Problem:
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A Point in a Triangle

There is a triangle formed by three points $(x_1, y_1)$, $(x_2, y_2)$, $(x_3, y_3)$ on a plain.

Write a program which prints "YES" if a point $P$ $(x_p, y_p)$ is in the triangle and "NO" if not.

Input

Input consists of several datasets. Each dataset consists of:

$x_1$ $y_1$ $x_2$ $y_2$ $x_3$ $y_3$ $x_p$ $y_p$

All the input are real numbers. Input ends with EOF. The number of datasets is less than or equal to 100.

Constraints

You can assume that:

$ -100 \leq x_1, y_1, x_2, y_2, x_3, y_3, x_p, y_p \leq 100$

1.0 $\leq$ Length of each side of a tringle

0.001 $\leq$ Distance between $P$ and each side of a triangle

Output

For each dataset, print "YES" or "NO" in a line.

Sample Input

0.0 0.0 2.0 0.0 2.0 2.0 1.5 0.5
0.0 0.0 1.0 4.0 5.0 3.0 -1.0 3.0

Output for the Sample Input

YES
NO

Solution in Ruby (judge verdict: Accepted)

def sub_vector(x1, y1, x2, y2)
	return x1 - x2, y1 - y2
end

while line = gets do
	x1, y1, x2, y2, x3, y3, xp, yp = line.split.map(&:to_f)

	*ab = sub_vector(x2, y2, x1, y1)
	*bp = sub_vector(xp, yp, x2, y2)

	*bc = sub_vector(x3, y3, x2, y2)
	*cp = sub_vector(xp, yp, x3, y3)

	*ca = sub_vector(x1, y1, x3, y3)
	*ap = sub_vector(xp, yp, x1, y1)
	
	c1 = ab[0] * bp[1] - ab[1] * bp[0]
	c2 = bc[0] * cp[1] - bc[1] * cp[0]
	c3 = ca[0] * ap[1] - ca[1] * ap[0]
	
	if (c1 > 0 && c2 > 0 && c3 > 0) ||
	   (c1 < 0 && c2 < 0 && c3 < 0); then
	   puts "YES"
	else
	   puts "NO"
	end
end