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 python3.

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:
```python
<your code here>
```

Execution time limit: 1.0 seconds
Memory limit: 256.0 MB

# Problem
No matter what trouble you're in, don't be afraid, but face it with a smile.

I've made another billion dollars!

— Boboniu

Boboniu has issued his currencies, named Bobo Yuan. Bobo Yuan (BBY) is a series of currencies. Boboniu gives each of them a positive integer identifier, such as BBY-1, BBY-2, etc.

Boboniu has a BBY collection. His collection looks like a sequence. For example:

We can use sequence $$$a=[1,2,3,3,2,1,4,4,1]$$$ of length $$$n=9$$$ to denote it.

Now Boboniu wants to fold his collection. You can imagine that Boboniu stick his collection to a long piece of paper and fold it between currencies:

Boboniu will only fold the same identifier of currencies together. In other words, if $$$a_i$$$ is folded over $$$a_j$$$ ($$$1\le i,j\le n$$$), then $$$a_i=a_j$$$ must hold. Boboniu doesn't care if you follow this rule in the process of folding. But once it is finished, the rule should be obeyed.

A formal definition of fold is described in notes.

According to the picture above, you can fold $$$a$$$ two times. In fact, you can fold $$$a=[1,2,3,3,2,1,4,4,1]$$$ at most two times. So the maximum number of folds of it is $$$2$$$.

As an international fan of Boboniu, you're asked to calculate the maximum number of folds.

You're given a sequence $$$a$$$ of length $$$n$$$, for each $$$i$$$ ($$$1\le i\le n$$$), you need to calculate the maximum number of folds of $$$[a_1,a_2,\ldots,a_i]$$$.

## Input Format
The first line contains an integer $$$n$$$ ($$$1\le n\le 10^5$$$).

The second line contains $$$n$$$ integers $$$a_1,a_2,\ldots,a_n$$$ ($$$1\le a_i\le n$$$).

## Output Format
Print $$$n$$$ integers. The $$$i$$$-th of them should be equal to the maximum number of folds of $$$[a_1,a_2,\ldots,a_i]$$$.

## Examples
```input
9
1 2 3 3 2 1 4 4 1
```
```output
0 0 0 1 1 1 1 2 2
```
-----
```input
9
1 2 2 2 2 1 1 2 2
```
```output
0 0 1 2 3 3 4 4 5
```
-----
```input
15
1 2 3 4 5 5 4 3 2 2 3 4 4 3 6
```
```output
0 0 0 0 0 1 1 1 1 2 2 2 3 3 0
```
-----
```input
50
1 2 4 6 6 4 2 1 3 5 5 3 1 2 4 4 2 1 3 3 1 2 2 1 1 1 2 4 6 6 4 2 1 3 5 5 3 1 2 4 4 2 1 3 3 1 2 2 1 1
```
```output
0 0 0 0 1 1 1 1 1 1 2 2 2 2 2 3 3 3 3 4 4 4 5 5 6 7 3 3 3 4 4 4 4 3 3 4 4 4 4 4 5 5 5 5 6 6 6 7 7 8
```

## Note
Formally, for a sequence $$$a$$$ of length $$$n$$$, let's define the folding sequence as a sequence $$$b$$$ of length $$$n$$$ such that:

- $$$b_i$$$ ($$$1\le i\le n$$$) is either $$$1$$$ or $$$-1$$$.
- Let $$$p(i)=[b_i=1]+\sum_{j=1}^{i-1}b_j$$$. For all $$$1\le i<j\le n$$$, if $$$p(i)=p(j)$$$, then $$$a_i$$$ should be equal to $$$a_j$$$.

($$$[A]$$$ is the value of boolean expression $$$A$$$. i. e. $$$[A]=1$$$ if $$$A$$$ is true, else $$$[A]=0$$$).

Now we define the number of folds of $$$b$$$ as $$$f(b)=\sum_{i=1}^{n-1}[b_i\ne b_{i+1}]$$$.

The maximum number of folds of $$$a$$$ is $$$F(a)=\max\{ f(b)\mid b \text{ is a folding sequence of }a \}$$$.

Now solve the problem and return the code.