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:
import math

e = 10 ** -6 
def getline(x1, y1, x2, y2):
    k = float(y2 - y1) / float(x2 - x1)
    b = y1 - k * x1
    return k, b

def f():
    res = "No"
    x1, y1, x2, y2, x3, y3 = list(map(int, raw_input().split()))
    if x1 == x2 == x3:
        res = "No"
        print(res)
        return 0
    if x1 != x2:
        k, b = getline(x1, y1, x2, y2)
        if abs(y3 - k * x3 - b) < e:
            res = "No"
            print(res)
            return 0
        
    d1 = abs(x1 - x2) ** 2 + abs(y1 - y2) ** 2
    d2 = abs(x2 - x3) ** 2 + abs(y2 - y3) ** 2
    if d1 - d2 == 0:
        res = "Yes"
        print(res)
        return 0
    print(res)
f()