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.lang.reflect.Array;
import java.util.*;

public class Main {
    // final CustomReader in = new CustomReader("input.txt");
    final CustomReader in = new CustomReader();
    final PrintWriter out = new PrintWriter(System.out);

    void solve() {
        int t = in.nextInt();
        while (t-- > 0) {
            int n = in.nextInt();
            String upS = in.nextLine();
            String downS = in.nextLine();

            boolean findZero = false;
            int answer = 0;
            for (int i = 0; i < n; i++) {
                int up = upS.charAt(i) - '0';
                int down = downS.charAt(i) - '0';

                if (up + down == 2) {
                    findZero = true;
                } else if (up + down == 1) {
                    answer += 2;
                    findZero = false;
                } else {
                    if (findZero) {
                        answer += 2;
                        findZero = false;
                    } else if (i + 1 < n) {
                        int nextUp = upS.charAt(i+1) - '0';
                        int nextDown = downS.charAt(i+1) - '0';
                        if (nextDown + nextUp == 2) {
                            answer += 2;
                            i++;
                        } else {
                            answer += 1;
                        }
                    } else {
                        answer += 1;
                    }

                }
            }
            out.println(answer);
        }
    }

    public static void main(String[] args) { Main s = new Main(); s.solve(); s.out.close(); }

    private static class CustomReader {
        private final InputStream stream;
        private final byte[] buf = new byte[8192];
        private int curChar;
        private int numChars;

        CustomReader() {
            stream = System.in;
        }

        CustomReader(String fileName) {
            InputStream temp = null;
            try {
                temp = new FileInputStream(fileName);
            } catch (FileNotFoundException e) {
                e.printStackTrace();
            }
            stream = temp;
        }

        String nextLine() {
            int c = read();
            StringBuilder res = new StringBuilder();
            while (!isEndOfLine(c)) {
                res.appendCodePoint(c);
                c = read();
            }
            if (c == '\r') read();
            return res.toString();
        }

        String nextString() {
            int c = read();
            while (isSpaceChar(c)) c = read();
            StringBuilder res = new StringBuilder();
            while (!isSpaceChar(c)) {
                res.appendCodePoint(c);
                c = read();
            }
            if (c == '\r') read();
            return res.toString();
        }

        long nextLong() {
            int c = read();
            while (isSpaceChar(c)) c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            while (!isSpaceChar(c)) {
                if (c < '0' || c > '9') throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '\r') read();
            return res * sgn;
        }

        int nextInt() {
            int c = read();
            while (isSpaceChar(c)) c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            while (!isSpaceChar(c)) {
                if (c < '0' || c > '9') throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '\r') read();
            return res * sgn;
        }

        int[] nextArray(int n) {
            int[] arr = new int[n];
            for (int i = 0; i < n; i++) arr[i] = nextInt();
            return arr;
        }

        double nextDouble() {
            return Double.parseDouble(nextString());
        }

        boolean hasNext() {
            if (numChars == -1) return false;
            return curChar < numChars || curChar == buf.length || numChars == 0; // Probably
        }

        private int read() {
            if (numChars == -1) throw new InputMismatchException();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) return -1;
            }
            return buf[curChar++];
        }

        private static boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        private static boolean isEndOfLine(int c) {
            return c == '\n' || c == '\r' || c == -1;
        }
    }
}
