Representative Edges

题意翻译

数组 $ a_1,a_2,a_3...a_n $ 是好的，当且仅当对于每一个区间 $ [l,r] (1 \leq l \leq r \leq n) $，满足： $ a_l+a_{l+1}+...+a_r = \frac{1}{2}(a_l+a_r) \cdot (r-l+1)$ 每一次操作你都可以用任意一个实数代替任意一个元素，问你最少要进行多少次操作才能使这个数组是好的。

题目描述

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.

输入输出格式

输入格式

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.

输出格式

For each test case, print one integer: the minimum number of elements that you need to replace to make the given array good.

输入输出样例

输入样例 #1

5
4
1 2 3 4
4
1 1 2 2
2
0 -1
6
3 -2 4 -1 -4 0
1
-100

输出样例 #1

0
2
0
3
0

说明

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] $ .