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:
a=map(int,raw_input().split())

x1=a[0]
y1=a[1]
x2=a[2]
y2=a[3]
x3=a[4]
y3=a[5]

q=((a[0]-a[2])**2 + (a[1]-a[3])**2)
b=((a[0]-a[4])**2 + (a[1]-a[5])**2)
c=((a[4]-a[2])**2 + (a[3]-a[5])**2)
f=0
s=(y3-y2)*(x2-x1)
t=(y2-y1)*(x3-x2)
if s!=t and q==c:
    print "Yes"
else:
    print "No"