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:
###modular exponentiation: a^n % M
#pow(a, n, M) 
### gcd: gcd(a, b)
#import fractions
#fractions.gcd(a, b)
### LCM (M, N)
#lcm = M*N/fractions.gcd(M, N)

def get_res(ax, ay, bx, by, cx, cy):
    ab2 = (ax-bx)**2 + (ay-by)**2
    bc2 = (bx-cx)**2 + (by-cy)**2
    ac2 = (ax-cx)**2 + (ay-cy)**2
    if bx-ax != 0:
        slope_ba = (by-ay)/float(bx-ax)
    else:
        slope_ba = 1000000000000
    if cx-bx != 0:
        slope_cb = (cy-by)/float(cx-bx)
    else:
        slope_cb = 1000000000000

    if ab2 == bc2 and slope_ba != slope_cb:
        return 'Yes'
    else:
        return 'No'

#N = int(raw_input())  
ax, ay, bx, by, cx, cy = [int(s) for s in raw_input().split(" ")]
result = get_res(ax, ay, bx, by, cx, cy)
print "{}".format(result)