The principal at a school with N number of students asks them to clean up the school's large yard before the beginning of school.
To do this, the principal prepares a list with the name of every student in the school exactly once and divides the yard into various sized areas.
The students then start cleaning the yard one by one in the order listed. Each area of the yard is cleaned by only one student.
The principal, who is watching the students, takes note of the size of the area each student cleans.
After the entire courtyard has been cleaned, the principal notices a very interesting feature about the size of the areas cleaned by the students.
The total area cleaned by the first student on the list is exactly 3 times larger than the arithmetic average of the areas cleaned by the students following her on the list.
Similarly, the total area cleaned by every student on the list is exactly 3 times larger than the arithmetic average of the areas cleaned by the students who come after him on the list.
Accordingly, the total area cleared by the (N - 1)'st ranked student is exactly 3 times larger than the area cleared by the last student.
In addition to this property, the principal realizes that the total area cleaned by the first student on the list is exactly 595 times larger than the total area cleaned by the last student on the list.
How many students are there in the school?