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B. Arpa and an exam about geometry

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputArpa 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 .

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

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

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