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C. Superior Periodic Subarrays

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou 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.

Input

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.

Output

Print a single integer — the sought number of pairs.

Examples

Input

4

7 1 2 3

Output

2

Input

2

2 1

Output

1

Input

3

1 1 1

Output

6

Note

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.

Codeforces (c) Copyright 2010-2022 Mike Mirzayanov

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