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:
from __future__ import division
from sys import stdin
from math import sqrt


def slop(a):
    try:
        return (a[0] - a[2]) / (a[1] - a[3])
    except:
        return float('inf')


rints = lambda: [int(x) for x in stdin.readline().split()]
euclidean = lambda x1, x2, y1, y2: pow(x1 - x2, 2) + pow(y1 - y2, 2)

ax, ay, bx, by, cx, cy = rints()
d1, d2 = euclidean(ax, bx, ay, by), euclidean(bx, cx, by, cy)
s1, s2 = slop([ax, ay, bx, by]), slop([bx, by, cx, cy])

# print(s1, s2, d1, d2)
if s1 == s2 or d1 != d2:
    print('no')
else:
    print('yes')