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 dist(x1,y1,x2,y2):
    d=(x1-x2)*(x1-x2)+(y1-y2)*(y1-y2)
    return d
ax,ay,bx,by,cx,cy=input().strip().split(' ')
ax,ay,bx,by,cx,cy=[int(ax),int(ay),int(bx),int(by),int(cx),int(cy)]
if((abs((ax-bx)*(cy-by)-(cx-bx)*(ay-by))!=0) and (dist(ax,ay,bx,by)==dist(bx,by,cx,cy))):
    print('Yes')
else:
    print('No')