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:
# _*_ coding:utf-8 _*_
import math
a1,a2,b1,b2,c1,c2 = [int(i) for i in raw_input().split()]
if a1 == b1 and a1 == c1: #横轴和纵轴
    print ('NO')
elif a2 == b2 and a2 ==c2:
    print ('NO')
else:
    d12 = math.sqrt(math.pow(b2-a2,2)+math.pow(b1-a1,2))
    if d12>10000000:
        d12 = abs(b2-a2)+abs(b1-a1)
    d13 = math.sqrt(math.pow(a2-c2,2)+math.pow(a1-c1,2))
    if d13>10000000:
        d13 = abs(c2-a2)+abs(c1-a1)
    d23 = math.sqrt(math.pow(c2-b2,2)+math.pow(c1-b1,2))
    if d23>10000000:
        d23 = abs(c2-b2)+abs(c1-b1)

    if b2==float((a2+c2)/2) and b1 == float((a1+c1)/2):
        print ('NO')
    elif d12==d23 and d13<=(d12+d23) and d13>0:
        print ('YES')
    else:
        print ('NO')