Beautiful SubSequence
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  Difficulty: Medium   Marks: 4
       

Nowadays Babul is solving problems on sub-sequence. He is struck with a problem in which he has to find the longest sub-sequence in an array A of size  N such that for all (i,j) where i!=j either A[i] divides A[j] or vice versa. If no such sub-sequence exists then print -1. Help him to accomplish this task.

Constraints :
1<=T<=100
2<=N<=1000
1<=A[i]<=1000

Input:
The First line contains T no. of test cases.
Each Test case is of two lines. 
The First line contains N size of the array.
Next line contains N-Space separated integers, denoting elements of an array.

Output:
For each T print the size of the longest sub-sequence satisfying the above criteria.

Example:
Input:
2
5
5 3 1 4 7
6
2 4 6 1 3 11

Output:
2
3

Explanation:
First Test Case :
Longest Sub Sequence are {5,1} , {4,1}, {3,1} etc. so size is 2.

Second Test Case :
Longest Sub Sequence are {1, 2, 6}, {1, 3, 6} so size is 3.

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

Author: Prithwish Dasgupta


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