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. 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. Print a single integer — the sought number of pairs. 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.