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.

输入描述:

The first line contains number n (1 ≤ n ≤ 2·105). The second line contains n numbers a0, a1, ..., an - 1 (1 ≤ ai ≤ 106), separated by a space.

输出描述:

Print a single integer — the sought number of pairs.

备注:

In the first sample the superior subarrays are (0, 1) and (3, 2).Subarray (0, 1) is superior, as a0 ≥ a0, a0 ≥ a1, a0 ≥ a2, a0 ≥ a3, a0 ≥ a0, ...Subarray (3, 2) is superior a3 ≥ a3, a0 ≥ a0, a3 ≥ a1, a0 ≥ a2, a3 ≥ a3, ...In the third sample any pair of (l, s) corresponds to a superior subarray as all the elements of an array are distinct.