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(long, raw_input().split())

# if the point exists, it must be the intersection of three (chuizhipingfenxian)
# meanwhile, if a->b, b->c and a,b,c on a same circle, then |ab| = |bc|

len_ab = (bx - ax) * (bx - ax) + (by - ay) * (by - ay)
len_bc = (cx - bx) * (cx - bx) + (cy - by) * (cy - by)

# whether b is the middle point of ac
mid_point = False
if bx * 2 == ax + cx and by * 2 == ay + cy:
    mid_point = True

if len_ab == len_bc and not mid_point:
    print "Yes"
else:
    print "No"