Description

A "terrain" is an $x$-monotone polygon defined by the points $p_1, \ldots, p_n$ where each point $p_i$ has coordinates $(x_i, y_i)$, and the following three conditions hold:

• $y_1 = y_n = 0$
• $y_i > 0$ for $1 < i < n$
• $x_i < x_{i+1}$ for $1 \leq i < n$

Given a terrain defined by the points $p_1, \ldots, p_n$, find the largest triangle that fits entirely within the terrain, and one of its three vertices is positioned at one of the terrain points $p_2$ through $p_{n-1}$.

:::align{center} :::

Input Format

The first line of input contains an integer $n$, representing the number of points in the terrain ($3 \leq n \leq 10^5$). The $i^{th}$ line in the following $n$ lines consists of two space-separated integers $x_i$ and $y_i$, representing the point $p_i$ of the terrain ($0 \leq x_i, y_i \leq 10^9$).

Output Format

Print the area of the largest triangle contained within the terrain. Your output will be considered correct if its absolute or relative error is at most $10^{-6}$.

11
0 0
2 10
4 5
6 7
8 8
10 4
12 6
14 4
15 4
16 7
17 0

53.666667