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

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