G. Chatteringtime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputThere 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?InputIn 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).OutputPrint n integers. i-th of them should equal the number of seconds that is needed for all parrots to start chattering if the i-th parrot is the first to start.ExamplesInput
4
1 1 4 1
Output
2 2 1 2 
Input
8
1 2 2 1 5 1 3 1
Output
3 3 2 2 1 2 2 3 

4
1 1 4 1

2 2 1 2  
['*2900']