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 fractions import gcd

def dist(ax,ay,bx,by):
    return (ax-bx)**2 + (ay-by)**2

ax,ay,bx,by,cx,cy = map(int,raw_input().strip().split())
s1_num = by-ay
s1_den = bx-ax
while gcd(abs(s1_num),abs(s1_den))!=1:
    s1_num/=gcd(abs(s1_num),abs(s1_den))
    s1_den/=gcd(abs(s1_num),abs(s1_den))
s2_num = by-cy
s2_den = bx-cx
while gcd(abs(s2_num),abs(s2_den))!=1:
    s2_num/=gcd(abs(s2_num),abs(s2_den))
    s2_den/=gcd(abs(s2_num),abs(s2_den))
#print s1_num,s1_den,s2_num,s2_den
#print dist(ax,ay,bx,by),dist(bx,by,cx,cy)
if (s1_num*s2_den)!=(s2_num*s1_den) and dist(ax,ay,bx,by)==dist(bx,by,cx,cy):
    print "Yes"
else:
    print "No"