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.
from collections import defaultdict, Counter
from math import ceil

test = int(input())
for t in range(test):
    n = int(input())
    s1 = input()
    s2 = input()
    b = [0]*n
    a = []
    
    for i in range(n):
        b[i] += int(s1[i]) + int(s2[i])
    #print(b)    
    i = 0
    while i < n-1:
        if (b[i] == 0 and b[i+1] == 2) or (b[i] == 2 and b[i+1] == 0):
            a.append(2)
            i += 1
        elif b[i] == 1:
            a.append(2)
        elif b[i] == 0 and b[i+1] == 0:
            a.append(1)
        i += 1
    
    if (len(b) == 1):
        if b[-1] == 0:
            a.append(1)
        elif b[-1] == 1:
            a.append(2)
    elif (len(b) > 1):
        if b[-2] == 1 and b[-1] == 0:
            a.append(1)
        elif b[-2] == 1 and b[-1] == 1:
            a.append(2)
        elif b[-2] == 0 and b[-1] == 0:
            a.append(1)
        elif b[-2] == 0 and b[-1] == 1:
            a.append(2)
    #print(a)    
    print(sum(a))