C. LIS or Reverse LIS?time limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou are given an array a of n positive integers. Let \text{LIS}(a) denote the length of longest strictly increasing subsequence of a. For example,  \text{LIS}([2, \underline{1}, 1, \underline{3}]) = 2.  \text{LIS}([\underline{3}, \underline{5}, \underline{10}, \underline{20}]) = 4.  \text{LIS}([3, \underline{1}, \underline{2}, \underline{4}]) = 3.  We define array a' as the array obtained after reversing the array a i.e. a' = [a_n, a_{n-1}, \ldots , a_1].The beauty of array a is defined as min(\text{LIS}(a),\text{LIS}(a')).Your task is to determine the maximum possible beauty of the array a if you can rearrange the array a arbitrarily.InputThe input consists of multiple test cases. The first line contains a single integer t (1 \leq t \leq 10^4)  — the number of test cases. Description of the test cases follows.The first line of each test case contains a single integer n (1 \leq n \leq 2\cdot 10^5)  — the length of array a.The second line of each test case contains n integers a_1,a_2, \ldots ,a_n (1 \leq a_i \leq 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 integer  — the maximum possible beauty of a after rearranging its elements arbitrarily.ExampleInput
3
3
6 6 6
6
2 5 4 5 2 4
4
1 3 2 2
Output
1
3
2
NoteIn the first test case, a = [6, 6, 6] and a' = [6, 6, 6]. \text{LIS}(a) = \text{LIS}(a') = 1. Hence the beauty is min(1, 1) = 1.In the second test case, a can be rearranged to [2, 5, 4, 5, 4, 2]. Then a' = [2, 4, 5, 4, 5, 2]. \text{LIS}(a) = \text{LIS}(a') = 3. Hence the beauty is 3 and it can be shown that this is the maximum possible beauty.In the third test case, a can be rearranged to [1, 2, 3, 2]. Then a' = [2, 3, 2, 1]. \text{LIS}(a) = 3, \text{LIS}(a') = 2. Hence the beauty is min(3, 2) = 2 and it can be shown that 2 is the maximum possible beauty.
3
3
6 6 6
6
2 5 4 5 2 4
4
1 3 2 2

1 3 2 
['constructive algorithms', 'greedy', 'implementation', 'math', '*1400']