C. MAX-MEX Cuttime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputA 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?InputThe input consists of multiple test cases. The first line contains a single integer t (1 \le t \le 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 \le n \le 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.OutputFor 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.ExampleInput
4
7
0101000
1101100
5
01100
10101
2
01
01
6
000000
111111
Output
8
8
2
12
NoteIn 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.
4
7
0101000
1101100
5
01100
10101
2
01
01
6
000000
111111

8 8 2 12 
['bitmasks', 'constructive algorithms', 'dp', 'greedy', '*1000']