Problem A. Altitude and visibility ≡

Statement

Consider a sequence of numbers a₁, …, a_N, representing heights. Let's say that element a_i has a visibility radius d if a_i ≥ a_j for all j such that 1 ≤ j ≤ N and |i − j| < d.

You task is to find maximum d_i for every a_i.

Input file format

Input file contains integer N followed by N integers a_i.

Output file format

Output file must contain N integers d_i — maximum visibility for every a_i. If maximum visibility radius for element a_i is unlimited, output d_i = 0.

Constraints

1 ≤ N ≤ 10⁶, 0 ≤ a_i ≤ 10⁹

Sample tests

1
10

0 

6
1 5 2 2 1 4

1 0 1 2 1 4