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:
def read_ints():
	return [int(i) for i in input().split()]

coords = read_ints()
a, b, c = [(coords[i], coords[i + 1]) for i in range(0, len(coords), 2)]
def length_sqr(a, b):
	return (a[0] - b[0]) ** 2 + (a[1] - b[1]) ** 2

if length_sqr(a, b) != length_sqr(b, c):
	print('No')
elif (c[0] - b[0]) * (b[1] - a[1]) == (c[1] - b[1]) * (b[0] - a[0]):
	print('No')
else:
	print('Yes')