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

ab_ = list(map(int, sys.stdin.readline().split()))

ab = (ab_[3] - ab_[1])**2 + (ab_[2] - ab_[0])**2
bc = (ab_[5] - ab_[3])**2 + (ab_[4] - ab_[2])**2
ca = (ab_[5] - ab_[1])**2 + (ab_[4] - ab_[0])**2

aa = math.sqrt(ab)
bb = math.sqrt(bc)
cc = math.sqrt(ca)

if ab == bc and (ab_[4] - ab_[0]) * (ab_[3] - ab_[1]) != (ab_[5] - ab_[1]) * (ab_[2] - ab_[0]):
    print("Yes")

else:
    print("No")