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:
def main():
    ax, ay, bx, by, cx, cy = tuple(map(int, input().split()))
    ab = (ax - bx)**2 + (ay - by)**2
    bc = (bx - cx)**2 + (by - cy)**2

    one_line = (bx - ax) * (cy - ay) == (by - ay) * (cx - ax) 

    if ab == bc and not one_line:
        print('Yes')
    else:
        print('No')

if __name__ == "__main__":
    main()