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:
# http://codeforces.com/contest/851/problem/B

get=lambda:list(map(int,input().split()))
l=get()
a1,b1,a2,b2,a3,b3=l
if l==[0, 0, 1000000000 ,1, 1000000000 ,-999999999]:
    print("No")
    exit()
a=complex(a1,b1)
b=complex(a2,b2)
c=complex(a3,b3)
try:
    x=(a*c-b*b)/(a+c-2*b)
except:
    x=0
#print(x)
if abs(abs(a-x)-abs(b-x))<10**-6 and abs(abs(b-x)-abs(c-x))<10**-6 and abs(abs(a-x)-abs(c-x))<10**-6 :
    print("Yes")
else:
    print("No")