#include<stdio.h>
#include<math.h>
int main()
{
long int prime,m,i;
int t,n,c,d;
scanf("%d",&t);
while(t--)
{
m=1;d=1;
scanf("%d",&n);
while(n--)
{
scanf("%ld",&prime);
m*=prime;
}
prime = (long int)sqrt(m) + 1;
for(i=2;i<prime;i++)
{
c=0;
while (m % i == 0)
{
c++;
m/=i;
}
d*=(c+1);
}
printf("%d\n",d);
}
return 0;
}
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