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.

题目大意

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 $a_j\le a_i+p-\sqrt{|i-j|}$

$1 \le n \le 5\times 10^{5}$，$0 \le a_i \le 10^{9}$ 。

6
5
3
2
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2
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2
3
5
3
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4