You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in c++17.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```cpp
<your code here>
```

Execution time limit: 2.0 seconds
Memory limit: 512.0 MB

# Problem
Your favorite music streaming platform has formed a perfectly balanced playlist exclusively for you. The playlist consists of $$$n$$$ tracks numbered from $$$1$$$ to $$$n$$$. The playlist is automatic and cyclic: whenever track $$$i$$$ finishes playing, track $$$i+1$$$ starts playing automatically; after track $$$n$$$ goes track $$$1$$$.

For each track $$$i$$$, you have estimated its coolness $$$a_i$$$. The higher $$$a_i$$$ is, the cooler track $$$i$$$ is.

Every morning, you choose a track. The playlist then starts playing from this track in its usual cyclic fashion. At any moment, you remember the maximum coolness $$$x$$$ of already played tracks. Once you hear that a track with coolness strictly less than $$$\frac{x}{2}$$$ (no rounding) starts playing, you turn off the music immediately to keep yourself in a good mood.

For each track $$$i$$$, find out how many tracks you will listen to before turning off the music if you start your morning with track $$$i$$$, or determine that you will never turn the music off. Note that if you listen to the same track several times, every time must be counted.

## Input Format
The first line contains a single integer $$$n$$$ ($$$2 \le n \le 10^5$$$), denoting the number of tracks in the playlist.

The second line contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \le a_i \le 10^9$$$), denoting coolnesses of the tracks.

## Output Format
Output $$$n$$$ integers $$$c_1, c_2, \ldots, c_n$$$, where $$$c_i$$$ is either the number of tracks you will listen to if you start listening from track $$$i$$$ or $$$-1$$$ if you will be listening to music indefinitely.

## Examples
```input
4
11 5 2 7
```
```output
1 1 3 2
```
-----
```input
4
3 2 5 3
```
```output
5 4 3 6
```
-----
```input
3
4 3 6
```
```output
-1 -1 -1
```

## Note
In the first example, here is what will happen if you start with...

- track $$$1$$$: listen to track $$$1$$$, stop as $$$a_2 < \frac{a_1}{2}$$$.
- track $$$2$$$: listen to track $$$2$$$, stop as $$$a_3 < \frac{a_2}{2}$$$.
- track $$$3$$$: listen to track $$$3$$$, listen to track $$$4$$$, listen to track $$$1$$$, stop as $$$a_2 < \frac{\max(a_3, a_4, a_1)}{2}$$$.
- track $$$4$$$: listen to track $$$4$$$, listen to track $$$1$$$, stop as $$$a_2 < \frac{\max(a_4, a_1)}{2}$$$.

In the second example, if you start with track $$$4$$$, you will listen to track $$$4$$$, listen to track $$$1$$$, listen to track $$$2$$$, listen to track $$$3$$$, listen to track $$$4$$$ again, listen to track $$$1$$$ again, and stop as $$$a_2 < \frac{max(a_4, a_1, a_2, a_3, a_4, a_1)}{2}$$$. Note that both track $$$1$$$ and track $$$4$$$ are counted twice towards the result.

Now solve the problem and return the code.