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 $10^{-12}$.

Sample Input 1

4
-2 -4 4 5

Sample Output 1

-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 $\-\\dfrac{1}{40}$.

Sample Input 2

4
1 1 1 1

Sample Output 2

3.000000000000000
3.000000000000000

Sample Input 3

5
1 2 3 4 5

Sample Output 3

0.200000000000000
1.000000000000000