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 out_prod(v1,v2)
	v1[0]*v2[1]-v1[1]*v2[0]
end

while(input=gets)
	input=input.split(" ")
	x1=input[0].to_f
	y1=input[1].to_f
	x2=input[2].to_f
	y2=input[3].to_f
	x3=input[4].to_f
	y3=input[5].to_f
	xp=input[6].to_f
	yp=input[7].to_f

	p0=out_prod([x2-x1,y2-y1],[xp-x2,yp-y2])
	p1=out_prod([x3-x2,y3-y2],[xp-x3,yp-y3])
	p2=out_prod([x1-x3,y1-y3],[xp-x1,yp-y1])
	if((p0>0&&p1>0&&p2>0)||(p0<0&&p1<0&&p2<0)) then puts "YES"
	else puts "NO"
	end
end