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:
a1,a2,b1,b2,c1,c2=[int(i) for i in input().split()]
if( (b2-a2)**2+(b1-a1)**2 ==(c2-b2)**2 +(c1-b1)**2):
    if(not (b1-a1)):
        if(b1-c1):
            print("Yes")
        else:
            print("No")
    elif(not (b1-c1)):
        print("Yes")
    elif((b2-a2)/(b1-a1) != (b2-c2)/(b1-c1)):
        print("Yes")
    else:
        print("No")
else:
    print("No")