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:
str=raw_input()
a=str.split()

def len(xx1,yy1,x2,y2):
    return (y2 - yy1) * (y2 - yy1) + (x2 - xx1) * (x2 - xx1)

for x in xrange(0,6):
    a[x]=int(a[x])
if(len(a[0],a[1],a[2],a[3])==len(a[2],a[3],a[4],a[5]) and ((a[5]-a[3])*(a[2]-a[0])!=(a[4]-a[2])*(a[3]-a[1]))):
    print 'Yes'
else:
    print 'No'