You are given a cyclic array $a_1, a_2, \ldots, a_n$.

You can perform the following operation on $a$ at most $n - 1$ times:

• Let $m$ be the current size of $a$, you can choose any two adjacent elements where the previous one is no greater than the latter one (In particular, $a_m$ and $a_1$ are adjacent and $a_m$ is the previous one), and delete exactly one of them. In other words, choose an integer $i$ ($1 \leq i \leq m$) where $a_i \leq a_{(i \bmod m) + 1}$ holds, and delete exactly one of $a_i$ or $a_{(i \bmod m) + 1}$ from $a$.

Your goal is to find the minimum number of operations needed to make all elements in $a$ equal.

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 $a$.

Output

For each test case, output a single line containing an integer: the minimum number of operations needed to make all elements in $a$ equal.

Note

In the first test case, there is only one element in $a$, so we can't do any operation.

In the second test case, we can perform the following operations to make all elements in $a$ equal:

• choose $i = 2$, delete $a_3$, then $a$ would become $[1, 2]$.
• choose $i = 1$, delete $a_1$, then $a$ would become $[2]$.

It can be proven that we can't make all elements in $a$ equal using fewer than $2$ operations, so the answer is $2$.

Samples

7
1
1
3
1 2 3
3
1 2 2
5
5 4 3 2 1
6
1 1 2 2 3 3
8
8 7 6 3 8 7 6 3
6
1 1 4 5 1 4

0
2
1
4
4
6
3