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:
#!/usr/bin/env python


def dist_2(x1, x2,y1, y2):
    return (x1 - y1) ** 2 + (x2-y2)**2
def outer_prod(x1,x2,y1,y2):
    return x1 * y2 - x2 * y1
def main():
    a1, a2, b1, b2, c1, c2 = map(int, input().split())
    cond1 = dist_2(a1, a2, b1, b2) == dist_2(b1,b2,c1,c2)
    cond2 = outer_prod(a1-b1, a2-b2, c1-b1, c2-b2) != 0
    if cond1 and cond2:
        print("YES")
    else:
        print("NO")

main()