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.

-----Input-----

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}| ≤ 10^9). It's guaranteed that the points are distinct.

-----Output-----

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

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

-----Examples-----

Input 0 1 1 1 1 0

Output Yes

Input 1 1 0 0 1000 1000

Output No

-----Note-----

In the first sample test, rotate the page around (0.5, 0.5) by $90^{\circ}$.

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