Your task is simple .Given a positive integer N . Let X be the factorial of N.

You have to calculate pf , sum and div where ,

pf=total number of distinct prime factors of X.

sum=sum of distinct prime factors of X.

div=total number of divisors of X.

Since the answers can be very large ,print pf % (10^9+7) , sum % (10^9+7) , div % (10^9+7).

Input:

First line contains a positive integer T (number of test cases). Next T lines contain a number N.

Output:

Print T lines of output each containing values of pf , sum , div where each of them is separated by a single space.

Constraints:

1<=T<=5000

2<=N<=10^6