a257: NCPC2011 Problem K Key Persons
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Content

Problem K

Key Persons

Input File: pk.in

Time Limit: 3 seconds

There is a secret club, named No-Communication-Permitted-Club (NCPC),
formed by n college students and every student has a unique ID which is a
positive integer. Two students can talk if and only if their ID have a common
factor bigger than 1. For convenience, we use the ID to represent the students.
Two students p and q are “relevant” if either they can talk or they can communicate
indirectly via other students. Otherwise they are “non-relevant”.

Hence, two students p and q are relevant if either p and q have a common
factor bigger than 1 or there is a sequence of integers (a1 = p, a2,…, ak = q)
in S such that ai and ai+1 for 1 ≦ i ≦ k-1 have a common factor bigger
than 1, where S is the setoff all ID of the students. The club needs to elect
some “key persons” to manage the club. A student x in S is a key person if
after excluding x from S, it can cause two relevant students p ∈S and q ∈S,
become non-relevant in S’ = S – x.

For example, consider S = (1,2,3,4,5,6,7,8,9). Then, 2 and 9 is relevant
because sequence (2,6,9) exists, where 2 and 6 have a common factor 2
(>1) and 6 and 9 have a common factor 3(>1). However, after excluding 6
from S, 2 and 9 becomes non-relevant in the resulting set S’ = S – 6 =
{1,2,3,4,5,6,7,8,9}. Hence, 6 is a key person.

Given a set club members S, your task is to write a computer program to conpute the number of key persons in S.

Technical Specification

All ID are integers at least one and at most 30000 and the number of
students in each test case is no more than 1000.

Input

The first line of the input file contains an integer, denoting the number if
test cases to follow. For each test case, the club S = {a1, a2, ... , an} is given
with the following format : The first line contains a positive integer n. In the
following n lines, each line represents one integer in S such that an integer in
the ith line represents ai .

Output

For each test case, output the number of key persons in S.

Sample Input #1
2
8
2
4
6
8
10
12
14
16
10
1
2
3
4
5
6
7
8
9
10
Sample Output #1
0
2

Hint ：
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