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 $10^{-12}$.