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:
entrada = list(map(int, input().split(" ")))
x = [entrada[0], entrada[2], entrada[4]]
y = [entrada[1], entrada[3], entrada[5]]


def colinear():
    ux = x[1] - x[0]
    uy = y[1] - y[0]
    vx = x[2] - x[1]
    vy = y[2] - y[1]
    return (ux * vy - uy * vx) == 0


def sq2(i, j):
    dx = x[i] - x[j]
    dy = y[i] - y[j]
    return dx ** 2 + dy ** 2


if colinear():
    print("No")
elif sq2(0, 1) == sq2(1, 2):
    print("YES")
else:
    print("NO")