Problem: Arpa is taking a geometry exam. Here is the last problem of the exam.

You are given three points a, b, c.

Find a point and an angle such that if we rotate the page around the point by the angle, the new position of a is the same as the old position of b, and the new position of b is the same as the old position of c.

Arpa is doubting if the problem has a solution or not (i.e. if there exists a point and an angle satisfying the condition). Help Arpa determine if the question has a solution or not.

Input

The only line contains six integers ax, ay, bx, by, cx, cy (|ax|, |ay|, |bx|, |by|, |cx|, |cy| ≤ 109). It's guaranteed that the points are distinct.

Output

Print "Yes" if the problem has a solution, "No" otherwise.

You can print each letter in any case (upper or lower).

Examples

Input

0 1 1 1 1 0


Output

Yes


Input

1 1 0 0 1000 1000


Output

No

Note

In the first sample test, rotate the page around (0.5, 0.5) by <image>.

In the second sample test, you can't find any solution.

Solution (in PYTHON):

Solution:
import sys
import math

def readArray():return map(int,sys.stdin.readline().split())
def readString():return sys.stdin.readline().strip()
def readNum():return readString()
def exp(t,x):
   MOD=1000000007
   if(x==0):return 1
   if(x==1):return t
   if(x%2==1):return exp((t*t)%MOD,x/2)
def gcd(x,y):
   if x%y==0:return y
   else: return gcd(y,x%y)
def lcm(x,y):return x*(y/gcd(x,y))
def isprime(x):
   i=2
   while (i*i<=x):
      	if (x%i==0):return False
	i+=1
   return True

ax,ay,bx,by,cx,cy=readArray()

d1=(ax-bx)*(ax-bx)+(ay-by)*(ay-by)
d2=(cx-bx)*(cx-bx)+(cy-by)*(cy-by)

m1=((ay - by) * (ax - cx) == (ay - cy) * (ax - bx))
if (ax==bx and ax==cx and ay==by and ay==cy):
    print 'YES'
elif (d1==d2) and m1==False:
    print 'YES'
else:
    print 'NO'