Lightning Conductor

Memory limit: 128 MB

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 .

Input

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.

Output

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.

Example

For the input data:

6
5
3
2
4
2
4

the correct result is:

2
3
5
3
5
4

Task author: Piotr Niedzwiedz.