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:
l=raw_input().split()
a1,a2,b1,b2,c1,c2 = [int(x) for x in l]
d1 = (a1-b1)*(a1-b1) + (a2-b2) * (a2-b2)
d2 = (b1-c1)*(b1-c1) + (b2-c2) * (b2-c2)
area =  a1 * (b2 - c2) + b1 * (c2 - a2) + c1 * (a2 - b2)
if area != 0 and d1==d2:
	print "Yes"
else:
	print "No"