A14728. AmShZ and G.O.A.T.

Let's call an array of $k$ integers $c_1, c_2, \ldots, c_k$ terrible, if the following condition holds:

- Let $AVG$ be the $\frac{c_1 + c_2 + \ldots + c_k}{k}$ (the average of all the elements of the array, it doesn't have to be integer). Then the number of elements of the array which are bigger than $AVG$ should be strictly larger than the number of elements of the array which are smaller than $AVG$ . Note that elements equal to $AVG$ don't count.

For example $c = \{1, 4, 4, 5, 6\}$ is terrible because $AVG = 4.0$ and $5$ -th and $4$ -th elements are greater than $AVG$ and $1$ -st element is smaller than $AVG$ .

Let's call an array of $m$ integers $b_1, b_2, \ldots, b_m$ bad, if at least one of its non-empty subsequences is terrible, and good otherwise.

You are given an array of $n$ integers $a_1, a_2, \ldots, a_n$ . Find the minimum number of elements that you have to delete from it to obtain a good array.

An array is a subsequence of another array if it can be obtained from it by deletion of several (possibly, zero or all) elements.

The first line contains an integer $t$ ( $1 \le t \le 10^4$ ) — the number of test cases. The description of test cases follows.

The first line of each test case contains a single integer $n$ ( $2 \le n \le 2 \cdot 10^5$ ) — the size of $a$ .

The second line of each testcase contains $n$ integers $a_1, a_2, \ldots, a_n$ ( $1 \le a_i \le 10^9$ ) — elements of array $a$ .

In each testcase for any $1 \le i \lt n$ it is guaranteed that $a_i \le a_{i+1}$ .

It is guaranteed that the sum of $n$ over all testcases doesn't exceed $2 \cdot 10^5$ .

For each testcase, print the minimum number of elements that you have to delete from it to obtain a good array.

In the first sample, the array $a$ is already good.

In the second sample, it's enough to delete $1$ , obtaining array $[4, 4, 5, 6]$ , which is good.