Temperature Conversion and Statistics

This problem requires you to process a list of temperature readings in Celsius and perform both a conversion and summary statistics. You are given a set of tokens representing temperatures. Some tokens may be non-numeric, and these should be ignored. From the valid numeric entries, compute the maximum, minimum, and average temperature.

The conversion from Celsius (C) to Fahrenheit (F) is given by the formula: \(F = \frac{9}{5}C + 32\). Your program should output a JSON object with the keys max, min, and average corresponding to the computed Fahrenheit values. If there are no valid numeric entries, all three values should be null.

Example:

Input:
5
0 10 20 30 40
Output:
{"max": 104.0, "min": 32.0, "average": 68.0}

</p>

inputFormat

The first line contains a single integer N representing the number of temperature entries. The second line contains N space-separated tokens. Each token may be a valid integer or floating point number (representing a temperature in Celsius), or an invalid entry which must be ignored.

outputFormat

Output a JSON object (as a string) with three keys: max, min, and average, which represent the maximum, minimum, and average temperature in Fahrenheit respectively. The conversion from Celsius to Fahrenheit is done using the formula: \(F = \frac{9}{5}C + 32\). If there are no valid temperatures, output null for all three fields.

## sample

5
0 10 20 30 40

{"max": 104.0, "min": 32.0, "average": 68.0}