Moon

题号：NC201114
时间限制：C/C++/Rust/Pascal 2秒，其他语言4秒
空间限制：C/C++/Rust/Pascal 256 M，其他语言512 M
Special Judge, 64bit IO Format: %lld

题目描述

Let ${S}$ be a sphere with radius ${1}$ and center ${(0, 0, 0)}$ . Let $a_0,a_1,\ldots,a_n$ be ${n+1}$ points on the surface of ${S}$ . The positions of $a_1,\ldots,a_n$ are fixed while the position of $a_0$ is a uniform random point on the surface of ${S}$ . Let ${f}$ be ${1}$ if there exists a hemisphere of ${S}$ that contains $a_0,\ldots,a_n$ and ${0}$ otherwise. Calculate the expected value of ${f}$ .

输入描述:

The first line contains an integer  denoting the number of points ().
The -th line of the next  lines contains three integers  denoting the point  ().
It is guaranteed that  are distinct.

输出描述:

Output the answer.
The answer will be considered correct if its absolute or relative error doesn't exceed .

示例1

输入

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输出

复制

0.875000000000