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
import sys
for line in sys.stdin.readlines():
    try:
        list=map(float,line.split())
        x=list[0:6:2]
        y=list[1:6:2]
        xp=list[6]
        yp=list[7]
        xv=[x[a%3]-x[(a+1)%3] for a in xrange(4)]
        yv=[y[a%3]-y[(a+1)%3] for a in xrange(4)]
        xpv=[xp-x[a] for a in xrange(3)]
        ypv=[yp-y[a] for a in xrange(3)]
        cross=[xv[i]*ypv[i]-yv[i]*xpv[i] for i in xrange(3)]
        if (cross[2]>0 and cross[1]>0  and cross[0]>0) or (cross[2]<0 and cross[1]<0 and cross[0]<0): 
            print "YES"
        else:
            print "NO"
    except:
        pass
#temp