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 math
x1,y1,x2,y2,x3,y3=map(int,raw_input().split())
def fun():
    x=0.5 * (x1 * (y2 - y3) + x2 * (y3 - y1) + x3 * (y1 - y2))
    if x==0:
        return False
    return True
def fun1(x1,y1,x2,y2):
    return ((x1-x2)**2+(y1-y2)**2)
if fun1(x1,y1,x2,y2)==fun1(x3,y3,x2,y2)and fun():
    print "Yes"
else:
    print "No"