MAX-MEX Cut solution codeforces
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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 $MEX$ of a bi-table be the smallest digit among $0$ , $1$ , or $2$ that does not occur in the bi-table. For example, $MEX$ for $[\begin{matrix} 0011 \\ 1010 \end{matrix}]$ is $2$ , because $0$ and $1$ occur in the bi-table at least once. $MEX$ for $[\begin{matrix} 111 \\ 111 \end{matrix}]$ 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 $MEX$ of all resulting bi-tables can be?

MAX-MEX Cut solution codeforces

The input consists of multiple test cases. The first line contains a single integer $t$ ( $1 \leq t \leq 10^{4}$ ) — 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 $n$ ( $1 \leq n \leq 10^{5}$ ) — 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 $10^{5}$ .

MAX-MEX Cut solution codeforces

For each test case print a single integer — the maximal sum of $MEX$ of all bi-tables that it is possible to get by cutting the given bi-table optimally.

Example

input

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MAX-MEX Cut solution codeforces

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Note

In the first test case you can cut the bi-table as follows:

$[\begin{matrix} 0 \\ 1 \end{matrix}]$ , its $MEX$ is $2$ .
$[\begin{matrix} 10 \\ 10 \end{matrix}]$ , its $MEX$ is $2$ .
$[\begin{matrix} 1 \\ 1 \end{matrix}]$ , its $MEX$ is $0$ .
$[\begin{matrix} 0 \\ 1 \end{matrix}]$ , its $MEX$ is $2$ .
$[\begin{matrix} 0 \\ 0 \end{matrix}]$ , its $MEX$ is $1$ .
$[\begin{matrix} 0 \\ 0 \end{matrix}]$ , its $MEX$ is $1$ .

The sum of $MEX$ is $8$ .

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MAX-MEX Cut solution codeforces- A binary string is a string that consists of characters 00 and 11. A bi-table is a table that has exactly two rows of equal length, each being a binary string.

MAX-MEX Cut solution codeforces

For Solution

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For Solution

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