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:
x = input()
#a=x.split()
#print(b[0],b[1],b[2])
a = [int(k) for k in x.split()]
flag=1
dist = (a[2]-a[0])*(a[2]-a[0])+(a[3]-a[1])*(a[3]-a[1])
dist1 = (a[5]-a[3])*(a[5]-a[3])+(a[4]-a[2])*(a[4]-a[2])
s1 = (a[3]-a[1])*(a[4]-a[2])
s2 = (a[5]-a[3])*(a[2]-a[0])
if(s1==s2):
    flag=0
if(flag==1 and dist==dist1):
    print("Yes")
else:
    print("No")