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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def face_to_vertex_color(mesh, face_colors, dtype=np.uint8):
 """ Convert a list of face colors into a list of vertex colors. Parameters mesh : trimesh.Trimesh object face_colors: (n, (3,4)) int, face colors dtype: data type of output Returns vertex_colors: (m,4) dtype, colors for each vertex """

    rgba = to_rgba(face_colors)
    vertex_colors = mesh.faces_sparse.dot(
        rgba.astype(np.float64))
    vertex_colors /= mesh.faces_sparse.sum(axis=1)
    vertex_colors = vertex_colors.astype(dtype)

    return vertex_colors