
	}
	
	static int minArr(int arr[]) {
		int mini = Integer.MAX_VALUE;
		for (int x : arr)
			mini = min(mini, x);
		return mini;
	}
	
	static long maxArr(long arr[]) {
		long maxi = Long.MIN_VALUE;
		for (long x : arr)
			maxi = max(maxi, x);
		return maxi;
	}
	
	static long minArr(long arr[]) {
		long mini = Long.MAX_VALUE;
		for (long x : arr)
			mini = min(mini, x);
		return mini;
	}
	
	static int gcd(int a, int b) {
		if (b == 0)
			return a;
		return gcd(b, a % b);
	}
	
	static long gcd(long a, long b) {
		if (b == 0)
			return a;
		return gcd(b, a % b);
	}
	
	static void ruffleSort(int[] a) {
		int n = a.length;
		Random r = new Random();
		for (int i = 0; i < a.length; i++) {
			int oi = r.nextInt(n);
			int temp = a[i];
			a[i] = a[oi];
			a[oi] = temp;
		}
		Arrays.sort(a);
	}
	
	public static int binarySearch(int a[], int target) {
		int left = 0;
		int right = a.length - 1;
		int mid = (left + right) / 2;
		int i = 0;
		while (left <= right) {
			if (a[mid] <= target) {
				i = mid + 1;
				left = mid + 1;
			} else {
				right = mid - 1;
			}
			mid = (left + right) / 2;
		}
		return i;
	}
	
	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;
		}
		
		long[] readLongArray(int n) {
			long[] a = new long[n];
			for (int i = 0; i < n; i++)
				a[i] = nextLong();
			return a;
		}
		
		int[][] read2dArray(int n, int m) {
			int arr[][] = new int[n][m];
			for (int i = 0; i < n; i++) {
				for (int j = 0; j < m; j++) {
					arr[i][j] = nextInt();
				}
			}
			return arr;
		}
		
		ArrayList<Integer> readArrayList(int n) {
			ArrayList<Integer> arr = new ArrayList<Integer>();
			for (int i = 0; i < n; i++) {
				int a = nextInt();
				arr.add(a);
			}
			return arr;
		}
		
		long nextLong() {
			return Long.parseLong(next());
		}
	}
	
	static class pair {
		int fr, sc;
		
		pair(int fr, int sc) {
			this.fr = fr;
			this.sc = sc;
		}
	}
	
////////////////////////////////////////////////////////////////////////////////////	
	
}
