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 math 
import sys
import decimal
decimal.getcontext().prec = 100

ax, ay, bx, by, cx, cy = list(map(decimal.Decimal, input().split()))

absq = (ax - bx) ** decimal.Decimal(2) + (ay - by) ** decimal.Decimal(2)
bcsq = (bx - cx) ** decimal.Decimal(2) + (by - cy) ** decimal.Decimal(2)
acsq = (ax - cx) ** decimal.Decimal(2) + (ay - cy) ** decimal.Decimal(2)

on_one_line = False
# print(absq, bcsq, acsq)
lengths = sorted([absq ** decimal.Decimal(.5), bcsq ** decimal.Decimal(.5), acsq ** decimal.Decimal(.5)])
# print(lengths)
if lengths[0] + lengths[1] - lengths[2] < sys.float_info.epsilon:# 0.0000000000000000000000000000000000001:
	on_one_line = True

if absq == bcsq and not on_one_line:
	print("Yes")
else:
	print("No")