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:
a_1,a_2,b_1,b_2,c_1,c_2=map(int,input().split())
temp_1=((a_1-b_1)**2+(a_2-b_2)**2)
temp_2=((b_1-c_1)**2+(b_2-c_2)**2)
if( temp_1 != temp_2 ):
    print('No')
else:
    if(b_1-a_1==0 and c_1-a_1==0):
        print('No')
    elif(b_1-a_1==0 or c_1-a_1==0):
        print('Yes')
    else:
        slope_1=(b_2-a_2)/(b_1-a_1)
        slope_2=(c_2-a_2)/(c_1-a_1)
        if( slope_1 == slope_2):
            print('No')
        else:
            print('Yes')