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 PYTHON):

Solution:
def square_distance(x1, y1, x2, y2):
    return (x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2)

def co_line(x1, y1, x2, y2, x3, y3):
    if (x1 - x3) * (y2 - y3) - (x2 - x3) * (y1 - y3) == 0:
        return True
    else:
        return False

if __name__ == "__main__":
    ax, ay, bx, by, cx, cy = map(int, raw_input().split())
    dis_a_b = square_distance(ax, ay, bx, by)
    dis_b_c = square_distance(bx, by, cx, cy)
    if dis_a_b == dis_b_c and not co_line(ax, ay, bx, by, cx, cy):
        print 'Yes'
    else:
        print 'No'