#!/usr/bin/env python import itertools import sys from collections.abc import Iterator from typing import NamedTuple class Point(NamedTuple): x: int y: int def neighbours(self) -> Iterator["Point"]: for dx, dy in itertools.product((-1, 0, 1), repeat=2): if dx == 0 and dy == 0: continue yield Point(self.x + dx, self.y + dy) def solve(input: str) -> int: def spiral() -> Iterator[Point]: yield Point(0, 0) for dist in itertools.count(1): side = dist * 2 + 1 for start, dx, dy in ( (Point(dist, -dist), 0, 1), (Point(dist, dist), -1, 0), (Point(-dist, dist), 0, -1), (Point(-dist, -dist), 1, 0), ): # We need a non-zero step for `range`, and to make it inclusive stepx = dx if dx != 0 else 1 stepy = dy if dy != 0 else 1 # Don't include the corner, which was already output in previous loop # Hence, `side - 1` points in the range xs = range(start.x + dx, start.x + (side - 1) * dx + stepx, stepx) ys = range(start.y + dy, start.y + (side - 1) * dy + stepy, stepy) yield from (Point(x, y) for x, y in itertools.product(xs, ys)) target = int(input) values = {Point(0, 0): 1} # Skip the origin, which we already know for p in itertools.islice(spiral(), 1, None): if (res := sum(values.get(n, 0) for n in p.neighbours())) > target: return res values[p] = res assert False # Sanity check def main() -> None: input = sys.stdin.read() print(solve(input)) if __name__ == "__main__": main()