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:
import math
class p(object):
    def __init__(self,x,y):
        self.x=x
        self.y=y
def dist(a,b):
    return (a.x-b.x)**2 + (a.y-b.y)**2
def sq(a,b,c):
    return a.x*(b.y-c.y)+b.x*(c.y-a.y)+c.x*(a.y-b.y)
t=list(map(int,input().split()))
a=p(t[0],t[1])
b=p(t[2],t[3])
c=p(t[4],t[5])
if dist(a,b)!=dist(b,c) or sq(a,b,c)==0:
    print('NO')
else:print('YES')