Different Divisors
Description
Positive integer $x$ is called divisor of positive integer $y$, if $y$ is divisible by $x$ without remainder. For example, $1$ is a divisor of $7$ and $3$ is not divisor of $8$.
We gave you an integer $d$ and asked you to find the smallest positive integer $a$, such that
- $a$ has at least $4$ divisors;
- difference between any two divisors of $a$ is at least $d$.
The first line contains a single integer $t$ ($1 \leq t \leq 3000$) — the number of test cases.
The first line of each test case contains a single integer $d$ ($1 \leq d \leq 10000$).
For each test case print one integer $a$ — the answer for this test case.
Input
The first line contains a single integer $t$ ($1 \leq t \leq 3000$) — the number of test cases.
The first line of each test case contains a single integer $d$ ($1 \leq d \leq 10000$).
Output
For each test case print one integer $a$ — the answer for this test case.
Samples
2
1
2
6
15
Note
In the first test case, integer $6$ have following divisors: $[1, 2, 3, 6]$. There are $4$ of them and the difference between any two of them is at least $1$. There is no smaller integer with at least $4$ divisors.
In the second test case, integer $15$ have following divisors: $[1, 3, 5, 15]$. There are $4$ of them and the difference between any two of them is at least $2$.
The answer $12$ is INVALID because divisors are $[1, 2, 3, 4, 6, 12]$. And the difference between, for example, divisors $2$ and $3$ is less than $d=2$.