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:
import math

def eucli(x1, x2, y1, y2):
  valor = (y1 - x1) ** 2 + (y2 - x2) ** 2
  #valor = math.sqrt(valor)
  return valor


entrada1 = (input())
vet=entrada1.split(" ")
a1 = int(vet[0])
a2 = int(vet[1])
b1 = int(vet[2])
b2 = int(vet[3])
c1 = int(vet[4])
c2 = int(vet[5])

poss = "No"

if eucli(a1, a2, b1, b2) == eucli(b1, b2, c1, c2):
  if (a1 + c1)/2 != b1 or (a2 + c2)/2 != b2:
    poss = "Yes"

print(poss)