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 PYTHON3):

Solution:
import math
ax,ay,bx,by,cx,cy = map(int, input().strip().split(' '))
d1=((bx-ax)**2 + (by-ay)**2)
d2=((cx-bx)**2 + (cy-by)**2)
if bx!=ax:
    m1=(by-ay)/(bx-ax)
else:
    m1=12345
if cx!=bx:
    m2=(cy-by)/(cx-bx)
else:
    m2=12345
if d1==d2 and m1!=m2:
    print('yes')
else:
    print('no')