CF851B.Arpa and an exam about geometry

Arpa is taking a geometry exam. Here is the last problem of the exam.

You are given three points a, b, c.

Find a point and an angle such that if we rotate the page around the point by the angle, the new position of a is the same as the old position of b, and the new position of b is the same as the old position of c.

Arpa is doubting if the problem has a solution or not (i.e. if there exists a point and an angle satisfying the condition). Help Arpa determine if the question has a solution or not.

Arpa 正在参加一场几何考试。以下是本次考试的最后一道题目。

给你三个点 $a$、$b$、$c$。

请找出一个点和一个角度，使得：若将纸面绕该点旋转该角度，则点 $a$ 的新位置恰好与点 $b$ 的原始位置重合，且点 $b$ 的新位置恰好与点 $c$ 的原始位置重合。

Arpa 怀疑该问题是否有解（即：是否存在满足上述条件的点和角度）。请帮助 Arpa 判断该问题是否有解。

The only line contains six integers a__x, a__y, b__x, b__y, c__x, c__y (|a__x|, |a__y|, |b__x|, |b__y|, |c__x|, |c__y| ≤ 109). It's guaranteed that the points are distinct.

唯一的一行包含六个整数 $a_x,\,a_y,\,b_x,\,b_y,\,c_x,\,c_y$（满足 $|a_x|,\,|a_y|,\,|b_x|,\,|b_y|,\,|c_x|,\,|c_y|\leq 10^9$）。保证这三个点互不相同。

Print "Yes" if the problem has a solution, "No" otherwise.

You can print each letter in any case (upper or lower).

如果该问题有解，输出“Yes”；否则输出“No”。

每个字母可以以任意大小写形式输出（大写或小写）。

In the first sample test, rotate the page around (0.5, 0.5) by .

In the second sample test, you can't find any solution.

在第一个样例测试中，将页面绕点 $(0.5,\,0.5)$ 旋转 。

在第二个样例测试中，无法找到任何解。