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).

Note

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.