A. Equal Occurrencestime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard output 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. InputEach 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 $$$a$$$.OutputFor each test case, output a single integer — the length of the longest balanced subsequence of $$$a$$$.ExampleInput451 1 4 4 421 2151 1 1 1 1 2 2 2 2 3 3 3 4 4 553 3 3 3 3Output4295NoteIn 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 $$$5$$$.