#include <iostream>
using namespace std;
int gcdd(int gcd,int no);
int main() {
int t,n,no,gcd;
cin>>t;
while(t--)
{
cin>>n;
cin>>no;
gcd=no;
for(int i=1;i<n;i++)
{
cin>>no;
gcd=gcdd(gcd,no);
if(gcd==1)
{
cout<<n<<endl;
break;
}
}
if(gcd!=1)
{
cout<<"-1"<<endl;
}
}
return 0;
}
int small;
int gcdd(int gcd,int no)
{
while(gcd!=no)
{
if(gcd<no)
small=gcd;
else
small=no;
(gcd%small==0)?gcd=small:gcd=gcd%small;
(no%small==0)?no=small:no=no%small;
}
return gcd;
}
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