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:
V = list(map(int, input().split()))

P = []
for i in range(3):
	P.append((V[0], V[1]))
	V = V[2:]



A, B, C = P

for i in range(1, 3):
	x, y = P[i]
	x0, y0 = P[0]
	P[i] = x-x0, y-y0
a, b = P[1]
c, d = P[2]
 
if a*d - b*c == 0:
	print("NO")
	exit(0)

def dist(A, B):
	x = A[0] - B[0]
	y = A[1] - B[1]
	return x**2 + y**2


print("YES" if dist(A, B) == dist(B, C) else "NO")