Micro has discovered new type of numbers, he is calling them Optimus Primes. He defined a function,\(f(x) = sum \space \space of \space powers \space of \space prime \space factors \space in \space x's \space prime \space factorization\) A number x is Optimus Prime if \(f(x)\) is exactly 1 less than its total number of divisors. Now, Micro is interested in finding out the smallest Optimus Prime having \(f(x) = N\). Help Micro with this task.

Input:
First line consists of a single integer T denoting the number of test cases.
Each of the following T lines consists of a single integer denoting N.

Output:
Print the required answer for each test case in a new line. Since answer can be large print it modulo \(10^9+7\).

Constraints:
\(1 \le T \le 10^5\)
\(1 \le N \le 10^{18}\)