13:I[87,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"Header"] 14:I[1742,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"ProblemView"] 15:T5fe,

There are $$$n$$$ parrots standing in a circle. Each parrot has a certain level of respect among other parrots, namely $$$r_i$$$. When a parrot with respect level $$$x$$$ starts chattering, $$$x$$$ neighbours to the right and to the left of it start repeating the same words in 1 second. Their neighbours then start repeating as well, and so on, until all the birds begin to chatter.

You are given the respect levels of all parrots. For each parrot answer a question: if this certain parrot starts chattering, how many seconds will pass until all other birds will start repeating it?

Input

In the first line of input there is a single integer $$$n$$$, the number of parrots ($$$1 \leq n \leq 10^5$$$).

In the next line of input there are $$$n$$$ integers $$$r_1$$$, ..., $$$r_n$$$, the respect levels of parrots in order they stand in the circle ($$$1 \leq r_i \leq n$$$).

Output

Print $$$n$$$ integers. $$$i$$$-th of t

Chattering

Examples