def problem465():
    """


    The kernel of a polygon is defined by the set of points from which the
       entire polygon's boundary is visible. We define a polar polygon as a
       polygon for which the origin is strictly contained inside its kernel.

       For this Problem, a polygon can have collinear consecutive vertices.
       However, a polygon still cannot have self-intersection and cannot have
       zero area.

       For example, only the first of the following is a polar polygon (the
       kernels of the second, third, and fourth do not strictly contain the
       origin, and the fifth does not have a kernel at all):

       Notice that the first polygon has three consecutive collinear vertices.

       Let P(n) be the number of polar polygons such that the vertices (x, y)
       have integer coordinates whose absolute values are not greater than n.

       Note that polygons should be counted as different if they have different
       set of edges, even if they enclose the same area. For example, the polygon
       with vertices [(0,0),(0,3),(1,1),(3,0)] is distinct from the polygon with
       vertices [(0,0),(0,3),(1,1),(3,0),(1,0)].

       For example, P(1) = 131, P(2) = 1648531, P(3) = 1099461296175 and P(343)
       mod 1 000 000 007 = 937293740.

       Find P(7^13) mod 1 000 000 007.
    """

    pass

def problem465():
    """


    The kernel of a polygon is defined by the set of points from which the
       entire polygon's boundary is visible. We define a polar polygon as a
       polygon for which the origin is strictly contained inside its kernel.

       For this Problem, a polygon can have collinear consecutive vertices.
       However, a polygon still cannot have self-intersection and cannot have
       zero area.

       For example, only the first of the following is a polar polygon (the
       kernels of the second, third, and fourth do not strictly contain the
       origin, and the fifth does not have a kernel at all):

       Notice that the first polygon has three consecutive collinear vertices.

       Let P(n) be the number of polar polygons such that the vertices (x, y)
       have integer coordinates whose absolute values are not greater than n.

       Note that polygons should be counted as different if they have different
       set of edges, even if they enclose the same area. For example, the polygon
       with vertices [(0,0),(0,3),(1,1),(3,0)] is distinct from the polygon with
       vertices [(0,0),(0,3),(1,1),(3,0),(1,0)].

       For example, P(1) = 131, P(2) = 1648531, P(3) = 1099461296175 and P(343)
       mod 1 000 000 007 = 937293740.

       Find P(7^13) mod 1 000 000 007.
    """

    pass

The kernel of a polygon is defined by the set of points from which the        entire polygon's boundary is visible. We define a polar polygon as a        polygon for which the origin is strictly contained inside its kernel.         For this Problem, a polygon can have collinear consecutive vertices.        However, a polygon still cannot have self-intersection and cannot have        zero area.         For example, only the first of the following is a polar polygon (the        kernels of the second, third, and fourth do not strictly contain the        origin, and the fifth does not have a kernel at all):         Notice that the first polygon has three consecutive collinear vertices.         Let P(n) be the number of polar polygons such that the vertices (x, y)        have integer coordinates whose absolute values are not greater than n.         Note that polygons should be counted as different if they have different        set of edges, even if they enclose the same area. For example, the polygon        with vertices [(0,0),(0,3),(1,1),(3,0)] is distinct from the polygon with        vertices [(0,0),(0,3),(1,1),(3,0),(1,0)].         For example, P(1) = 131, P(2) = 1648531, P(3) = 1099461296175 and P(343)        mod 1 000 000 007 = 937293740.         Find P(7^13) mod 1 000 000 007.