+ محدودیت زمان: ۱ ثانیه
+ محدودیت حافظه: ۲۵۶ مگابایت
----------
A “terrain” is an $x$-monotone polygon defined by the points $p_1,\dots , p_n$ 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 $p_1, \dots , p_n$, 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 $p_{n-1}$.
# ورودی
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.
$$0 \leq x_i, y_i \leq 10^9$$
# خروجی
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 $10^{-6}$.
# مثال
### ورودی نمونه ۱
```
11
0 0
2 10
4 5
6 7
8 8
10 4
12 6
14 4
15 4
16 7
17 0
```
### خروجی نمونه ۱
```
53.666667
```