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 sys
#sys.stdin = open('input.txt', 'r')
#sys.stdout = open('output.txt','w')
def fun(x1,y1,c1,x2,y2,c2) :
    tmp1, tmp2 = x2*y1-x1*y2, y2*x1-y1*x2
    if tmp1 !=0 and tmp2 != 0 :
        return True
    return False

a1,a2,b1,b2,c1,c2 = map(int, sys.stdin.readline().strip().split(' '))
if (a1-b1)**2 + (a2-b2)**2 == (b1-c1)**2 + (b2-c2)**2  and fun(-2*a1+2*b1,-2*a2+2*b2, b1**2+b2**2-a1**2-a2**2, -2*b1+2*c1, -2*b2+2*c2,c1**2+c2**2-b1**2-b2**2 ):
    print 'Yes'
else :
    print 'No'