A. Common Multiple
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given an array of integers $$$a_1, a_2, \ldots, a_n$$$. An array $$$x_1, x_2, \ldots, x_m$$$ is beautiful if there exists an array $$$y_1, y_2, \ldots, y_m$$$ such that the elements of $$$y$$$ are distinct (in other words, $$$y_i\neq y_j$$$ for all $$$1 \le i \lt j \le m$$$), and the product of $$$x_i$$$ and $$$y_i$$$ is the same for all $$$1 \le i \le m$$$ (in other words, $$$x_i\cdot y_i = x_j\cdot y_j$$$ for all $$$1 \le i \lt j \le m$$$).

Your task is to determine the maximum size of a subsequence$$$^{\text{∗}}$$$ of array $$$a$$$ that is beautiful.

$$$^{\text{∗}}$$$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 $$$n$$$ ($$$1 \le n \le 100$$$) — the length of the array $$$a$$$.

The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \le a_i \le n$$$) — the elements of array $$$a$$$.

Note that there are no constraints on the sum of $$$n$$$ over all test cases.

Output

For each test case, output the maximum size of a subsequence of array $$$a$$$ that is beautiful.

Example
Input
3
3
1 2 3
5
3 1 4 1 5
1
1
Output
3
4
1
Note

In the first test case, the entire array $$$a = [1, 2, 3]$$$ is already beautiful. A possible array $$$y$$$ is $$$[6, 3, 2]$$$, which is valid since the elements of $$$y$$$ are distinct, and $$$1\cdot 6 = 2\cdot 3 = 3\cdot 2$$$.

In the second test case, the subsequence $$$[3, 1, 4, 5]$$$ is beautiful. A possible array $$$y$$$ is $$$[20, 60, 15, 12]$$$. It can be proven that the entire array $$$a = [3, 1, 4, 1, 5]$$$ is not beautiful, so the maximum size of a subsequence of array $$$a$$$ that is beautiful is $$$4$$$.