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 sys
import math

ax, ay, bx, by, cx, cy = [int(x) for x in sys.stdin.readline().strip().split(" ")]

def dist(ax, ay, bx, by):
  return (bx - ax) ** 2 + (by - ay) ** 2

def slope(ax, ay, bx, by):
  if(bx - ax == 0):
    return float("inf")
  return ((by - ay + 0.0) / (bx - ax))
  
def collinear(ax, ay, bx, by, cx, cy):
  if(slope(ax, ay, bx, by) == slope(bx, by, cx, cy)):
    return True
  else:
    return False
  
if(dist(ax, ay, bx, by) == dist(bx, by, cx, cy) and not collinear(ax, ay, bx, by, cx, cy)):
  print("yes")
else:
  print("no")