A11336 | Equalize

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.