A Heap of Heaps

有一个小根堆，但是因为奇奇怪怪的原因，这个堆变成了一个k叉堆，而且不一定是合法的（即有若干个节点小于它的父亲）。问现在这个堆有多少不合法的元素。

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!

The first line contains a single integer $ n $ ( $ 2<=n<=2·10^{5} $ ). The second line contains $ n $ space-separated integers $ a_{1} $ , $ ... $ , $ a_{n} $ ( $ -10^{9}<=a_{i}<=10^{9} $ ).

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 $ .

5
1 5 4 3 2

3 2 1 0

6
2 2 2 2 2 2

0 0 0 0 0

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.