Time Limit: 2 seconds
Memory Limit: 256 megabytes
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.
The only line contains six integers ax, ay, bx, by, cx, cy (|ax|, |ay|, |bx|, |by|, |cx|, |cy| ≤ 109). It's guaranteed that the points are distinct.
Print "Yes" if the problem has a solution, "No" otherwise.
You can print each letter in any case (upper or lower).
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.