[POI2011]Lightning Conductor
题意翻译
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 $a_j\le a_i+p-\sqrt{|i-j|}$
$1 \le n \le 5\times 10^{5}$,$0 \le a_i \le 10^{9}$ 。
题目描述
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 .
输入输出格式
输入格式
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.
输出格式
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.
输入输出样例
输入样例 #1
6
5
3
2
4
2
4
输出样例 #1
2
3
5
3
5
4