#290. LIS 翻转

LIS 翻转

题面翻译

设一个长为 nn 的整数序列 aa{a1,a2,a3,,an}\{a_1,a_2,a_3,\cdots,a_n\},那么 aa' 表示 {an,an1,an2,,a1}\{a_n,a_{n-1},a_{n-2},\cdots,a_1\}LIS(a)\operatorname{LIS}(a) 表示 aa 的最长严格上升子序列的长度。

现在给定 aa 数组,请你将 aa 数组重新排列,使得重排后的 min(LIS(a),LIS(a))\min(\operatorname{LIS}(a),\operatorname{LIS}(a')) 最大。

输入 tt 组数据,每组数据先输入 nn ,然后输入 nn 个整数,所有 nn 之和不超过 2×1052 \times 10^5

输出 tt 行,每行一组数据的答案,按输入顺序输出。

题目描述

You are given an array a a of n n positive integers.

Let LIS(a) \text{LIS}(a) denote the length of longest strictly increasing subsequence of a a . For example,

  • LIS([2,1,1,3]) \text{LIS}([2, \underline{1}, 1, \underline{3}]) = 2 2 .
  • LIS([3,5,10,20]) \text{LIS}([\underline{3}, \underline{5}, \underline{10}, \underline{20}]) = 4 4 .
  • LIS([3,1,2,4]) \text{LIS}([3, \underline{1}, \underline{2}, \underline{4}]) = 3 3 .

We define array a a' as the array obtained after reversing the array a a i.e. a=[an,an1,,a1] a' = [a_n, a_{n-1}, \ldots , a_1] .

The beauty of array a a is defined as min(LIS(a),LIS(a)) min(\text{LIS}(a),\text{LIS}(a')) .

Your task is to determine the maximum possible beauty of the array a a if you can rearrange the array a a arbitrarily.

输入格式

The input consists of multiple test cases. The first line contains a single integer t t (1t104) (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 n (1n2105) (1 \leq n \leq 2\cdot 10^5) — the length of array a a .

The second line of each test case contains n n integers a1,a2,,an a_1,a_2, \ldots ,a_n (1ai109) (1 \leq a_i \leq 10^9) — the elements of the array a a .

It is guaranteed that the sum of n n over all test cases does not exceed 2105 2\cdot 10^5 .

输出格式

For each test case, output a single integer — the maximum possible beauty of a a after rearranging its elements arbitrarily.

样例 #1

样例输入 #1

3
3
6 6 6
6
2 5 4 5 2 4
4
1 3 2 2

样例输出 #1

1
3
2

提示

In the first test case, a a = [6,6,6] [6, 6, 6] and a a' = [6,6,6] [6, 6, 6] . LIS(a)=LIS(a) \text{LIS}(a) = \text{LIS}(a') = 1 1 . Hence the beauty is min(1,1)=1 min(1, 1) = 1 .

In the second test case, a a can be rearranged to [2,5,4,5,4,2] [2, 5, 4, 5, 4, 2] . Then a a' = [2,4,5,4,5,2] [2, 4, 5, 4, 5, 2] . LIS(a)=LIS(a)=3 \text{LIS}(a) = \text{LIS}(a') = 3 . Hence the beauty is 3 3 and it can be shown that this is the maximum possible beauty.

In the third test case, a a can be rearranged to [1,2,3,2] [1, 2, 3, 2] . Then a a' = [2,3,2,1] [2, 3, 2, 1] . LIS(a)=3 \text{LIS}(a) = 3 , LIS(a)=2 \text{LIS}(a') = 2 . Hence the beauty is min(3,2)=2 min(3, 2) = 2 and it can be shown that 2 2 is the maximum possible beauty.