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:
def helper():
	ax, ay, bx, by, cx, cy = map(int, raw_input().split())
	if abs(cal(ax, ay, bx, by) - cal(bx, by, cx, cy)) < 1e-5:
		if (ax == bx and bx == cx) or (ay == by and by == cy) or cal_k(ax, ay, bx, by, cx, cy):
			return False
		# print cal(ax, ay, bx, by) - cal(bx, by, cx, cy)
		return True
	else:
		return False

def cal(x1, y1, x2, y2):
	return (x2 - x1)**2 + (y2 - y1)**2

def cal_k(x1, y1, x2, y2, x3, y3):
	if (x3 - x2) * (y2 - y1) == (y3 - y2) * (x2 - x1):
		return True
	else:
		return False

if helper():
	print "Yes"
else:
	print "No"