"Password?" said the Fat lady. "Caput Draconis," said Percy.
It is your first day at Hogwarts. You are heading towards the Gryffindor Chambers, accompanied by Chotu and Neville, but the three of you are faced with a problem !
"How can we forget the password, now how are we going to enter the Gryffindor Chambers?" says Chotu Potter.
“What was it ‘Capital Dragon’ or something like that?” mutters Neville.
Overhearing the young wizards the Fat lady tells them that she can open the door for them if they answer the security question.
“You are given a magical number N, how many divisors of N! exist?” asked the Fat Lady.
Help Chotu answer the security question!
As the answer can be very large print answer modulo 109 + 7
Note- N! denotes the factorial of number N (i.e. product of first N natural numbers).
Input
First line of input contains an integer T denoting number of test cases.
Next T lines contains an integer N .
Output
For each test case output the required answer.
Constraints
1 <= T <= 102
1 <= N <= 105
For N = 5, N! = 120.
S = {1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120}, denotes the set of divisors of N!.
|S| = 16.