[POI2011] Lightning Conductor

给定一个长度为 $n$ 的序列 $\{a_n\}$，对于每个 $i\in [1,n]$ ，求出一个最小的非负整数 $p$ ，使得 $\forall j\in[1,n]$，都有 $a_j\le a_i+p-\sqrt{|i-j|}$ $1 \le n \le 5\times 10^{5}$，$0 \le a_i \le 10^{9}$ 。

Progressive climate change has forced the Byteburg authorities to build a huge lightning conductor that would protect all the buildings within the city. These buildings form a row along a single street, and are numbered from  to . The heights of the buildings and the lightning conductor are non-negative integers. Byteburg's limited funds allow construction of only a single lightning conductor. Moreover, as you would expect, the higher it will be, the more expensive. The lightning conductor of height  located on the roof of the building  (of height ) protects the building  (of height ) if the following inequality holds:  where  denotes the absolute value of the difference between  and . Byteasar, the mayor of Byteburg, asks your help. Write a program that, for every building , determines the minimum height of a lightning conductor that would protect all the buildings if it were put on top of the building .

In the first line of the standard input there is a single integer  () that denotes the number of buildings in Byteburg. Each of the following  lines holds a single integer  () that denotes the height of the -th building.

Your program should print out exactly  lines to the standard output. The -th line should give a non-negative integer  denoting the minimum height of the lightning conductor on the -th building.

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