There is a chessboard of size n by n. The square in the i-th row from top and j-th column from the left is labelled (i,j).

Currently, Gregor has some pawns in the n-th row. There are also enemy pawns in the 1-st row. On one turn, Gregor moves one of his pawns. A pawn can move one square up (from (i,j) to (i-1,j)) if there is no pawn in the destination square. Additionally, a pawn can move one square diagonally up (from (i,j) to either (i-1,j-1) or (i-1,j+1)) if and only if there is an enemy pawn in that square. The enemy pawn is also removed.

Gregor wants to know what is the maximum number of his pawns that can reach row 1?

Note that only Gregor takes turns in this game, and the enemy pawns never move. Also, when Gregor's pawn reaches row 1, it is stuck and cannot make any further moves.

Input

The first line of the input contains one integer t (1≤ t≤ 2⋅ 10^4) — the number of test cases. Then t test cases follow.

Each test case consists of three lines. The first line contains a single integer n (2≤ n≤ 2⋅{10}^{5}) — the size of the chessboard.

The second line consists of a string of binary digits of length n, where a 1 in the i-th position corresponds to an enemy pawn in the i-th cell from the left, and 0 corresponds to an empty cell.

The third line consists of a string of binary digits of length n, where a 1 in the i-th position corresponds to a Gregor's pawn in the i-th cell from the left, and 0 corresponds to an empty cell.

It is guaranteed that the sum of n across all test cases is less than 2⋅{10}^{5}.

Output

For each test case, print one integer: the maximum number of Gregor's pawns which can reach the 1-st row.

Example

Input


4
3
000
111
4
1111
1111
3
010
010
5
11001
00000


Output


3
4
0
0

Note

In the first example, Gregor can simply advance all 3 of his pawns forward. Thus, the answer is 3.

In the second example, Gregor can guarantee that all 4 of his pawns reach the enemy row, by following the colored paths as demonstrated in the diagram below. Remember, only Gregor takes turns in this "game"!

<image>

In the third example, Gregor's only pawn is stuck behind the enemy pawn, and cannot reach the end.

In the fourth example, Gregor has no pawns, so the answer is clearly 0.
1
20
01001100111111000100
00101100011010001110

8

import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.util.Arrays;
import java.util.InputMismatchException;

/**
 * @author ethan55
 */
public class Solution {

  public static void main(String[] args) {
    TestRunner.run();
  }

  public static class TestCase {

    static final boolean MULTIPLE = true;

    public void solve(InputReader in, OutputWriter out) {
      int n = in.nextInt();
      char[] top = in.nextCharArray(n);
      char[] bottom = in.nextCharArray(n);
      int result = 0;
      for (int i = 0; i < bottom.length; i++) {
        if (bottom[i] == '0') {
          continue;
        }
        if (top[i] == '0') {
          result++;
        } else {
          if (i < bottom.length - 1 && top[i + 1] == '1') {
            result += 2;
            top[i] = '0';
            top[i + 1] = '0';
            bottom[i + 1] = '0';
          }
        }
      }
      out.println(result);
    }
  }

  public static class TestRunner {

    public static void run() {
      InputReader in = new InputReader(System.in);
      try (OutputWriter out = new OutputWriter(System.out)) {
        int testCases = TestCase.MULTIPLE ? in.nextInt() : 1;
        for (int i = 1; i <= testCases; i++) {
          new TestCase().solve(in, out);
        }
      }
    }

  }

  public static class InputReader {

    private final InputStream inputStream;
    private final byte[] inputBuffer = new byte[1024];
    private int bytesRead = 0;
    private int inputBufferIndex = 0;

    public InputReader(InputStream inputStream) {
      this.inputStream = inputStream;
    }

    private int readByte() {
      if (bytesRead == -1) {
        throw new InputMismatchException();
      }
      if (inputBufferIndex >= bytesRead) {
        inputBufferIndex = 0;
        try {
          bytesRead = inputStream.read(inputBuffer);
        } catch (IOException e) {
          throw new InputMismatchException();
        }
        if (bytesRead <= 0) {
          return -1;
        }
      }
      return inputBuffer[inputBufferIndex++];
    }

    private int skip() {
      int b;
      do {
        b = readByte();
      } while (b != -1 && Character.isWhitespace(b));
      return b;
    }

    public int nextInt() {
      return (int) nextLong();
    }

    public long nextLong() {
      long num = 0;
      int b;
      boolean minus = false;
      do {
        b = readByte();
      } while (b != -1 && !((b >= '0' && b <= '9') || b == '-'));
      if (b == '-') {
        minus = true;
        b = readByte();
      }

      while (true) {
        if (b >= '0' && b <= '9') {
          num = num * 10 + (b - '0');
        } else {
          return minus ? -num : num;
        }
        b = readByte();
      }
    }

    public char[] nextCharArray(int n) {
      char[] buf = new char[n];
      int b = skip(), p = 0;
      while (p < n && !Character.isWhitespace(b)) {
        buf[p++] = (char) b;
        b = readByte();
      }
      return n == p ? buf : Arrays.copyOf(buf, p);
    }

  }

  public static class OutputWriter implements AutoCloseable {

    private static final int BUFFER_SIZE = 1 << 13;
    private final byte[] outputBuffer = new byte[BUFFER_SIZE];
    private final OutputStream outputStream;
    private int outputBufferIndex = 0;

    public OutputWriter(OutputStream os) {
      this.outputStream = os;
    }

    public OutputWriter println(int x) {
      return writeln(x);
    }

    public void flush() {
      innerFlush();
      try {
        outputStream.flush();
      } catch (IOException e) {
        throw new IllegalStateException("Failed to flush");
      }
    }

    private OutputWriter write(byte b) {
      outputBuffer[outputBufferIndex++] = b;
      if (outputBufferIndex == BUFFER_SIZE) {
        innerFlush();
      }
      return this;
    }

    private OutputWriter write(String s) {
      s.chars()
          .forEach(
              c -> {
                outputBuffer[outputBufferIndex++] = (byte) c;
                if (outputBufferIndex == BUFFER_SIZE) {
                  innerFlush();
                }
              });
      return this;
    }

    private OutputWriter write(int x) {
      if (x == Integer.MIN_VALUE) {
        return write((long) x);
      }
      if (outputBufferIndex + 12 >= BUFFER_SIZE) {
        innerFlush();
      }
      if (x < 0) {
        write((byte) '-');
        x = -x;
      }
      int d = countDigits(x);
      for (int i = outputBufferIndex + d - 1; i >= outputBufferIndex; i--) {
        outputBuffer[i] = (byte) ('0' + x % 10);
        x /= 10;
      }
      outputBufferIndex += d;
      return this;
    }

    private static int countDigits(long l) {
      if (l >= 1000000000000000000L) {
        return 19;
      }
      if (l >= 100000000000000000L) {
        return 18;
      }
      if (l >= 10000000000000000L) {
        return 17;
      }
      if (l >= 1000000000000000L) {
        return 16;
      }
      if (l >= 100000000000000L) {
        return 15;
      }
      if (l >= 10000000000000L) {
        return 14;
      }
      if (l >= 1000000000000L) {
        return 13;
      }
      if (l >= 100000000000L) {
        return 12;
      }
      if (l >= 10000000000L) {
        return 11;
      }
      if (l >= 1000000000L) {
        return 10;
      }
      if (l >= 100000000L) {
        return 9;
      }
      if (l >= 10000000L) {
        return 8;
      }
      if (l >= 1000000L) {
        return 7;
      }
      if (l >= 100000L) {
        return 6;
      }
      if (l >= 10000L) {
        return 5;
      }
      if (l >= 1000L) {
        return 4;
      }
      if (l >= 100L) {
        return 3;
      }
      if (l >= 10L) {
        return 2;
      }
      return 1;
    }

    private OutputWriter write(long x) {
      if (x == Long.MIN_VALUE) {
        return write("" + x);
      }
      if (outputBufferIndex + 21 >= BUFFER_SIZE) {
        innerFlush();
      }
      if (x < 0) {
        write((byte) '-');
        x = -x;
      }
      int d = countDigits(x);
      for (int i = outputBufferIndex + d - 1; i >= outputBufferIndex; i--) {
        outputBuffer[i] = (byte) ('0' + x % 10);
        x /= 10;
      }
      outputBufferIndex += d;
      return this;
    }

    private OutputWriter writeln(int x) {
      return write(x).writeln();
    }

    private OutputWriter writeln() {
      return write((byte) '\n');
    }

    private void innerFlush() {
      try {
        outputStream.write(outputBuffer, 0, outputBufferIndex);
        outputBufferIndex = 0;
      } catch (IOException e) {
        throw new IllegalStateException("Failed to inner flush");
      }
    }

    @Override
    public void close() {
      flush();
    }
  }
}