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:
# -*- coding: utf-8 -*-

import math
import collections
import bisect
import heapq
import time
import random
import itertools

"""
created by shhuan at 2017/10/19 17:24

"""

ax, ay, bx, by, cx, cy = map(int, input().split())

#(x2-x1)×(y3-y2)=(x3-x2)×(y2-y1)

if (bx-ax)*(cy-by) == (cx-bx)*(by-ay) or (by-ay)**2+(bx-ax)**2 != (cy-by)**2+(cx-bx)**2:
    print('No')
else:
    print('Yes')