A15267 | Maximums and Minimums
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题目描述
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.
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.
输入格式
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 $5 \cdot 10^5$ .
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 $5 \cdot 10^5$ .
输出格式
For each test case, print a single integer — the number of pairs of indices that pass the check.
输入输出样例
输入 #1
6 1 1 2 2 4 2 2 3 4 2 4 7 14 7 16 5 18 7 7 12 14 6 16 14 2 6 16 2
输出 #1
1 3 2 7 10 19
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.
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.
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评测结果：Accepted