## Code Golf Challenge P4 - Function Minimization

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Points: 12 (partial)
Time limit: 2.0s
Memory limit: 512M

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Problem types

You are given a function:

$f(x) = \begin{cases} x & \text{if } (x−1)!+1 \equiv 0\pmod x \\ -x & \text{if } (x−1)!+1 \not\equiv 0\pmod x \end{cases}$

where $$!$$ denotes the factorial operation. In other words, the function returns $$x$$ if $$(x−1)!+1$$ is divisible by $$x$$, and $$−x$$ otherwise.

Given an array $$a$$, print out the minimum value of $$f(x)$$ for all elements in $$a$$.

#### Input Specification

The first line will contain the integer $$N\ (1 \le N \le 10^5)$$.

The second line will contain $$N$$ integers, $$a_1, a_2, \ldots, a_N\ (2 \le a_i \le 10^6)$$.

#### Output Specification

Print the minimum value of $$f(x)$$ for all elements in $$a$$.

#### Scoring

Let $$L$$ represent the number of characters in your solution.

If $$L$$ is less than $$160$$, your score will be $$\min (1, 1-\frac{L-137}{40}) \times 100\%$$.

If $$L$$ is greater than or equal to $$160$$, and less than $$1\ 000$$, your score is $$(\frac{150}{L})^2 \times 50\%$$.

Otherwise, your score is $$0$$.

#### Sample Input

8
2 5 3 9 3 5 7 12

#### Sample Output

-12