You are given a sequence $A=(A_1,A_2,\ldots,A_N)$ of length $N$.  
For each $k=1,2,\ldots,N$, solve the following problem:

-   Find the maximum possible average value of the $k$-th to $r$-th terms of the sequence $A$ when choosing an integer $r$ such that $k\leq r\leq N$.  
    Here, the average value of the $k$-th to $r$-th term of the sequence $A$ is defined as $\frac{1}{r-k+1}\displaystyle\sum_{i=k}^r A_i$.

The input is given from Standard Input in the following format:

```
$N$
$A_1$ $A_2$ $\ldots$ $A_N$
```

Print $N$ lines.  
The $i$-th line $(1\leq i\leq N)$ should contain the answer to the problem for $k=i$.  
Your output will be considered correct if, for every line, the absolute or relative error of the printed value from the true value is at most $10^{-6}$.

-   $1\leq N\leq 2\times 10^5$
-   $1\leq A_i\leq 10^6$
-   All input values are integers.

2.80000000
3.33333333
4.50000000
5.00000000
3.00000000

For k=1, the possible choices for r are r=1,2,3,4,5, and the average value for each of them is:

• $\frac{1}{1}=1$
• $\frac{1}{2}(1+1)=1$
• $\frac{1}{3}(1+1+4)=2$
• $\frac{1}{4}(1+1+4+5)=2.75$
• $\frac{1}{5}(1+1+4+5+3)=2.8$

Thus, the maximum is achieved when r=5, and the answer for k=1 is 2.8.
Similarly, for k=2,3,4,5, the maximum is achieved when r=4,4,4,5, respectively, with the values of $\frac{10}{3}=3.333…, \frac{9}{2}=4.5, \frac{5}{1}=5, \frac{3}{1}=3$.