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:
data = tuple(map(int, input().split()))

a = (data[0], data[1])
b = (data[2], data[3])
c = (data[4], data[5])

def d(a, b):
    dx = a[0] - b[0]
    dy = a[1] - b[1]
    return dx * dx + dy * dy

def v(a, b):
    return (b[0] - a[0], b[1] - a[1])

def m(a, b):
    return a[0] * b[1] - a[1] * b[0]

print("NO" if d(a, b) != d(b, c) or m(v(a, b), v(b, c)) == 0 else "YES")