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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

SAMPLE INPUT
2
3
4

SAMPLE OUTPUT
2 5 4
2 5 8

Explanation

Test case #2:

factorial of 4 is 24 (equal to X)

prime factorization of X is 2 2 2 3

divisors of 24 are 1,2,3,4,6,8,12,24

Therefore , pf=2 , sum= 5, div=8

Source: hackerearth | Difficulty: UNKNOWN_DIFFICULTY


Solutions: