Average Student Grades

You are given data for a number of students. For each student, their name and a list of integer grades are provided. Your task is to calculate the average grade for each student. The average is computed as \(\frac{\text{sum of grades}}{\text{number of grades}}\) and must be rounded to two decimal places. If a student has no grades, then the average is defined to be null.

The final output should be a JSON object (dictionary) mapping each student's name to their average grade (using a JSON number rounded to two decimal places) or null if there are no grades. Read input from standard input (stdin) and output the result to standard output (stdout).

inputFormat

The input is given through stdin in the following format:

1. The first line contains an integer \(n\), which represents the number of students.
2. For each student, there are multiple lines:
   1. A line containing the student's name (a string without spaces).
   2. A line containing an integer \(m\), representing the number of grades.
   3. If \(m > 0\), a line containing \(m\) space-separated integers representing the grades.

outputFormat

Output a single line to stdout: a valid JSON object (dictionary) where each key is a student's name and the value is the average grade (rounded to two decimal places) or null if the student has no grades.

3
Alice
3
85 90 78
Bob
2
70 80
Charlie
0

{"Alice":84.33,"Bob":75.00,"Charlie":null}