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:
ax,ay,bx,by,cx,cy=map(float,input().split())

A=ax*ax+ay*ay
B=bx*bx+by*by
C=cx*cx+cy*cy
G=(cy-by)*ax+(ay-cy)*bx+(by-ay)*cx

try:
    x=( (B-C)*ay+(C-A)*by+(A-B)*cy )/(2*G)
    y=( (C-B)*ax+(A-C)*bx+(B-A)*cx )/(2*G)
except:
    print('No')
    exit()

if (ax-x)*(bx-x)+(ay-y)*(by-y) == (bx-x)*(cx-x)+(by-y)*(cy-y):
    print('Yes')
else:
    print('No')