Description

题面翻译

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

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

输入 $t$ 组数据，每组数据先输入 $n$ ，然后输入 $n$ 个整数，所有 $n$ 之和不超过 $2 \times 10^5$。

输出 $t$ 行，每行一组数据的答案，按输入顺序输出。

Input

The 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 $2\cdot 10^5$.

Output

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

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

1
3
2

Note

In 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.