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 modulo(x1, y1, x2, y2):
    x = pow(x1-x2,2)
    y = pow(y1-y2,2)
    return (x+y)

row = input().split()
ax = int(row[0])
ay = int(row[1])
bx = int(row[2])
by = int(row[3])
cx = int(row[4])
cy = int(row[5])
AB = modulo(ax, ay, bx, by)
AC = modulo(ax, ay, cx, cy)
BC = modulo(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")