#include <iostream>
#include <cstdio>
using namespace std;
int prime(int);
int main()
{
int t,n,i,s,tot,y;
scanf("%d",&t);
while(t>0)
{
scanf("%d",&n);
int a;
int b[999989]={0};
tot=1;
for(i=0;i<n;i++)
{
//printf("\n taking values...");
scanf("%d",&a);
s=2;
while(a>1)
{
if(s<=a)
{
y=prime(s);
if(y==1)
{if(a%s==0)
{
b[s]=b[s]+1;
a/=s;
//printf(" \n now b =%d and a =%d",b[s],a);
}
}
else
s++;
}
};
}
for(i=0;i<999989;i++)
{
if(b[i]>0)
tot*=(b[i]+1);
}
printf("%d\n",tot);
t--;
};
return 0;
}
int prime(int n)
{
int flag=0;
if(n==2)
return 1;
for(int i=2;i<n;i++)
{
if(n%i==0)
{
flag=1;
break;
}
}
if(flag==0)
return 1;
else
return 0;
}
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