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:
from math import gcd
ax,ay,bx,by,cx,cy = map(int, input().split())
def slope(x1,y1,x2,y2):
	dx = x2 - x1
	dy = y2 - y1
	g = gcd(dx,dy)
	dx /= g
	dy /= g
	return (dx,dy)
def dis(x1,y1,x2,y2):
	return (x1 - x2)**2 + (y1 - y2)**2
def collinear(x1,y1,x2,y2,x3,y3):
	return slope(x1,y1,x2,y2) == slope(x2,y2,x3,y3) 
print('Yes' if dis(ax,ay,bx,by) == dis(bx,by,cx,cy) and not collinear(ax,ay,bx,by,cx,cy) else 'No')