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.

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.

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.