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 PYTHON3):

Solution:
class pp:
     x = 0
     y = 0

def ort(a,b):
    c=pp()
    c.x=a.y-b.y
    c.y=b.x-a.x
    return c

def len(a,b):
    return (a.x-b.x)**2+(a.y-b.y)**2



a=pp()
b=pp()
c=pp()

a.x,a.y,b.x,b.y,c.x,c.y=map(int,input().split())

d=ort(a,b)
r=ort(b,c)



if(d.x*r.y==d.y*r.x or len(a,b)!=len(b,c)):
    print("No")
else:
    print("Yes")