#!/usr/bin/env python32
 
# from __future__ import division
from functools import lru_cache
 
def lose_condition(x):
  return x<1
 
def action_A(x):
  return x-1
 
def action_B(x):
  return x/2
 
ACTIONS = (action_A, action_B)
 
@lru_cache(maxsize=100)
def detect_winner(n, cond=lose_condition, actions=ACTIONS):
  if cond(n):
    return True
  return not all(detect_winner(action(n)) for action in actions)
 
if __name__ == '__main__':
 
  assert not detect_winner(1)
  assert not detect_winner(1.5)
  assert detect_winner(2)
  assert detect_winner(2.5)
  assert detect_winner(3)
  assert not detect_winner(4)
  assert detect_winner(5)
  assert not detect_winner(6)
  print("OK")
 

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