CF1474B.Different Divisors

普及/提高-

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题目描述

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 $d$ .

输入格式

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 $d$ ( $1 \leq d \leq 10000$ ).

输出格式

For each test case print one integer $a$ — the answer for this test case.

输入输出样例

输入#1
```
2
1
2
```
输出#1
```
6
15
```

说明/提示

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 $d=2$ .

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