There is a school that has classes of students and each class will be having a final exam. You are given a 2D integer array `classes`

, where `classes[i] = [passi, totali]`

. You know beforehand that in the `ith`

class, there are `totali`

total students, but only `passi`

number of students will pass the exam.

You are also given an integer `extraStudents`

. There are another `extraStudents`

brilliant students that are **guaranteed** to pass the exam of any class they are assigned to. You want to assign each of the `extraStudents`

students to a class in a way that **maximizes** the **average** pass ratio across **all** the classes.

The **pass ratio** of a class is equal to the number of students of the class that will pass the exam divided by the total number of students of the class. The **average pass ratio** is the sum of pass ratios of all the classes divided by the number of the classes.

Return *the ***maximum** possible average pass ratio after assigning the `extraStudents`

* students. *Answers within `10-5`

of the actual answer will be accepted.

**Example 1:**

**Input:** classes = [[1,2],[3,5],[2,2]], `extraStudents`

= 2
**Output:** 0.78333
**Explanation:** You can assign the two extra students to the first class. The average pass ratio will be equal to (3/4 + 3/5 + 2/2) / 3 = 0.78333.

**Example 2:**

**Input:** classes = [[2,4],[3,9],[4,5],[2,10]], `extraStudents`

= 4
**Output:** 0.53485

**Constraints:**

`1 <= classes.length <= 105`

`classes[i].length == 2`

`1 <= passi <= totali <= 105`

`1 <= extraStudents <= 105`