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:
from sys import stdin
def dis(x1,y1,x2,y2):
 return (x1-x2)**2 + (y1-y2)**2
x1,y1,x2,y2,x3,y3 = map(int,stdin.readline().split())
s = set()
a=dis(x1,y1,x2,y2)
b=dis(x3,y3,x2,y2)
if a==b and (x1*(y2-y3) + x2*(y3-y1) + x3*(y1-y2))!=0:
 print 'Yes'
else:
 print 'No'