Problem Statement

You are given two sets S=${(a_1,b_1),(a_2,b_2),\ldots,(a_N,b_N)$} and T=${(c_1,d_1),(c_2,d_2),\ldots,(c_N,d_N)$} of N points each on a two-dimensional plane.
Determine whether it is possible to do the following operations on S any number of times (possibly zero) in any order so that S matches T.

• Choose a real number p\ $(0 \lt p \lt 360)$ and rotate every point in S p degrees clockwise about the origin.
• Choose real numbers q and r and move every point in S by q in the x-direction and by r in the y-direction. Here, q and r can be any real numbers, be it positive, negative, or zero.

Input

Input is given from Standard Input in the following format:
N
a_1 b_1
a_2 b_2
$\hspace{0.6cm}\vdots$
a_N b_N
c_1 d_1
c_2 d_2
$\hspace{0.6cm}\vdots$
c_N d_N

Output

If we can match S with T, print Yes; otherwise, print No.

Constraints

• $1 \leq N \leq 100$
• -$10 \leq a_i,b_i,c_i,d_i \leq 10$
• $(a_i,b_i) \neq (a_j,b_j)$ if $i \neq j$.
• $(c_i,d_i) \neq (c_j,d_j)$ if $i \neq j$.
• All values in input are integers.

Sample Input 1

3
0 0
0 1
1 0
2 0
3 0
3 1

Sample Output 1

Yes

The figure below shows the given sets of points, where the points in S and T are painted red and green, respectively:

In this case, we can match S with T as follows:

• Rotate every point in S 270 degrees clockwise about the origin.
• Move every point in S by 3 in the x-direction and by 0 in the y-direction.

Sample Input 2

3
1 0
1 1
3 0
-1 0
-1 1
-3 0

Sample Output 2

No

The figure below shows the given sets of points:

Although S and T are symmetric about the y-axis, we cannot match S with T by rotations and translations as stated in Problem Statement.

Sample Input 3

4
0 0
2 9
10 -2
-6 -7
0 0
2 9
10 -2
-6 -7

Sample Output 3

Yes

Sample Input 4

6
10 5
-9 3
1 -5
-6 -5
6 9
-9 0
-7 -10
-10 -5
5 4
9 0
0 -10
-10 -2

Sample Output 4

Yes

见题面 Input 部分

见题面 Output 部分