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:
from sys import stdin
input = lambda :stdin.readline().strip()

a1, a2, b1, b2, c1, c2 = map(int, input().split())
dist = lambda x1,y1,x2,y2: (x1-x2)**2 + (y1-y2)**2
print(["NO", "YES"][a1 * b2 + b1 * c2 + c1 * a2 - a2*b1 - b2*c1 - c2 *a1 != 0 and dist(a1,a2,b1,b2) == dist(b1,b2,c1,c2)])