Given an array of N elements, find the minimum number of insertions to convert the given array into a co-prime array pair-wise.

Input:
The first line of the input contains an integer T, denoting number of test cases. The first line of each test case contains an integer N denoting the size of the array. The second line of each test cases N space separated integers.

Output:
For each test case, print  a single line of output containing minimum no. of insertions.

Constraints:
1<=T<=100
1<=N<=100
1<=arr<=1000

Example:
Input:
2
3
2 7 28
3
5 10 20
Output:
1
2

Explanation:
Testcase 1:
Here, 1st pair = {2, 7} are co-primes( gcd(2, 7) = 1).
2nd pair = {7, 28} are not co-primes, insert 9
between them. gcd(7, 9) = 1 and gcd(9, 28) = 1.

Testcase 2:
Here, there is no pair which are co-primes.
Insert 7 between (5, 10) and 1 between (10, 20).

** For More Input/Output Examples Use 'Expected Output' option **