Score : $500$ points

Problem Statement

You are given non-zero integers $x_1, \ldots, x_N$. Find the minimum and maximum values of $\dfrac{x_i+x_j+x_k}{x_ix_jx_k}$ for integers $i$, $j$, $k$ such that $1\leq i < j < k\leq N$.

Constraints

• $3\leq N\leq 2\times 10^5$
• $-10^6\leq x_i \leq 10^6$
• $x_i\neq 0$

Input

The input is given from Standard Input in the following format:

$N$

$x_1$ $\ldots$ $x_N$

Output

Print the minimum value of $\dfrac{x_i+x_j+x_k}{x_ix_jx_k}$ in the first line and the maximum value in the second line.

Your output will be considered correct when the absolute or relative error is at most $10^{-12}$.

4
-2 -4 4 5

-0.175000000000000
-0.025000000000000

$\dfrac{x_i+x_j+x_k}{x_ix_jx_k}$ can take the following four values.

• $(i,j,k) = (1,2,3)$: $\dfrac{(-2) + (-4) + 4}{(-2)\cdot (-4)\cdot 4} = -\dfrac{1}{16}$.
• $(i,j,k) = (1,2,4)$: $\dfrac{(-2) + (-4) + 5}{(-2)\cdot (-4)\cdot 5} = -\dfrac{1}{40}$．
• $(i,j,k) = (1,3,4)$: $\dfrac{(-2) + 4 + 5}{(-2)\cdot 4\cdot 5} = -\dfrac{7}{40}$．
• $(i,j,k) = (2,3,4)$: $\dfrac{(-4) + 4 + 5}{(-4)\cdot 4\cdot 5} = -\dfrac{1}{16}$.

Among them, the minimum is $-\dfrac{7}{40}$, and the maximum is $-\dfrac{1}{40}$.

4
1 1 1 1

3.000000000000000
3.000000000000000

5
1 2 3 4 5

0.200000000000000
1.000000000000000