Plus Minus

Source: HackerRank

Version: Phuoc Hung OJ Extended

Problem Statement

Given an integer array $A=(a_0,a_1,\ldots,a_{n-1})$, let $P$, $N$, and $Z$ be the counts of positive, negative, and zero elements, respectively.

Compute the three ratios $P/n$, $N/n$, and $Z/n$.

Input

• The first line contains an integer $n$.
• The second line contains $n$ integers $a_0,a_1,\ldots,a_{n-1}$.

Output

Print exactly three lines in this order:

1. the ratio of positive elements;
2. the ratio of negative elements;
3. the ratio of zero elements.

Print each value with exactly $6$ digits after the decimal point. The judge accepts an absolute or relative error of at most $10^{-6}$.

Subtasks

Subtask 1 (100 points): $1\le n\le100$ and $-100\le a_i\le100$.

Examples

Input

6
-4 3 -9 0 4 1

Output

0.500000
0.333333
0.166667

Explanation

There are $3$ positive values, $2$ negative values, and $1$ zero. Their ratios are $3/6=0.5$, $2/6\approx0.333333$, and $1/6\approx0.166667$.