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.

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

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.

Output

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

Example

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

YES
NO
#include <iostream>
using namespace std;
int isintersecter(double x1,double y1,double x2,double y2,double px,double py,
		  double qx,double qy){
  if(((py-y1)*(x1-x2)-(y1-y2)*(px-x1))*((qy-y1)*(x1-x2)-(y1-y2)*(qx-x1)) < 0)return 1;
  else return 0;
}
int main(){
  double x1,y1,x2,y2,x3,y3,xp,xy;
  while(cin>>x1>>y1>>x2>>y2>>x3>>y3>>xp>>xy)
    {
      if(isintersecter(x1,y1,x2,y2,x3,y3,xp,xy) || 
	 isintersecter(x2,y2,x3,y3,x1,y1,xp,xy) || 
	 isintersecter(x1,y1,x3,y3,x2,y2,xp,xy) )cout << "NO" << endl;
      else cout << "YES" << endl;
    }
}