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.

我们称一个数组是平衡的，当且仅当其中任意元素的出现次数均相同。例如，$[1,1,3,3,6,6]$ 和 $[2,2,2,2]$ 是平衡的，但 $[1,2,3,3]$ 不是平衡的（元素 $1$ 与 $3$ 的出现次数不同）。注意：空数组始终是平衡的。

给定一个长度为 $n$ 的非递减整数数组 $a$。求其最长平衡子序列$^{\text{∗}}$ 的长度。

$^{\text{∗}}$ 序列 $b$ 是序列 $a$ 的一个子序列，当且仅当 $b$ 可通过从 $a$ 中任意位置删除若干（可能为零个或全部）元素而得到。

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 $a$.

每个测试包含多个测试用例。第一行包含测试用例的数量 $t$（$1 \le t \le 500$）。随后是各测试用例的描述。

每个测试用例的第一行包含一个整数 $n$（$1 \leq n \leq 100$）—— 数组 $a$ 的长度。

第二行包含 $n$ 个整数 $a_1,a_2,\ldots,a_n$（$1\le a_1\le a_2\le \cdots \le a_n\le n$）—— 数组 $a$ 的元素。

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

对于每个测试用例，输出一个整数——数组 $a$ 的最长平衡子序列的长度。

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 $5$.

在第一个测试用例中，整个数组 $a = [1, 1, 4, 4, 4]$ 不是平衡的，因为元素 $1$ 的出现次数为 $2$，而元素 $4$ 的出现次数为 $3$，二者不相等。子序列 $[1, 1, 4, 4]$ 是平衡的，因为元素 $1$ 和 $4$ 的出现次数均为 $2$。因此，数组 $a$ 的最长平衡子序列的长度为 $4$。

在第二个测试用例中，整个数组 $a = [1, 2]$ 已经是平衡的，所以数组 $a$ 的最长平衡子序列的长度为 $2$。

在第三个测试用例中，数组 $a$ 的最长平衡子序列是 $[1,1,1,2,2,2,3,3,3]$。

在第四个测试用例中，整个数组 $a = [3, 3, 3, 3, 3]$ 已经是平衡的，所以数组 $a$ 的最长平衡子序列的长度为 $5$。