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`

## Comments