It’s universally acknowledged that there’re innumerable trees in the campus of HUST.

Coach Yin possesses a triangular garden below his office. He wants to decorate his garden with a beautiful tree. He believes that a tree planted in place will bring good luck. A tree in place means that this tree is located at the orthocenter, centroid, incenter or circumcenter of the triangle.

Orthocenter is the intersection of the three(possibly extended) altitudes. Centroid is the intersection of the three midian line. Incenter is the intersection of three inner angular bisector. Circumcenter is the intersection of three perpendicular bisector.

It's guaranteed that the given points can form a triangle.

输入描述:

There areexactly 4 lines in each test sample.
The first to the third line consists of two integers xi and yi, denoting coordinatesof three points in plate.
The last line also consists of two integers xo and yo, denotingcoordinates the tree’s position.
The absolute valueof all coordinates are no larger than 106.

输出描述:

Print “Yes” if this tree will bring good luck, or “No” if not. Note that a tree will bring good luck if and only if it coincides with any of the four center with no error.

0 1
4 2
5 0
3 1

Yes

10 5
3 29
3 5
6 8

Yes

20 18
5 6
1 4
0 0

No