Student Ranking

You are given data for n students. For each student, you are provided with the student's name and scores in three subjects: Math, Science, and English.

Your task is to rank the students based on their average score calculated as \(\frac{\text{Math} + \text{Science} + \text{English}}{3}\). In case of ties in the average score, the tie is broken by the Math score (in descending order). If there is still a tie, then the students are ranked by their names in lexicographical (alphabetical) order.

Note: All scores are integers. The final output should be the names of the students sorted according to the above criteria, printed on a single line separated by spaces.

inputFormat

The first line contains an integer n (\(1 \le n \le 10^5\)), representing the number of students.

Each of the following n lines contains the student's information in the following format:

name Math Science English

where name is a string without spaces and Math, Science, English are integers.

outputFormat

Print a single line containing the names of the students sorted based on the ranking criteria. The names should be separated by a single space.

4
John 80 90 85
Doe 90 70 80
Jane 85 80 80
Smith 90 85 90

Smith John Jane Doe