• محدودیت زمان: ۱ ثانیه
• محدودیت حافظه: ۲۵۶ مگابایت

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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