CF582C.Superior Periodic Subarrays

普及/提高-

通过率：0%

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题目描述

You are given an infinite periodic array $a_{0},a_{1},...,a_{n-1},...$ with the period of length $n$ . Formally, . A periodic subarray $(l,s)$ ( 0<=l<n , 1<=s<n ) of array $a$ is an infinite periodic array with a period of length $s$ that is a subsegment of array $a$ , starting with position $l$ .

A periodic subarray $(l,s)$ is superior, if when attaching it to the array $a$ , starting from index $l$ , any element of the subarray is larger than or equal to the corresponding element of array $a$ . An example of attaching is given on the figure (top — infinite array $a$ , bottom — its periodic subarray $(l,s)$ ):

Find the number of distinct pairs $(l,s)$ , corresponding to the superior periodic arrays.

输入格式

The first line contains number $n$ ( $1<=n<=2·10^{5}$ ). The second line contains $n$ numbers $a_{0},a_{1},...,a_{n-1}$ ( $1<=a_{i}<=10^{6}$ ), separated by a space.

输出格式

Print a single integer — the sought number of pairs.

输入输出样例

输入#1
```
4
7 1 2 3
```
输出#1
```
2
```
输入#2
```
2
2 1
```
输出#2
```
1
```
输入#3
```
3
1 1 1
```
输出#3
```
6
```

说明/提示

In the first sample the superior subarrays are (0, 1) and (3, 2).

Subarray (0, 1) is superior, as $a_{0}>=a_{0},a_{0}>=a_{1},a_{0}>=a_{2},a_{0}>=a_{3},a_{0}>=a_{0},...$

Subarray (3, 2) is superior $a_{3}>=a_{3},a_{0}>=a_{0},a_{3}>=a_{1},a_{0}>=a_{2},a_{3}>=a_{3},...$

In the third sample any pair of $(l,s)$ corresponds to a superior subarray as all the elements of an array are distinct.

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