import java.util.*;
class Ideone
{
static int maxn=5000+1;
static int gcd(int a,int b)
{
while(b!=0)
{
int temp=a%b;
a=b;
b=temp;
}
return a;
}
public static void main
(String[] args
) {
Scanner sc
=new Scanner
(System.
in); int t=sc.nextInt();
while(t-->0)
{
int n=sc.nextInt();
int arr[]=new int[n];
for(int i=0;i<n;i++)
arr[i]=sc.nextInt();
int g=0;
for(int i=0;i<n;i++)
g=gcd(g,arr[i]);
int gcount=0;
for(int i=0;i<n;i++)
{
if(arr[i]==g)
gcount++;
}
if(gcount>0)
else
{
Queue<Integer> q=new LinkedList<>();
boolean visited[]=new boolean[maxn];
int dp[]=new int[maxn];
for(int i=0;i<n;i++)
{
q.add(arr[i]);
visited[arr[i]]=true;
dp[arr[i]]=0;
}
while(!q.isEmpty())
{
int temp=q.poll();
for(int ele:arr)
{
int val=gcd(temp,ele);
if(!visited[val])
{
q.add(val);
visited[val]=true;
dp[val]=dp[temp]+1;
}
}
}
System.
out.
println(n
-1 +dp
[g
]); }
}
}
}
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