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 PYTHON):

Solution:
from __future__ import print_function

from fractions import Fraction
from math import atan2

def get_array(typ = int):
    return [typ(w) for w in raw_input().split()]

ax, ay, bx, by, cx, cy = get_array()

d1 = (ax - bx) ** 2 + (ay - by) ** 2
d2 = (bx - cx) ** 2 + (by - cy) ** 2
d3 = (cx - ax) ** 2 + (cy - ay) ** 2

s1 = (ax - bx) * (by - cy)
s2 = (bx - cx) * (ay - by)

if d1 == d2 and s1 != s2:
    print("Yes")
else:
    print("No")