CF2146A Equal Occurrences

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.

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 $ .

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

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 $ .