At a geometry lesson Gerald was given a task: to get vector B out of vector A. Besides, the teacher permitted him to perform the following operations with vector А:

  * Turn the vector by 90 degrees clockwise.
  * Add to the vector a certain vector C.



Operations could be performed in any order any number of times.

Can Gerald cope with the task?

Input

The first line contains integers x1 и y1 — the coordinates of the vector A ( - 108 ≤ x1, y1 ≤ 108). The second and the third line contain in the similar manner vectors B and C (their coordinates are integers; their absolute value does not exceed 108).

Output

Print "YES" (without the quotes) if it is possible to get vector B using the given operations. Otherwise print "NO" (without the quotes).

Examples

Input

0 0
1 1
0 1


Output

YES


Input

0 0
1 1
1 1


Output

YES


Input

0 0
1 1
2 2


Output

NO
//package DIV_79;

import java.util.Scanner;

public class E {
private static long x1;
private static long y1;
private static long x2;
private static long y2;
private static long x3;
private static long y3;

public static void main(String[] args) {
	 Scanner sc=new Scanner(System.in);
	  x1=sc.nextLong();
	  y1=sc.nextLong();
	  x2=sc.nextLong();
	  y2=sc.nextLong();
	  x3=sc.nextLong();
	  y3=sc.nextLong();
	  if(check(x1,y1)||check(-x1,-y1) || check(-y1,x1) || check(y1,-x1) )
			System.out.println("YES");else System.out.println("NO");
	
}
public static boolean check(long x,long y){
	long xx = x3*x3+y3*y3, tx= x2+x,ty = y2+y;
	if(xx==0)return x==x2 && y==y2;
	long ret1= tx*x3+ty*y3, ret2 = tx*y3-ty*x3;
	if(ret1%xx !=0 || ret2%xx !=0 )return false;
	return true;
}
}
