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.

Input

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 $$$2 \cdot 10^5$$$.

Output

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

Note

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.

AmShZ and G.O.A.T.

Examples