Problem A
Horizontal Ray–Segment Intersection

You are given a horizontal ray and a line segment in the 2D plane. The ray starts at point $ q = (q_x, q_y)$ and extends infinitely in the positive $x$-direction (“East”). That is, the ray consists of all points $(x, y)$ such that $x \geq q_x$ and $y = q_y$. The line segment has endpoints $a=(a_x, a_y)$ and $b=(b_x, b_y)$, ordered such that $b_y\geq a_y$. The line segment is closed at $a$ and open at $b$; that is, point $a$ is considered part of the line segment, while point $b$ is not.

The task is to determine whether the ray intersects the line segment.

In the $1$st and $4$th of the examples below, the answer is “yes.”

       

Input

The input consists of:

• One line with the coordinates $q_x$ and $q_y$ of $q$.

• One line with the coordinates $a_x$ and $a_y$ of $a$.

• One line with the coordinates $b_x$ and $b_y$ of $b$, with $b_y\geq a_y$.

Each coordinate is given as a floating point number $z$ with $0\leq z \leq 90$. The Euclidean distance between the query point and the line segment is at least $10^{-6}$. The Euclidean distance between $a$ and $b$ is at least $10^{-6}$.

Output

Write “yes” if the ray intersects the line segment. Else write “no”.

1.0 1.0
0.5 0.0
2.0 2.0

yes

1.0 1.0
2.0 0.0
0.0 1.5

no

1.0 1.0
2.0 2.0
3.0 2.0

no

1.0 1.0
2.0 1.0
2.0 2.0

yes

1.0 2.0
2.0 1.0
2.0 2.0

no