You are given an integer array nums representing a class of students.

A group of students needs to be selected. A student at index i is happy if and only if one of the following conditions is satisfied:

• The student is selected and the total number of selected students is strictly greater than nums[i].

• The student is not selected and the total number of selected students is strictly less than nums[i].

Return the total number of ways to choose a group of students such that every student in the class is happy.

Constraints:

• $1 \leq$ nums.length $\leq 10^5$

• $0 \leq$ nums[i] $<$ nums.length

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

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