B. Equalizetime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputVasya 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).InputEach 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.OutputFor each test case, output a single number — the maximum number of elements equal to the same number after the operation of adding a permutation.ExampleInput
721 247 1 4 13103 102 10451 101 1 100 151 10 100 1000 123 131000000000 999999997 999999999Output
2
2
3
2
1
1
2
NoteIn 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.
721 247 1 4 13103 102 10451 101 1 100 151 10 100 1000 123 131000000000 999999997 999999999
2 2 3 2 1 1 2 
['binary search', 'greedy', 'sortings', 'two pointers', '*1200']