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 as mt 
import sys,string,bisect
input=sys.stdin.readline
from collections import deque,defaultdict
L=lambda : list(map(int,input().split()))
Ls=lambda : list(input().split())
M=lambda : map(int,input().split())
I=lambda :int(input())
def dist(x,y,c,d):
    return (x-c)**2+(y-d)**2
def circle(x1, y1, x2,y2, r1, r2): 
  
    distSq = (((x1 - x2)* (x1 - x2))+ ((y1 - y2)* (y1 - y2)))**(.5) 
  
    if (distSq + r2 <= r1): 
        return True
    else: 
        return False
a,b,c,d,e,f=M()
x=dist(a,b,c,d)
y=dist(c,d,e,f)
z=dist(e,f,a,b)
p=(c-a)*(f-b)-(d-b)*(e-a)
if(p==0):
    print("No")
else:
    if(x==y):
        print("Yes")
    else:
        print("No")