CF1032G Chattering

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?

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 $ ).

Print $ 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.