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:
def main():
    a1, a2, b1, b2, c1, c2 = map(int, input().split())

    ans = True

    if((a1 - b1) * (a2 - c2) - (a1 - c1) * (a2 - b2) == 0):
        ans = False
    ab = [(b1 - a1), (b2 - a2)]
    bc = [(b1 - c1), (b2 - c2)]
    mod1 = ab[0] ** 2 + ab[1] ** 2
    mod2 = bc[0] ** 2 + bc[1] ** 2

    if(mod1 != mod2):
        ans = False

    if(ans):
        print("Yes")
    else:
        print("No")
main()