Codeforces 1C Ancient Berland Circus

English

Desc

Nowadays all circuses in Berland have a round arena with diameter 13 meters, but in the past things were different.

In Ancient Berland arenas in circuses were shaped as a regular (equiangular) polygon, the size and the number of angles could vary from one circus to another. In each corner of the arena there was a special pillar, and the rope strung between the pillars marked the arena edges.

Recently the scientists from Berland have discovered the remains of the ancient circus arena. They found only three pillars, the others were destroyed by the time.

You are given the coordinates of these three pillars. Find out what is the smallest area that the arena could have.

Input

The input file consists of three lines, each of them contains a pair of numbers –– coordinates of the pillar. Any coordinate doesn’t exceed 1000 by absolute value, and is given with at most six digits after decimal point.

Output

Output the smallest possible area of the ancient arena. This number should be accurate to at least 6 digits after the decimal point. It’s guaranteed that the number of angles in the optimal polygon is not larger than 100.

Examples

input

0.000000 0.0000001.000000 1.0000000.000000 1.000000

output

1.00000000

中文

简介

现代的马戏团标准的大小都是13米直径的圆形，但是古代的不是。

古代马戏团是由不确定边的等角多边形边组成的，每个马戏团都有一些柱子来做标志，并且柱子与柱子之间连上线（作为马戏团的边境）。

科学家考察古代马戏团的时候只知道了三个柱子。

现在我们需要根据这三个柱子的坐标来计算出这个马戏团古代的时候的最小面积。

输入格式

输入有三行
每行输入x,y代表柱子坐标
x,y的绝对值不超过1000，保留小数点后6位。

输出格式

输出马戏团可能的最小面积，保留小数点后6位。
这里保证等角多边形的角不超过100度。

测试用例

测试输入

0.000000 0.0000001.000000 1.0000000.000000 1.000000

测试输出

1.00000000