- Practice
- Algorithms
- Greedy
- Team Formation

# Team Formation

# Team Formation

For an upcoming programming contest, Roy is forming some teams from the students of his university. A team can have any number of contestants.

Roy knows the skill level of each contestant. To make the teams work as a unit, he forms the teams based on some rules. Each of the team members must have a unique skill level for the team. If a member's skill level is where , there exists another team member whose skill level is . Note that a contestant can write buggy code and thus can have a negative skill level.

The more contestants on the team, the more problems they can attempt at a time so Roy wants to form teams such that the smallest team is as large as possible.

For example, there are contestants with skill levels . There are many ways teams could be formed, e.g. [-1], [0],...,[3]. At the other end of the spectrum, we could form and . We're looking for the largest smaller team size though. Two sets that meet the criteria are and . The largest smaller team size possible is .

**Note:** There is an edge case where contestants have registered. As no teams are to be created, the largest team created will have members.

**Input Format**

The first line contains an integer , the number of test cases.

Each of the next lines contains a string of space-separated integers, followed by integers , a list of the contestants' skill levels.

**Constraints**

**Output Format**

For each test case, print the size of largest possible smallest team on a separate line.

**Sample Input**

```
4
7 4 5 2 3 -4 -3 -5
1 -4
4 3 2 3 1
7 1 -2 -3 -4 2 0 -1
```

**Sample Output**

```
3
1
1
7
```

**Explanation**

For the first case, Roy can form two teams: one with contestants with skill levels `{-4,-3,-5}`

and the other one with `{4,5,2,3}`

. The first group containing `3`

members is the smallest.

In the second case, the only team is `{-4}`

In the third case, the teams are `{3}`

, `{1,2,3}`

, the size of the smaller group being `1`

.

In the last case, you can build one group containing all of the contestants. The size of the group equals the total number of contestants.

**Time limits**

Time limits for this challenge are given here

**Note**

If n = 0, print 0.