1class Egg:
  2    def __init__(self):
  3        self.painted_part = 0.0
  4        self.top_strength = 0.0
  5        self.bottom_strength = 0.0
  6        self.top_cracked = False
  7        self.bottom_cracked = False
  8        self.paint_jobs = []
  9        self.tournament = None
 10
 11    def paint(self, *args):
 12        total_percent_to_add = sum(p[1] for p in args)
 13        if self.painted_part + total_percent_to_add > 100.0:
 14            raise ValueError("Cannot overpaint the egg!")
 15        for p in args:
 16            color = p[0].upper()
 17            percent = p[1]
 18            red = int(color[:2], 16)
 19            green = int(color[2:4], 16)
 20            blue = int(color[4:], 16)
 21            paint_strength = red + green + blue
 22            
 23            if self.painted_part < 50.0:
 24                top_part = min(percent, 50.0 - self.painted_part)
 25                self.top_strength += top_part * paint_strength
 26                bottom_part = percent - top_part
 27                if bottom_part > 0:
 28                    self.bottom_strength += bottom_part * paint_strength
 29            else:
 30                self.bottom_strength += percent * paint_strength
 31                
 32            self.painted_part += percent
 33            self.paint_jobs.append((color, percent))
 34
 35    def __mul__(self, other):
 36        if self.top_cracked or other.top_cracked:
 37            raise TypeError("Cannot battle with a cracked top!")
 38        
 39        if self.top_strength > other.top_strength or (self.top_strength == other.top_strength and self.painted_part > other.painted_part):
 40            winner, loser = self, other
 41        else:
 42            winner, loser = other, self
 43            
 44        loser.top_cracked = True
 45        
 46        if self.tournament and other.tournament:
 47            self.tournament._record_battle(self, other, "top", winner)
 48            
 49        return winner
 50
 51    def __matmul__(self, other):
 52        if self.bottom_cracked or other.bottom_cracked:
 53            raise TypeError("Cannot battle with a cracked bottom!")
 54            
 55        if self.bottom_strength > other.bottom_strength or (self.bottom_strength == other.bottom_strength and self.painted_part > other.painted_part):
 56            winner, loser = self, other
 57        else:
 58            winner, loser = other, self
 59            
 60        loser.bottom_cracked = True
 61        
 62        if self.tournament and other.tournament:
 63            self.tournament._record_battle(self, other, "bottom", winner)
 64            
 65        return winner
 66
 67
 68class EggTournament:
 69    def __init__(self):
 70        self.eggs = {}
 71        self.victories = {}
 72        self.history = {}
 73
 74    def register(self, egg, name):
 75        if type(name) is not str or not name.isidentifier():
 76            raise ValueError("Invalid registration name")
 77        if name in self.eggs:
 78            raise ValueError(f"Egg with name {name} has already been registered")
 79        if egg.tournament is not None:
 80            raise ValueError("An egg cannot be registered in multiple tournaments")
 81            
 82        self.eggs[name] = egg
 83        self.victories[egg] = 0
 84        egg.tournament = self
 85
 86    def _record_battle(self, egg1, egg2, side, winner):
 87        key = (frozenset({egg1, egg2}), side)
 88        self.history[key] = winner
 89        self.victories[winner] += 1
 90
 91    def __getitem__(self, item):
 92        if isinstance(item, tuple):
 93            egg1, egg2, side = item
 94        elif isinstance(item, slice):
 95            egg1, egg2, side = item.start, item.stop, item.step
 96        else:
 97            raise KeyError()
 98            
 99        key = (frozenset({egg1, egg2}), side)
100        if key not in self.history:
101            raise KeyError()
102        return self.history[key]
103
104    def __rmatmul__(self, place):
105        sorted_wins = sorted(set(self.victories.values()), reverse=True)
106        if place < 1 or place > len(sorted_wins):
107            raise IndexError()
108        target_wins = sorted_wins[place - 1]
109        eggs_at_place = {egg for egg, wins in self.victories.items() if wins == target_wins}
110        return list(eggs_at_place)[0] if len(eggs_at_place) == 1 else eggs_at_place
111
112    def __getattr__(self, name):
113        if name not in self.eggs:
114            raise AttributeError("Apologies, there is no such egg registered")
115            
116        egg = self.eggs[name]
117        wins = self.victories[egg]
118        sorted_wins = sorted(set(self.victories.values()), reverse=True)
119        position = sorted_wins.index(wins) + 1
120        return {"position": position, "victories": wins}
121
122    def __contains__(self, egg):
123        return egg in self.victories