Kata

Task

Consider an n-th-degree polynomial with integer coefficients:

Let's call this polynomial compact if it has only integer roots which are non-repeating and non-zero and $\mathrm{\mid }{a}_n\mathrm{\mid }|a\_n|$ is minimal.

Your task is to find the maximum and minimum values of $a_{1}a\_1$ in the compact polynomial.

You're given the degree of the polynomial: $nn$ $(1\le n\le 10^{18})(1\le n\le 10^\{18\})$.

Return a tuple (min, max).

Note

Test feedback is minimal as part of this puzzle.

Examples

first_coefficient(1) => (-1, 1)