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: Wrong Answer)

def intersect_segment?(p,q,r,s)
  # ----p---q---- with r---s
  ((p[0] - q[0]) * (r[1] - p[1]) + (p[1] - q[1]) * (p[0] - r[0])) * \
  ((p[0] - q[0]) * (s[1] - p[1]) + (p[1] - q[1]) * (p[0] - s[0])) <= 0
end

def intersect?(p,q,r,s)
  intersect_segment?(p,q,r,s) && intersect_segment?(r,s,p,q)
end

def inner_triangle?(p,q,r,t)
  not (intersect?(p,q,r,t) || intersect?(q,r,p,t) || intersect?(r,p,q,t))
end

$<.to_a.each do |line|
  t = line.chomp.split(' ').map(&:to_f)
  p1 = t[0..1]
  p2 = t[2..3]
  p3 = t[4..5]
  target = t[6..7]

  puts inner_triangle?(p1,p2,p3,target) ? 'YES' : 'NO'
end