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Given an array of integers, calculate the fractions of its elements that are *positive*, *negative*, and are *zeros*. Print the decimal value of each fraction on a new line.

**Note:** This challenge introduces precision problems. The test cases are scaled to six decimal places, though answers with absolute error of up to are acceptable.

**Input Format**

The first line contains an integer, , denoting the size of the array.

The second line contains space-separated integers describing an array of numbers .

**Output Format**

You must print the following lines:

- A decimal representing of the fraction of
*positive*numbers in the array compared to its size. - A decimal representing of the fraction of
*negative*numbers in the array compared to its size. - A decimal representing of the fraction of
*zeros*in the array compared to its size.

**Sample Input**

```
6
-4 3 -9 0 4 1
```

**Sample Output**

```
0.500000
0.333333
0.166667
```

**Explanation**

There are positive numbers, negative numbers, and zero in the array.

The proportions of occurrence are positive: , negative: and zeros: .