A15761 | Going to the Cinema

A company of $n$ people is planning a visit to the cinema. Every person can either go to the cinema or not. That depends on how many other people will go. Specifically, every person $i$ said: "I want to go to the cinema if and only if at least $a_i$ other people will go, not counting myself". That means that person $i$ will become sad if:

- they go to the cinema, and strictly less than $a_i$ other people go; or
- they don't go to the cinema, and at least $a_i$ other people go.

In how many ways can a set of people going to the cinema be chosen so that nobody becomes sad?

Each test contains multiple test cases. The first line contains the number of test cases $t$ ( $1 \le t \le 10^4$ ). The description of the test cases follows.

Each test case consists of two lines. The first line contains a single integer $n$ ( $2 \le n \le 2 \cdot 10^5$ ) — the number of people in the company.

The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ( $0 \le a_i \le n - 1$ ) — integers from peoples' claims.

It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$ .

For each test case, print a single integer — the number of different ways to choose a set of people going to the cinema so that nobody becomes sad.