You are given an integer array $$$a_1, a_2, \dots, a_n$$$, all its elements are distinct.
First, you are asked to insert one more integer $$$a_{n+1}$$$ into this array. $$$a_{n+1}$$$ should not be equal to any of $$$a_1, a_2, \dots, a_n$$$.
Then, you will have to make all elements of the array equal. At the start, you choose a positive integer $$$x$$$ ($$$x > 0$$$). In one operation, you add $$$x$$$ to exactly one element of the array. Note that $$$x$$$ is the same for all operations.
What's the smallest number of operations it can take you to make all elements equal, after you choose $$$a_{n+1}$$$ and $$$x$$$?
The first line contains a single integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of testcases.
The first line of each testcase contains a single integer $$$n$$$ ($$$1 \le n \le 2 \cdot 10^5$$$).
The second line contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$-10^9 \le a_i \le 10^9$$$). All $$$a_i$$$ are distinct.
The sum of $$$n$$$ over all testcases doesn't exceed $$$2 \cdot 10^5$$$.
For each testcase, print a single integer — the smallest number of operations it can take you to make all elements equal, after you choose integers $$$a_{n+1}$$$ and $$$x$$$.
331 2 351 -19 17 -3 -15110
6 27 1
In the first testcase, you can choose $$$a_{n+1} = 4$$$, the array becomes $$$[1, 2, 3, 4]$$$. Then choose $$$x = 1$$$ and apply the operation $$$3$$$ times to the first element, $$$2$$$ times to the second element, $$$1$$$ time to the third element and $$$0$$$ times to the fourth element.
In the second testcase, you can choose $$$a_{n+1} = 13, x = 4$$$.
In the third testcase, you can choose $$$a_{n+1} = 9, x = 1$$$. Then apply the operation once to $$$a_{n+1}$$$.
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