Equalize
Description
Vasya has two hobbies — adding permutations$^{\dagger}$ to arrays and finding the most frequently occurring element. Recently, he found an array $a$ and decided to find out the maximum number of elements equal to the same number in the array $a$ that he can obtain after adding some permutation to the array $a$.
More formally, Vasya must choose exactly one permutation $p_1, p_2, p_3, \ldots, p_n$ of length $n$, and then change the elements of the array $a$ according to the rule $a_i := a_i + p_i$. After that, Vasya counts how many times each number occurs in the array $a$ and takes the maximum of these values. You need to determine the maximum value he can obtain.
$^{\dagger}$A permutation of length $n$ is an array consisting of $n$ distinct integers from $1$ to $n$ in arbitrary order. For example, $[2,3,1,5,4]$ is a permutation, but $[1,2,2]$ is not a permutation ($2$ appears twice in the array), and $[1,3,4]$ is also not a permutation ($n=3$ but there is $4$ in the array).
Each test consists of multiple test cases. The first line contains a single integer $t$ ($1 \leq t \leq 2 \cdot 10^4$) — the number of test cases. Then follows the description of the test cases.
The first line of each test case contains a single integer $n$ ($1 \le n \le 2 \cdot 10^5$) — the length of the array $a$.
The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \le a_i \le 10^9$) — the elements of the array $a$.
It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$.
For each test case, output a single number — the maximum number of elements equal to the same number after the operation of adding a permutation.
Input
Each test consists of multiple test cases. The first line contains a single integer $t$ ($1 \leq t \leq 2 \cdot 10^4$) — the number of test cases. Then follows the description of the test cases.
The first line of each test case contains a single integer $n$ ($1 \le n \le 2 \cdot 10^5$) — the length of the array $a$.
The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \le a_i \le 10^9$) — the elements of the array $a$.
It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$.
Output
For each test case, output a single number — the maximum number of elements equal to the same number after the operation of adding a permutation.
7
2
1 2
4
7 1 4 1
3
103 102 104
5
1 101 1 100 1
5
1 10 100 1000 1
2
3 1
3
1000000000 999999997 999999999
2
2
3
2
1
1
2
Note
In the first test case, it is optimal to choose $p = [2, 1]$. Then after applying the operation, the array $a$ will be $[3, 3]$, in which the number $3$ occurs twice, so the answer is $2$.
In the second test case, one of the optimal options is $p = [2, 3, 1, 4]$. After applying the operation, the array $a$ will be $[9, 4, 5, 5]$. Since the number $5$ occurs twice, the answer is $2$.