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:
b=[i for i in map(int, input().split())]

a=[b[:2],b[2:4],b[4:]]

def slope(a,b):
    try:
        return (a[1]-b[1])/(a[0]-b[0])
    except:
        return None

def l(a,b):
    return (a[0]-b[0])**2+(a[1]-b[1])**2

if l(a[0],a[1])==l(a[1],a[2]) and slope(a[0],a[1])!= slope(a[1],a[2]):
    print("Yes")
else:
    print("No")