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:
import math
a0,a1,b0,b1,c0,c1=map(int,input().split())
try:
    slope1=(c1-a1)/(c0-a0)
except:
    slope1=math.inf
try:
    slope2=(b1-a1)/(b0-a0)
except:
    slope2=math.inf
if((b0-c0)**2+(b1-c1)**2==(a0-b0)**2+(a1-b1)**2 and slope1!=slope2):
    print('Yes')
else:
    print('No')