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:
ax,ay,bx,by,cx,cy = map(int,input().split())
if (ax-bx)*(ax-bx) + (ay-by)*(ay-by) == (bx-cx)*(bx-cx) + (by-cy)*(by-cy):
    if (ax==bx and bx==cx):
        print("NO")
    elif ax==bx or bx==cx:
        print("YES")
    elif (by-ay)/(bx-ax)*(cy-by)/(cx-bx)>=0 and abs((by-ay)/(bx-ax)-(cy-by)/(cx-bx))<pow(10,-13):
        print("NO")
    else:
        print("YES")
else:
    print("NO")