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

inputedRow = input().split(" ")
ax = int(inputedRow[0])
bx = int(inputedRow[2])
cx = int(inputedRow[4])

ay = int(inputedRow[1])
by = int(inputedRow[3])
cy = int(inputedRow[5])

ab = dist(ax, ay, bx, by)
ac = dist(ax, ay, cx, cy)
bc = dist(bx, by, cx, cy)

if(((ax * (by - cy)) + (bx * (cy - ay)) + (cx * (ay - by)) != 0) and (ab == ac or ab == bc)):
    print("YES")
else:
    print("NO")