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 sys import exit
from math import sqrt, acos, pi

class Vector2D:
    def __init__(self, x, y):
        self.x = x
        self.y = y

    def abs_sqr(self):
        return self.x ** 2 + self.y ** 2

    def dot(self, other):
        return self.x * other.x + self.y * other.y

    def __sub__(self, other):
        return Vector2D(self.x - other.x, self.y - other.y)

ax, ay, bx, by, cx, cy = map(int, raw_input().split(' '))

a = Vector2D(ax, ay)
b = Vector2D(bx, by)
c = Vector2D(cx, cy)

ab = b - a
bc = c - b

if ab.abs_sqr() == bc.abs_sqr() and ab.dot(bc) ** 2 != ab.abs_sqr() * bc.abs_sqr():
    print "Yes"
else:
    print "No"