Description:
An array $$$a_1, a_2, \ldots, a_n$$$ is good if and only if for every subsegment $$$1 \leq l \leq r \leq n$$$, the following holds: $$$a_l + a_{l + 1} + \ldots + a_r = \frac{1}{2}(a_l + a_r) \cdot (r - l + 1)$$$.
You are given an array of integers $$$a_1, a_2, \ldots, a_n$$$. In one operation, you can replace any one element of this array with any real number. Find the minimum number of operations you need to make this array good.
Input Format:
The first line of input contains one integer $$$t$$$ ($$$1 \leq t \leq 100$$$): the number of test cases.
Each of the next $$$t$$$ lines contains the description of a test case.
In the first line you are given one integer $$$n$$$ ($$$1 \leq n \leq 70$$$): the number of integers in the array.
The second line contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$-100 \leq a_i \leq 100$$$): the initial array.
Output Format:
For each test case, print one integer: the minimum number of elements that you need to replace to make the given array good.
Note:
In the first test case, the array is good already.
In the second test case, one of the possible good arrays is $$$[1, 1, \underline{1}, \underline{1}]$$$ (replaced elements are underlined).
In the third test case, the array is good already.
In the fourth test case, one of the possible good arrays is $$$[\underline{-2.5}, -2, \underline{-1.5}, -1, \underline{-0.5}, 0]$$$.