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 slope(i,j):
    try:
        return float(j[1]-i[1])/float(j[0]-i[0])
    except:
        return -200
def len(i,j):
    return (j[1]-i[1])**2 +(i[0]-j[0])**2
ax,ay,bx,by,cx,cy=map(int,raw_input().split())
a=(ax,ay)
b=(bx,by)
c=(cx,cy)
if slope(a,b)==slope(b,c):
    print 'No'
else:
    x=len(a,b)
    y=len(b,c)
    z=len(c,a)
    



    if x==y:
        print 'Yes'
    else:
        print 'No'