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 metrika(x1, y1, x2, y2):
    return (x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1)


def povorot(x1, y1, x2, y2, x3, y3):
    if (y2 - y1) * (x3 - x2) != (y3 - y2) * (x2 - x1) and metrika(x1, y1, x2, y2) == metrika(x2, y2, x3, y3):
        return "Yes"
    return "No"


X1, Y1, X2, Y2, X3, Y3 = [int(i) for i in input().split()]
print(povorot(X1, Y1, X2, Y2, X3, Y3))