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:
$1 \le T \le 10^5$
$1 \le N \le 10^{18}$