Are They Similar Polygons? Task

Given the x,y coordinates (coordinates are guaranteed to be integers) of the vertices of two simple polygons in clockwise or anti-clockwise order. Output a Truthy value if both the polygons are similar otherwise a Falsy value

A simple polygon is a polygon that does not intersect itself and has no holes. That is, it is a flat shape consisting of straight, non-intersecting line segments or "sides" that are joined pairwise to form a single closed path. If the sides intersect then the polygon is not simple. Two edges meeting at a corner are required to form a an angle that is not not straight (180°)

Two polygons are similar if either polygon can be rescaled, repositioned, and reflected, so as to coincide precisely with the other polygon.

Testcases

Input

[(0, 0), (1, 0), (1, 1), (0, 1)]
[(-1, 0), (2, 1), (1, 4), (-2, 3)]


Graph

Output

Truthy




Input

[(2, 3), (0, 0), (4, 0)]
[(-3, 0), (-2, 2), (0, 1), (1, -1), (-1, -2), (-2, -2)]


Graph

Output

Falsy




Input

[(1, 4), (1, 3), (0, 2), (1, 1), (-3, 2)]
[(2, 0), (2, -1), (3, -1), (4, -2), (-2, -2)]


Graph

Output

Falsy




Input

[(-1, 0), (2, 1), (1, 4), (-2, 3)]
[(1, 4), (2, 1), (-1, 0), (-2, 3)]


Graph

Output

Truthy




Input

[(-2, 0), (-1, 1), (0, 1), (1, 3), (1, 0)]
[(5, 4), (4, 2), (3, 2), (2, 1), (5, 1)]


Graph

Output

Truthy




Input

[(2, 13), (4, 8), (2, 3), (0, 8)]
[(0, 0), (5, 0), (8, 4), (3, 4)]


Graph

Output

Falsy




Input

[(-1, 0), (-5, 3), (-5, 9), (-1, 6)]
[(0, 0), (5, 0), (8, 4), (3, 4)]


Graph

Output

Falsy




Input

[(0, 0), (1, 2), (1, 0)]
[(2, 0), (2, 2), (3, 0)]


Graph

Output

Truthy
Mathematica, 97 bytes (SBCS)



Or@@(Equal@@(a@u/#)&amp;/@(a/@NestList[RotateLeft,v,Length@v]))
a@l_:=Norm[#〚1〛-#〚2〛]&amp;/@l~Subsets~{2}


You can try it online!

The function a computes all the pairwise distances between any two vertices of the polygon. 

The main function applies this to the first list and to every rotation of the second list, to try and find the corresponding vertices. The rotation of the second list is correct if all the corresponding distances have been scaled accordingly.

Thanks to @J42161217 for saving me some 3 bytes