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:
import math


def IsPossible(ax, ay, bx, by, cx, cy):
	if pow(bx-ax,2) + pow(by-ay,2) == pow(cx-bx,2) + pow(cy-by,2) and (by-ay)*(cx-bx) != (cy-by)*(bx-ax):		#ab and bc are of the same length and are not on the same line
		return 'Yes'
	else:
		return 'No'
	
	
ax, ay, bx, by, cx, cy = map(int, raw_input().split(' '))

print(IsPossible(ax, ay, bx, by, cx, cy))