Class Average and Student Ranking

You are given a list of students with their names and grades. Your task is to calculate the class average grade rounded to 2 decimal places and to produce a ranking list of the students based on their grades.

The ranking is determined by the following rules:

• Students are ordered in descending order of grade.
• If multiple students have the same grade, they are ordered alphabetically by name.
• Students with the same grade share the same rank. The rank for a student is equal to 1 + (number of students with a strictly higher grade).

If there are no students (i.e. n = 0), the average should be 0.00 and no ranking should be printed.

Note: All formulas are calculated using the formula
\( \text{average} = \frac{\sum_{i=1}^{n} \text{grade}_i}{n} \)

inputFormat

The input will be read from stdin and has the following format:

n
name1 grade1
name2 grade2
... 
nameN gradeN

Where n is a non-negative integer representing the number of students. Each of the following n lines contains a student's name (a string without spaces) and an integer grade separated by a space.

outputFormat

The output should be printed to stdout and must include:

1. The first line is the class average grade rounded to 2 decimal places.
2. Each of the following lines represents a student in the ranking list in the format rank. name.

## sample

3
John 75
Alice 85
Bob 90

83.33

Bob
Alice
John
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