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 JAVA):

Solution:
import java.util.*;
import java.io.*;
import java.lang.*;
public class Solution{
    static long calcDist(long a,long b,long c,long d){
        return ((c-a)*(c-a)+(d-b)*(d-b));
    }
    public static void main(String[] args){
        
    
    Scanner in = new Scanner(System.in); 
    long ax = in.nextLong();
    long ay = in.nextLong();
    long bx = in.nextLong();
    long by = in.nextLong();
    long cx = in.nextLong();
    long cy = in.nextLong();
    
    long distab = calcDist(ax,ay,bx,by);
    long distbc = calcDist(bx,by,cx,cy);
    long distac = calcDist(ax,ay,cx,cy);
    // float slopeab = (by-ay)/(bx-ax);
    // float slopebc = (cy-by)/(cx-bx);
    //determinant----> |A|=0
    // |ax ay 1|
    // |bx by 1|
    // |cx cy 1|
    if(ax*(by-cy)-ay*(bx-cx)+bx*cy-cx*by==0){
        System.out.println("No");
    }
    else if(distab!=distbc){System.out.println("No");}
     
    // else if((by-ay)*(cx-bx)==(cy-by)*(bx-ax)){
    //     System.out.println("No");
    // }
    
    else System.out.println("Yes");
    
    }
}