Chattering

有 n 只鹦鹉围成一圈站着。每个鹦鹉叫声的影响范围用 ri 表示。 当一只叫声范围为 x 的鹦鹉开始叫时，它的左右两侧距离 x 之内（包括 x）的邻居会在 1 秒钟之后也叫起来。然后，他们的邻居也开始重复，依此类推，直到所有鸟儿都开 始叫。 对于每只鹦鹉，都回答一个问题：如果这只鹦鹉开始叫，那么将经过几秒钟，所有其他鸟类都开始叫？

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.

4
1 1 4 1

2 2 1 2 

8
1 2 2 1 5 1 3 1

3 3 2 2 1 2 2 3