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:
import sys
import math

lines = sys.stdin.read().splitlines()
ax, ay, bx, by, cx, cy = [int(x) for x in lines[0].split()]
def dist(p1x, p1y, p2x, p2y):
    return (p1x-p2x)**2+(p1y-p2y)**2 
dist1 = dist(ax, ay, bx, by)
dist2 = dist(bx, by, cx, cy)
if dist1 == dist2 and not ((ax-bx == bx-cx) and (ay-by == by-cy)) :
    print('Yes')
else:
    print('No')