[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 ![](http://main.edu.pl/images/OI18/pio-en-tex.1.png) to ![](http://main.edu.pl/images/OI18/pio-en-tex.2.png). 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 ![](http://main.edu.pl/images/OI18/pio-en-tex.3.png) located on the roof of the building ![](http://main.edu.pl/images/OI18/pio-en-tex.4.png) (of height ![](http://main.edu.pl/images/OI18/pio-en-tex.5.png)) protects the building ![](http://main.edu.pl/images/OI18/pio-en-tex.6.png) (of height ![](http://main.edu.pl/images/OI18/pio-en-tex.7.png)) if the following inequality holds: ![](http://main.edu.pl/images/OI18/pio-en-tex.8.png) where ![](http://main.edu.pl/images/OI18/pio-en-tex.9.png) denotes the absolute value of the difference between ![](http://main.edu.pl/images/OI18/pio-en-tex.10.png) and ![](http://main.edu.pl/images/OI18/pio-en-tex.11.png). Byteasar, the mayor of Byteburg, asks your help. Write a program that, for every building ![](http://main.edu.pl/images/OI18/pio-en-tex.12.png), determines the minimum height of a lightning conductor that would protect all the buildings if it were put on top of the building ![](http://main.edu.pl/images/OI18/pio-en-tex.13.png).

输入输出格式

输入格式


In the first line of the standard input there is a single integer ![](http://main.edu.pl/images/OI18/pio-en-tex.14.png) (![](http://main.edu.pl/images/OI18/pio-en-tex.15.png)) that denotes the number of buildings in Byteburg. Each of the following ![](http://main.edu.pl/images/OI18/pio-en-tex.16.png) lines holds a single integer ![](http://main.edu.pl/images/OI18/pio-en-tex.17.png) (![](http://main.edu.pl/images/OI18/pio-en-tex.18.png)) that denotes the height of the ![](http://main.edu.pl/images/OI18/pio-en-tex.19.png)-th building.

输出格式


Your program should print out exactly ![](http://main.edu.pl/images/OI18/pio-en-tex.20.png) lines to the standard output. The ![](http://main.edu.pl/images/OI18/pio-en-tex.21.png)-th line should give a non-negative integer ![](http://main.edu.pl/images/OI18/pio-en-tex.22.png) denoting the minimum height of the lightning conductor on the ![](http://main.edu.pl/images/OI18/pio-en-tex.23.png)-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