human
PYTHON3 solution for "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...":


 ... Give me a Python code to 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?
assistant
#Here is Python code to 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.
 def can_be_paired_up(current_pair, next_pair):
    all_pairs = []
    all_pairs.extend(list(current_pair))
    all_pairs.extend(list(next_pair))
    if '01' == next_pair:
        return False
    if '0' in all_pairs and\
       '1' in all_pairs:
        return True
    return False

def solve():
    n = int(input())
    s = [list(input()),
         list(input())]
    b = []
    for i in range(n):
        ss = '{}{}'.format(s[0][i], s[1][i])
        if ss[0] == '1':
            ss = '{}{}'.format(ss[1], ss[0])
        b.append(ss)
    s = b
    index = 0
    mex = 0
    while index < n:
        current = s[index]
        if '01' == current:
            mex += 2
            index += 1
            continue
        if index + 1 >= n:
            mex += 1 if '0' in current else 0
            index += 1
            continue
        next = s[index + 1]
        if can_be_paired_up(current, next):
            mex += 2
            index += 2
            continue
        mex += 1 if '0' in current else 0
        index += 1
    return mex

if __name__=='__main__':
    for _ in range(int(input())):
        print(solve())