We call an array balanced if and only if the numbers of occurrences of any of its elements are the same. For example, $[1,1,3,3,6,6]$ and $[2,2,2,2]$ are balanced, but $[1,2,3,3]$ is not balanced (the numbers of occurrences of elements $1$ and $3$ are different). Note that an empty array is always balanced.

You are given a non-decreasing array $a$ consisting of $n$ integers. Find the length of its longest balanced subsequence$^{\text{∗}}$.

$^{\text{∗}}$A sequence $b$ is a subsequence of a sequence $a$ if $b$ can be obtained from $a$ by the deletion of several (possibly, zero or all) element from arbitrary positions.

Input

Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 500$). The description of the test cases follows.

The first line of each test case contains a single integer $n$ ($1 \leq n \leq 100$) — the length of $a$.

The second line contains $n$ integers $a_1,a_2,\ldots,a_n$ ($1\le a_1\le a_2\le \cdots \le a_n\le n$) — the elements of $a$.

Output

For each test case, output a single integer — the length of the longest balanced subsequence of $a$.

Note

In the first test case, the whole array $a = [1, 1, 4, 4, 4]$ is not balanced because the number of occurrences of element $1$ is $2$, while the number of occurrences of element $4$ is $3$, which are not equal. The subsequence $[1, 1, 4, 4]$ is balanced because the numbers of occurrences of elements $1$ and $4$ are both $2$. Thus, the length of the longest balanced subsequence of $a$ is $4$.

In the second test case, the whole array $a = [1, 2]$ is already balanced, so the length of the longest balanced subsequence of $a$ is $2$.

In the third test case, the longest balanced subsequence of $a$ is $[1,1,1,2,2,2,3,3,3]$.

In the fourth test case, the whole array $a = [3, 3, 3, 3, 3]$ is already balanced, so the length of the longest balanced subsequence of $a$ is $5$.

Samples

4
5
1 1 4 4 4
2
1 2
15
1 1 1 1 1 2 2 2 2 3 3 3 4 4 5
5
3 3 3 3 3

4
2
9
5