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 solve():
	x1,y1,x2,y2,x3,y3 = map(int,input().split());
	a = [x1,y1];
	b = [x2,y2];
	c = [x3,y3];
	if(x1-x2>=0):
		angular1 = (y1-y2)/((x1-x2)+0.000001);
	elif(x1-x2<0):
		angular1 = (y1-y2)/((x1-x2)-0.000001);
	if(x2-x3>=0):
		angular2 = (y2-y3)/((x2-x3)+0.000001);
	elif(x2-x3<0):
		angular2 = (y2-y3)/((x2-x3)-0.000001);
	#print(angular1,angular2);
	res = False;
	alinhado = False;
	if angular1==angular2:
		alinhado = True;
	dAB = (a[0]-b[0])**2 + (a[1]-b[1])**2
	dAC = (a[0]-c[0])**2 + (a[1]-c[1])**2
	dBC = (c[0]-b[0])**2 + (c[1]-b[1])**2
	if(dAB==dBC):
		res = True;
	if(res and not alinhado):
		print("Yes")
	else:
		print("No")
solve()