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


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

ba = [ax - bx, ay - by]
bc = [cx - bx, cy - by]

ba_mul_bc = (ba[0] * bc[0] + ba[1] * bc[1]) ** 2
ba_dist = ba[0] ** 2 + ba[1] ** 2
bc_dist = bc[0] ** 2 + bc[1] ** 2

dist_ab = (ax - bx) ** 2 + (ay - by) ** 2
dist_bc = (bx - cx) ** 2 + (by - cy) ** 2
#print(ba_mul_bc, ba_dist, bc_dist)
if dist_ab == dist_bc and ba_mul_bc != ba_dist*bc_dist and ba_mul_bc + ba_dist*bc_dist != 0:
    print("Yes")
else:
    print("No")