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:
ax,ay,bx,by,cx,cy=map(int,raw_input().split())
k=pow(cx-bx,2)+pow(cy-by,2)
k2=pow(by-ay,2)+pow(bx-ax,2)

if cx!=bx:
    t=float(cy-by)/(cx-bx)
else:
    t=10000000001
if bx!=ax:
    t2=float(by-ay)/(bx-ax)
else:
    t2=10000000001
print "Yes" if k==k2 and t!=t2 else "No"