407538: GYM102823 G Greatest Common Divisor

There is an array of length $$$n$$$, containing only positive numbers.

Now you can add all numbers by $$$1$$$ many times. Please find out the minimum times you need to perform to obtain an array whose greatest common divisor(gcd) is larger than $$$1$$$ or state that it is impossible.

You should notice that if you want to add one number by $$$1$$$, you need to add all numbers by $$$1$$$ at the same time.

The first line of input file contains an integer $$$T$$$ ($$$1\le T\le 20$$$), describing the number of test cases.

Then there are $$$2 \times T$$$ lines, with every two lines representing a test case.

The first line of each case contains a single integer $$$n$$$ ($$$1\le n \le 10^5$$$) described above.

The second line of that contains $$$n$$$ integers ranging in $$$[1,10^9]$$$.

You should output exactly $$$T$$$ lines.

For each test case, print Case $$$d$$$: ($$$d$$$ represents the order of the test case) first. Then output exactly one integer representing the answer. If it is impossible, print -1 instead.

3
1
2
5
2 5 9 5 7
5
3 5 7 9 11

Case 1: 0
Case 2: -1
Case 3: 1

• Sample 1: You do not need to do anything because its gcd is already larger than $$$1$$$.
• Sample 2: It is impossible to obtain that array.
• Sample 3: You just need to add all number by $$$1$$$ so that gcd of this array is $$$2$$$.