[USACO08DEC] Patting Heads S

今天是贝茜的生日，为了庆祝自己的生日，贝茜邀你来玩一个游戏。 贝茜让 $N$ ($1\leq N\leq 10^5$) 头奶牛坐成一个圈。除了 $1$ 号与 $N$ 号奶牛外，$i$ 号奶牛与 $i-1$ 号和 $i+1$ 号奶牛相邻。$N$ 号奶牛与 $1$ 号奶牛相邻。农夫约翰用很多纸条装满了一个桶，每一张包含了一个不一定是独一无二的 $1$ 到 $10^6$ 的数字。 接着每一头奶牛 $i$ 从桶中取出一张纸条 $A_i$。每头奶牛轮流走上一圈，同时拍打所有手上数字能整除在自己纸条上的数字的牛的头，然后坐回到原来的位置。牛们希望你帮助他们确定，每一头奶牛需要拍打的牛的数量。

It's Bessie's birthday and time for party games! Bessie has instructed the N (1 <= N <= 100,000) cows conveniently numbered 1..N to sit in a circle (so that cow i [except at the ends] sits next to cows i-1 and i+1; cow N sits next to cow 1). Meanwhile, Farmer John fills a barrel with one billion slips of paper, each containing some integer in the range 1..1,000,000. Each cow i then draws a number A\_i (1 <= A\_i <= 1,000,000) (which is not necessarily unique, of course) from the giant barrel. Taking turns, each cow i then takes a walk around the circle and pats the heads of all other cows j such that her number A\_i is exactly divisible by cow j's number A\_j; she then sits again back in her original position. The cows would like you to help them determine, for each cow, the number of other cows she should pat.

\* Line 1: A single integer: N \* Lines 2..N+1: Line i+1 contains a single integer: A\_i

\* Lines 1..N: On line i, print a single integer that is the number of other cows patted by cow i.

5 
2 
1 
2 
3 
4 

2 
0 
2 
1 
3 

The 5 cows are given the numbers 2, 1, 2, 3, and 4, respectively. The first cow pats the second and third cows; the second cows pats no cows; etc.