MAX-MEX Cut

题目描述

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?

输入输出格式

输入格式

The 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 $ .

输出格式

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.

输入输出样例

输入样例 #1

4
7
0101000
1101100
5
01100
10101
2
01
01
6
000000
111111

输出样例 #1

8
8
2
12

说明

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 $ .