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 $$$5$$$.

Equal Occurrences

Examples