CF2210C1.A Simple GCD Problem (Easy Version)

This is the easy version of the problem. The difference between the versions is that in this version, $ 1 \leq n \leq 2 \cdot 10^{5} $ and $ b_i = a_i $ for $ 1 \leq i \leq n $ . Note that a solution for one version does not necessarily solve the other version. You can hack only if you solved all versions of this problem.

You are given two arrays $ a $ and $ b $ of length $ n $ .

For each index $ i $ ( $ 1 \le i \le n $ ) of array $ a $ , you can perform the following operation at most once:

• choose an arbitrary integer $ m $ ( $ \mathbf{m \neq a_i} $ ) such that $ 1 \leq m \le b_i $ , and set $ a_i := m $ .

Let the array after performing all the operations be $ a' $ . You can only perform operations in such a way that the following condition holds:

• for all $ 1\leq l \lt r\leq n $ , $ \operatorname{gcd}(a_l,a_{l+1},\ldots,{a_r})=\operatorname{gcd}(a'l,a'{l+1},\ldots,a'_r). $

Here, $ \gcd(x, y) $ denotes the greatest common divisor (GCD) of integers $ x $ and $ y $ .

You have to determine the maximum number of operations that can be performed while ensuring that the condition remains satisfied.

Each test contains multiple test cases. The first line contains the number of test cases $ t $ ( $ 1 \le t \le 10^4 $ ). The description of the test cases follows.

The first line of each test case contains an integer $ n $ ( $ 2 \leq n \leq 2\cdot 10^5 $ ) — the length of $ a $ .

The following line of each test case contains $ n $ space-separated integers $ a_1, a_2, \ldots, a_n $ ( $ 1 \leq a_i \leq 10^9 $ ).

The next line of each test case contains $ n $ space-separated integers $ b_1, b_2, \ldots, b_n $ ( $ \color{red}{b_i = a_i} $ ).

It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 2\cdot10^5 $ .

For each test case, output the maximum number of operations that can be done on a newline.

For the first test case, the GCD of all subarrays is $ 1 $ . Hence, we can perform $ 6 $ operations and change the array to $ a' = [1, 1, 1, 1, 1, 1, 1] $ . It can be shown that the maximum number of operations that can be performed in this case is $ 6 $ .

For the second test case, note that all the values are equal, and reducing any value causes the GCD of subarrays to decrease. Hence, $ 0 $ operations can be performed.

For the third test case, it can be shown that at most $ 2 $ operations can be performed.