Progressive climate change has forced the Byteburg authorities to build a huge lightning conductor that would protect all the buildings with_in the city. These buildings form a row along a single street, and are numbered from 1 to n.

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 p located on the roof of the building i (of height h_i) protects the building j (of height h_j) if the following inequality holds:

h_j ≤ h_i + p - sqrt(|i - j|)

where |i - j| denotes the absolute value of the difference between i and j.

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 i.

Input

In the first line of the standard input there is a single integer n (1 ≤ n ≤ 500,000) that denotes the number of buildings in Byteburg. Each of the following n lines holds a single integer h_i (1 ≤ h_i ≤ 1,000,000,000) that denotes the height of the i-th building.

Output

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

Example

Input:
6
5
3
2
4
2
4

Output:
2
3
5
3
5
4