# Problem B

Most Difficult

You are an expert on the most difficult field of math — primes! Indeed, you have actually proven the Riemann Hypothesis, but unfortunately, this margin is too narrow to contain the proof.

Being considered a prime expert, $q$ people have come to you for help.
The $i$-th person has a
favorite number $x_ i$,
and they want to find the *primmest* prime number with
respect to $x_ i$ — that
is, the smallest prime number $p$ such that **both
$p$ and $x_ i + p$ are prime**!

Unfortunately, there are too many people, and you don’t want to spend your time answering such trivial questions. Instead, you decide to write a program to answer all of their questions!

## Input

The first line contains an integer $q$, denoting the number of people ($1 \leq q \leq 100$).

The next $q$ lines each contain an integer $x_ i$, denoting the favorite number of the $i$-th person ($1 \leq x_ i \leq 10^{18}$).

## Output

Output $q$ lines, where
the $i$-th line contains
the *primmest prime* $p$ with respect to $x_ i$. If there is no such prime
$p$ where both
$p$ and $x_ i + p$ are primes, output
$-1$ instead.

Sample Input 1 | Sample Output 1 |
---|---|

10 1 2 3 4 5 3233 4200 1000000000 969268337140823504 1000000000000000000 |
2 3 2 3 2 -1 11 7 2837 3 |