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 PYTHON):

Solution:
from math import *
from decimal import *
getcontext().prec = 20

def mp():
    return map(int,str(raw_input()).split())

mod=10**9+7

a,b,c,d,e,f=mp()
a,b,c,d,e,f=Decimal(a),Decimal(b),Decimal(c),Decimal(d),Decimal(e),Decimal(f)
#print (d-b)*(e-c),(f-d)*(c-a),(c-a)**2+(d-b)**2,(e-c)**2+(f-d)**2
if (d-b)*(e-c)!=(f-d)*(c-a) and (c-a)**2+(d-b)**2==(e-c)**2+(f-d)**2:
    print "Yes"
else:
    print "No"