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The greatest common divisor (GCD) of a sequence is the greatest positive integer which divides each element of this sequence.

You are given a sequence $A$ of positive integers with size $N$. You are allowed to delete up to $N-1$ elements from this sequence. (I.e., you may delete any number of elements, including zero, as long as the resulting sequence is non-empty.)

Please find the minimum number of elements which have to be deleted so that the GCD of the resulting sequence would be equal to $1$, or determine that it is impossible.

------ Input ------
The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
The first line of each test case contains a single integer $N$.
The second line contains $N$ space-separated integers $A_{1}, A_{2}, \dots, A_{N}$.

------ Output ------
For each test case, print a single line containing one integer — the minimum number of elements to delete, or $-1$ if it is impossible to make the GCD equal to $1$.

------ Constraints ------
$1 ≤ T ≤ 100$
$2 ≤ N ≤ 1,000$
$1 ≤ A_{i} ≤ 50,000$ for each valid $i$

------ Subtasks ------
Subtask #1 (20 points): $2 ≤ N ≤ 3$

Subtask #2 (80 points): original constraints

----- Sample Input 1 ------
2

2

2 3

2

2 4
----- Sample Output 1 ------
0

-1
----- explanation 1 ------
Example case 1: The GCD is already equal to $1$, so the answer is $0$.

Example case 2: It is impossible to make the GCD equal to $1$, so the answer is $-1$.

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