Andrew skipped lessons on the subject 'Algorithms and Data Structures' for the entire term. When he came to the final test, the teacher decided to give him a difficult task as a punishment. The teacher gave Andrew an array of n numbers a 1 , ..., a n . After that he asked Andrew for each k from 1 to n - 1 to build a k -ary heap on the array and count the number of elements for which the property of the minimum-rooted heap is violated, i.e. the value of an element is less than the value of its parent. Andrew looked up on the Wikipedia that a k -ary heap is a rooted tree with vertices in elements of the array. If the elements of the array are indexed from 1 to n , then the children of element v are elements with indices k(v - 1) + 2, ..., kv + 1 (if some of these elements lie outside the borders of the array, the corresponding children are absent). In any k -ary heap every element except for the first one has exactly one parent; for the element 1 the parent is absent (this element is the root of the heap). Denote p(v) as the number of the parent of the element with the number v . Let's say that for a non-root element v the property of the heap is violated if a v a p(v) . Help Andrew cope with the task!

输入描述:

The first line contains a single integer n (2 ≤ n ≤ 2·105).The second line contains n space-separated integers a1, ..., an ( - 109 ≤ ai ≤ 109).

输出描述:

in a single line print n - 1 integers, separate the consecutive numbers with a single space — the number of elements for which the property of the k-ary heap is violated, for k = 1, 2, ..., n - 1.

备注:

Pictures with the heaps for the first sample are given below; elements for which the property of the heap is violated are marked with red.In the second sample all elements are equal, so the property holds for all pairs.