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 PYTHON3):

Solution:
s = [int(x) for x in input().split()]
a, b, c = s[:2], s[2:4], s[4:]

def sqdist(a, b):
    return (b[0] - a[0])**2 + (b[1] - a[1])**2
def same_line(a, b, c):
    return (b[1] - a[1]) * (c[0] - a[0]) == (c[1] - a[1]) * (b[0] - a[0])
print('Yes' if sqdist(a, b) == sqdist(b, c) and not same_line(a, b, c) else 'No')