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:


from math import fabs


EPS = 10 ** -6

def equal(a, b):
    return fabs(a - b) < EPS


def dist_sq(ax, ay, bx, by):
    return (ax - bx) * (ax - bx) + (ay - by) * (ay - by)


def triangle_area(ax, ay, bx, by, cx, cy):
    return ax * (by - cy) + bx * (cy - ay) + cx * (ay - by)


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

    if (equal(dist_sq(ax, ay, bx, by), dist_sq(bx, by, cx, cy)) and
        not equal(triangle_area(ax, ay, bx, by, cx, cy), 0.0)):
            print("Yes")
    else:
        print("No")


if __name__ == "__main__":
    main()