Problem Statement

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 $\frac{1}{r-k+1}\displaystyle\sum_{i=k}^r A_i$.

Input

The input is given from Standard Input in the following format:
N
$A_1 A_2 \ldots A_N$

Output

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}.

Constraints

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

Sample Input 1

5
1 1 4 5 3

Sample Output 1

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 $\frac{10}{3}=3.333\ldots, \frac{9}{2}=4.5, \frac{5}{1}=5, \frac{3}{1}=3$.

Sample Input 2

3
999999 1 1000000

Sample Output 2

999999.00000000
500000.50000000
1000000.00000000

见题面 Input 部分

见题面 Output 部分