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:
from sys import stdin, stdout

def readline():
    return stdin.readline().rstrip()

def writeline(s):
    stdout.write(str(s)+"\n")

from math import atan2, isclose, inf, sqrt
from decimal import Decimal

ax, ay, bx, by, cx, cy = [int(x) for x in readline().split()]

def dist(p, q):
    return sum(Decimal(px - qx) ** Decimal(2.0) for px, qx in zip(p, q))

def slope(x1, y1, x2, y2):
    dy = y2 - y1
    dx = x2 - x1
    return dy / dx if dx != 0 else inf

line = isclose(slope(ax, ay, bx, by), slope(bx, by, cx, cy)) 
distance = dist((ax, ay), (bx, by)) == dist((bx, by), (cx, cy))
result = not line and distance
writeline("Yes" if result else "No")