Maximize the Minimum Team Energy

You are given n participants, each with a certain energy level. Your task is to form a team such that the minimum energy level among the team members is maximized. More formally, after sorting the energy levels in non-decreasing order, you want to choose a subset of participants and maximize the value

$$\max_{0\le i<n} \min\bigl(\text{energy}[i],\, n-i\bigr) $$

For each test case:

1. The first line contains an integer n representing the number of participants.
2. The second line contains n space-separated integers denoting the energy levels of the participants.

You are to process T test cases. For each test case, output the maximum possible value as described above. This value represents the highest achievable minimum energy level, given that if you select a group of size k, the minimum energy level in that group must be at least k in order for the team to be considered strong.

inputFormat

The input is read from stdin and has the following format:

T
n
energy1 energy2 ... energyn
... (repeated T times)

Where T represents the number of test cases. For each test case, n is the number of participants followed by a line of n integers indicating their energy levels.

outputFormat

For each test case, output a single integer on a new line representing the maximum possible minimum energy level of the team formed. The output is written to stdout.

## sample

2
4
1 3 6 2
5
4 2 7 1 3

2
3

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