Representative Edges
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.
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.
For each test case, print one integer: the minimum number of elements that you need to replace to make the given array good.
Input
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
For each test case, print one integer: the minimum number of elements that you need to replace to make the given array good.
Samples
5
4
1 2 3 4
4
1 1 2 2
2
0 -1
6
3 -2 4 -1 -4 0
1
-100
0
2
0
3
0
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 $[\underline{-2.5}, -2, \underline{-1.5}, -1, \underline{-0.5}, 0]$.