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)

while line = gets
  x1, y1, x2, y2, x3, y3, xp, yp = line.chomp.split.map(&:to_f)
  if (x1 == xp && y1 == yp) || (x2 == xp && y2 == yp)|| (x3 == xp && y3 == yp)
      puts "NO"
  else
    v12 = [x2-x1, y2-y1]
    v23 = [x3-x2, y3-y2]
    v31 = [x1-x3, y1-y3]
    v1p = [xp-x1, yp-y1]
    v2p = [xp-x2, yp-y2]
    v3p = [xp-x3, yp-y3]
    z1 = v12[0] * v2p[1] - v12[1] * v2p[0]
    z2 = v23[0] * v3p[1] - v23[1] * v3p[0]
    z3 = v31[0] * v1p[1] - v31[1] * v1p[0]
    if ((z1 > 0 && x2 > 0 && z3 > 0) || (z1 < 0 && z2 < 0 && z3 < 0)) then
      puts "YES"
    else
      puts "NO"
    end
  end
end