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.*;
import java.util.*;

public class A {

	static Scanner sc = new Scanner(System.in);
	// static Reader sc = new Reader();
	static StringBuilder out = new StringBuilder();

	static String testCase = "Case #";
	static long mod = 998244353;
	static long fac[] = new long[3 * (int) 1e5];

	public static void main(String[] args) throws IOException {
		// TODO Auto-generated method stub

		int t =  sc.nextInt();

		int tc = 0;

		fac[0] = 1;

		for (int i = 1; i < fac.length; i++) {

			fac[i] = fac[i - 1] * i;
			fac[i] %= mod;
		}

		while (tc++ < t) {
			// out.append(testCase + tc + ": ");
			A run = new A();

			run.run();
		}

		System.out.println(out);

	}

	static int a[][];

	static ArrayList<Long> al = new ArrayList<>();

	static class pair implements Comparable<pair> {

		int f, s;

		pair(int f, int s) {
			this.f = f;
			this.s = s;

		}

		@Override
		public int compareTo(pair o) {
			// TODO Auto-generated method stub

			return o.s - this.s;

		}

	}

	public void run() throws IOException {

		
		int n=sc.nextInt();

	
		String s=sc.next(),s1=sc.next();
		
		
		
		
		
		int i=0;
		int ans=0;
		while(i<n) {
			
			
			int z=0;
			int o=0;
			
			if(s.charAt(i)=='0')z=1;
			else o=1;
			
			if(s1.charAt(i)=='0')z=1;
			else o=1;
			
			if(z==1 && o==1) {
				ans+=2;
				i++;
				continue;
				
			}
			
			if(i<n-1) {
				
				
				if(s.charAt(i+1)=='0')z++;
				else o++;
				
				if(s1.charAt(i+1)=='0')z++;
				else o++;
				
			}
			
			if(z>0 && o>0) {
				
				ans+=2;
				i+=2;
				continue;
			}
			
			if(z>0)ans++;
			
			i++;
			
		}
		
		out.append(ans+"\n");
		

	}

	static long modInverse(long a, long m) {
		long m0 = m;
		long y = 0, x = 1;

		if (m == 1)
			return 0;

		while (a > 1) {
			// q is quotient
			long q = a / m;

			long t = m;

			m = a % m;
			a = t;
			t = y;

			// Update x and y
			y = x - q * y;
			x = t;
		}

		// Make x positive
		if (x < 0)
			x += m0;

		return x;
	}

	static class Reader {
		final private int BUFFER_SIZE = 1 << 16;
		private DataInputStream din;
		private byte[] buffer;
		private int bufferPointer, bytesRead;

		public Reader() {
			din = new DataInputStream(System.in);
			buffer = new byte[BUFFER_SIZE];
			bufferPointer = bytesRead = 0;
		}

		public Reader(String file_name) throws IOException {
			din = new DataInputStream(new FileInputStream(file_name));
			buffer = new byte[BUFFER_SIZE];
			bufferPointer = bytesRead = 0;
		}

		public String readLine() throws IOException {
			byte[] buf = new byte[64]; // line length
			int cnt = 0, c;
			while ((c = read()) != -1) {
				if (c == '\n') {
					if (cnt != 0) {
						break;
					} else {
						continue;
					}
				}
				buf[cnt++] = (byte) c;
			}
			return new String(buf, 0, cnt);
		}

		public int nextInt() throws IOException {
			int ret = 0;
			byte c = read();
			while (c <= ' ') {
				c = read();
			}
			boolean neg = (c == '-');
			if (neg)
				c = read();
			do {
				ret = ret * 10 + c - '0';
			} while ((c = read()) >= '0' && c <= '9');

			if (neg)
				return -ret;
			return ret;
		}

		public long nextLong() throws IOException {
			long ret = 0;
			byte c = read();
			while (c <= ' ')
				c = read();
			boolean neg = (c == '-');
			if (neg)
				c = read();
			do {
				ret = ret * 10 + c - '0';
			} while ((c = read()) >= '0' && c <= '9');
			if (neg)
				return -ret;
			return ret;
		}

		public double nextDouble() throws IOException {
			double ret = 0, div = 1;
			byte c = read();
			while (c <= ' ')
				c = read();
			boolean neg = (c == '-');
			if (neg)
				c = read();

			do {
				ret = ret * 10 + c - '0';
			} while ((c = read()) >= '0' && c <= '9');

			if (c == '.') {
				while ((c = read()) >= '0' && c <= '9') {
					ret += (c - '0') / (div *= 10);
				}
			}

			if (neg)
				return -ret;
			return ret;
		}

		private void fillBuffer() throws IOException {
			bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
			if (bytesRead == -1)
				buffer[0] = -1;
		}

		private byte read() throws IOException {
			if (bufferPointer == bytesRead)
				fillBuffer();
			return buffer[bufferPointer++];
		}

		public void close() throws IOException {
			if (din == null)
				return;
			din.close();
		}
	}

}