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:
import decimal
D = decimal.Decimal
def main():
    l=map(long,raw_input().split())
    dist1=(D((l[2]-l[0])**2+(l[3]-l[1])**2)).sqrt()
    dist2=(D((l[4]-l[2])**2+(l[5]-l[3])**2)).sqrt()
    dist3=(D((l[4]-l[0])**2+(l[5]-l[1])**2)).sqrt()
    if dist1==dist2 and (dist1+dist2)>dist3:
        print "Yes"
    else:
        print "No"
main()