CF1730E.Maximums and Minimums

You are given an array $a_1, a_2, \ldots, a_n$ of positive integers.

Find the number of pairs of indices $(l, r)$ , where $1 \le l \le r \le n$ , that pass the check. The check is performed in the following manner:

1. The minimum and maximum numbers are found among $a_l, a_{l+1}, \ldots, a_r$ .
2. The check is passed if the maximum number is divisible by the minimum number.

The first line contains a single integer $t$ ( $1 \le t \le 10$ ) — the number of test cases. Then the test cases follow.

Each test case consists of two lines.

The first line contains a single integer $n$ ( $1 \le n \le 5 \cdot 10^5$ ) — the size of the array.

The second line contains $n$ integers $a_1, a_2, \dots, a_n$ ( $1 \le a_i \le 10^6$ ).

It is guaranteed that the sum of $n$ over all test cases does not exceed $5 \cdot 10^5$ .

For each test case, print a single integer — the number of pairs of indices that pass the check.

Below $x \mid y$ denotes that $y$ is divisible by $x$ .

In the first test case, there is one pair $(1, 1)$ , the maximum for this pair is $1$ , the minimum is also $1$ , $1 \mid 1$ , so the check is passed, and the answer is $1$ .

In the second test case, there are $3$ segments:

• $(1, 1)$ : the maximum is $2$ , the minimum is $2$ , $2 \mid 2$ , so the check is passed.
• $(1, 2)$ : the maximum is $4$ , the minimum is $2$ , $2 \mid 4$ , so the check is passed.
• $(2, 2)$ : the maximum is $4$ , the minimum is $4$ , $4 \mid 4$ , so the check is passed.

In the third test case, there are $3$ segments:

• $(1, 1)$ : the maximum is $2$ , the minimum is $2$ , $2 \mid 2$ , so the check is passed.
• $(1, 2)$ : the maximum is $3$ , the minimum is $2$ , $3$ isn't divisible by $2$ , so the check is failed.
• $(2, 2)$ : the maximum is $3$ , the minimum is $3$ , $3 \mid 3$ , so the check is passed.