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 is given from Standard Input in the following format:

```
$N$
$a_1$ $b_1$
$a_2$ $b_2$
$\hspace{0.6cm}\vdots$
$a_N$ $b_N$
$c_1$ $d_1$
$c_2$ $d_2$
$\hspace{0.6cm}\vdots$
$c_N$ $d_N$
```

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

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

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:

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

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.