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:
ax,ay,bx,by,cx,cy = [ int(x) for x in input().split() ]

if (ax - bx) * (ax - bx) + (ay - by) * (ay - by) == (cx - bx) * (cx - bx) + (cy - by) * (cy - by):
    if (ax == bx or bx == cx):
        if ax == cx:
            print("No")
        else:
            print("Yes")
    elif (ay - by) / (ax - bx) != (by - cy) / (bx - cx):
        print("Yes")
    else:
        print("No")
else:
    print("No")