algorithms/genetic/common.py

@@ -1,4 +1,7 @@
 from dataclasses import dataclass
+
+import numpy as np
+
 from const import *
 from typing import List, Dict, Tuple
 
@@ -11,6 +14,56 @@ class Position:
     col: int
 
 
+@dataclass
+class Area:
+    position: Position
+    width: int
+    height: int
+
+
+AREAS_TO_CROSS = [
+    # up above left knights spawn
+    Area(position=Position(row=0, col=0),
+         width=KNIGHTS_SPAWN_WIDTH,
+         height=LEFT_KNIGHTS_SPAWN_FIRST_ROW),
+
+    # down below left knights spawn
+    Area(position=Position(row=LEFT_KNIGHTS_SPAWN_FIRST_ROW + KNIGHTS_SPAWN_HEIGHT, col=0),
+         width=KNIGHTS_SPAWN_WIDTH,
+         height=ROWS - LEFT_KNIGHTS_SPAWN_FIRST_ROW - KNIGHTS_SPAWN_HEIGHT),
+
+    # between left knights spawn and castle
+    Area(position=Position(row=0, col=KNIGHTS_SPAWN_WIDTH),
+         width=CASTLE_SPAWN_FIRST_COL - KNIGHTS_SPAWN_WIDTH,
+         height=ROWS),
+
+    # up above castle
+    Area(position=Position(row=0, col=CASTLE_SPAWN_FIRST_COL),
+         width=2,
+         height=CASTLE_SPAWN_FIRST_ROW),
+
+    # down below castle
+    Area(position=Position(row=CASTLE_SPAWN_FIRST_ROW + 2, col=CASTLE_SPAWN_FIRST_COL),
+         width=2,
+         height=ROWS - CASTLE_SPAWN_FIRST_ROW - 2),
+
+    # between castle and right knights spawn
+    Area(position=Position(row=0, col=CASTLE_SPAWN_FIRST_COL + 2),
+         width=RIGHT_KNIGHTS_SPAWN_FIRST_COL - CASTLE_SPAWN_FIRST_COL - 2,
+         height=ROWS),
+
+    # up above right knights spawn
+    Area(position=Position(row=0, col=RIGHT_KNIGHTS_SPAWN_FIRST_COL),
+         width=KNIGHTS_SPAWN_WIDTH,
+         height=RIGHT_KNIGHTS_SPAWN_FIRST_ROW),
+
+    # down below right knights spawn
+    Area(position=Position(row=RIGHT_KNIGHTS_SPAWN_FIRST_ROW + KNIGHTS_SPAWN_HEIGHT, col=RIGHT_KNIGHTS_SPAWN_FIRST_COL),
+         width=KNIGHTS_SPAWN_WIDTH,
+         height=ROWS - RIGHT_KNIGHTS_SPAWN_FIRST_ROW - KNIGHTS_SPAWN_HEIGHT),
+]
+
+
 def dfs(grid: npt.NDArray, visited: Dict[Tuple[int, int], bool], position: Position, rows: int, cols: int) -> None:
     visited[(position.row, position.col)] = True
 
@@ -51,3 +104,19 @@ def get_islands(grid: npt.NDArray, positions: List[Position], rows: int = ROWS,
             islands += 1
 
     return roots
+
+
+def find_neighbours(grid: npt.NDArray, col: int, row: int) -> List[Position]:
+    dr = [-1, 1, 0, 0]
+    dc = [0, 0, -1, 1]
+
+    neighbours = []
+
+    for i in range(4):
+        rr = row + dr[i]
+        cc = col + dc[i]
+
+        if 0 <= rr < ROWS and 0 <= cc < COLUMNS and grid[rr][cc] == MAP_ALIASES.get('GRASS'):
+            neighbours.append(Position(row=rr, col=cc))
+
+    return neighbours

algorithms/genetic/const.py

@@ -13,6 +13,8 @@ LEFT_KNIGHTS_SPAWN_FIRST_ROW = 6
 LEFT_KNIGHTS_SPAWN_FIRST_COL = 0
 RIGHT_KNIGHTS_SPAWN_FIRST_ROW = 6
 RIGHT_KNIGHTS_SPAWN_FIRST_COL = 20
+CASTLE_SPAWN_FIRST_ROW = 7
+CASTLE_SPAWN_FIRST_COL = 11
 
 # map aliases
 MAP_ALIASES = {
@@ -24,4 +26,4 @@ MAP_ALIASES = {
     "CASTLE": 5,
     "KNIGHT_RED": 6,
     "KNIGHT_BLUE": 7,
-}
+}

algorithms/genetic/genome.py

@@ -1,10 +1,13 @@
+import math
+import random
+from copy import deepcopy
 from random import randrange
 from typing import List
 
 import numpy as np
 import numpy.typing as npt
 
-from common import Position
+from common import Position, get_islands, AREAS_TO_CROSS, find_neighbours
 from const import *
 
 
@@ -16,11 +19,15 @@ class Genome:
     trees: List[Position]
     sands: List[Position]
     monsters: List[Position]
+    fitness: int
+    sand_islands: List[Position]
+    tree_islands: List[Position]
+    water_islands: List[Position]
 
     def __init__(self):
         self.grid = np.zeros((ROWS, COLUMNS), dtype=int)
+        self.fitness = 0
 
-        # todo: spawning castle, monsters, sand, trees in the same way as bellow
         self.knights_red = spawn_objects_in_given_area(
             grid=self.grid,
             object_alias=MAP_ALIASES.get("KNIGHT_RED"),
@@ -43,7 +50,7 @@ class Genome:
             grid=self.grid,
             object_alias=MAP_ALIASES.get("CASTLE"),
             objects_count=4,
-            spawn_position_start=Position(row=7, col=9),
+            spawn_position_start=Position(row=CASTLE_SPAWN_FIRST_ROW, col=CASTLE_SPAWN_FIRST_COL),
             width=2,
             height=2
         )
@@ -57,6 +64,62 @@ class Genome:
         self.monsters = spawn_objects_in_given_area(grid=self.grid, object_alias=MAP_ALIASES.get("MONSTER"),
                                                     objects_count=MONSTERS_COUNT)
 
+        self.sand_islands = get_islands(self.grid, self.sands)
+        self.tree_islands = get_islands(self.grid, self.trees)
+        self.water_islands = get_islands(self.grid, self.waters)
+
+    def calc_fitness(self):
+        score = SAND_COUNT + TREE_COUNT + WATER_COUNT
+        score = score - len(self.sand_islands) - len(self.tree_islands) - len(self.water_islands)
+
+        # todo: odległość manhattan od każdej wyspy
+
+        self.fitness = score
+
+    def crossover(self, partner):
+        # replace a randomly selected part of the grid with partner's part
+        child = Genome()
+        child.grid = deepcopy(self.grid)
+        area_to_cross = random.choice(AREAS_TO_CROSS)
+
+        for row in range(area_to_cross.position.row, area_to_cross.position.row + area_to_cross.height):
+            for col in range(area_to_cross.position.col, area_to_cross.position.col + area_to_cross.width):
+                child.grid[row][col] = partner.grid[row][col]
+
+        child.sand_islands = get_islands(self.grid, self.sands)
+        child.tree_islands = get_islands(self.grid, self.trees)
+        child.water_islands = get_islands(self.grid, self.waters)
+
+        return child
+
+    def mutate(self, mutation_rate: float):
+        # remove 1 item from a random island and add a neighbor to another island
+        if random.random() < mutation_rate:
+
+            # select islands of the same, random type
+            islands_of_same_type = random.choice([self.sand_islands, self.tree_islands, self.water_islands])
+            random_index = random.randint(0, len(islands_of_same_type) - 1)
+            island = islands_of_same_type[random_index]
+            next_island = islands_of_same_type[(random_index + 1) % len(islands_of_same_type)]
+
+            free_tiles_nearby = find_neighbours(self.grid, next_island.col, next_island.row)
+
+            tile_type = self.grid[island.row][island.col]
+
+            self.grid[island.row][island.col] = MAP_ALIASES.get('GRASS')
+            islands_of_same_type.remove(island)
+
+            # todo: if there are no free tiles around then randomize another next_island
+            if len(free_tiles_nearby) > 0:
+                random_free_tile = random.choice(free_tiles_nearby)
+                island.row = random_free_tile.row
+                island.col = random_free_tile.col
+                self.grid[island.row][island.col] = tile_type
+
+                self.sand_islands = get_islands(self.grid, self.sands)
+                self.tree_islands = get_islands(self.grid, self.trees)
+                self.water_islands = get_islands(self.grid, self.waters)
+
 
 def is_empty(grid: npt.NDArray, position: Position) -> bool:
     return grid[position.row, position.col] in [MAP_ALIASES.get("GRASS"), MAP_ALIASES.get("SAND")]

algorithms/genetic/map_generator.py

@@ -1,16 +1,25 @@
-from map_importer_exporter import export_map
+from algorithms.genetic.genome import Genome
-from genome import Genome
+from algorithms.genetic.map_importer_exporter import export_map
-from common import get_islands
+from population import Population
 
 
 def main() -> None:
-    example_genome = Genome()
+    population_size = 500
-    print(example_genome.knights_red)
+    mutation_rate = 0.4
-    print(example_genome.knights_blue)
+
-    print(example_genome.grid)
+    population = Population(mutation_rate, population_size, 27)
-    islands = get_islands(example_genome.grid, example_genome.knights_red)
+
-    print(f'Roots {islands} and islands count {len(islands)}')
+    while not population.evaluate():
-    # export_map(example_genome.grid) fixme: FileNotFoundError
+        # create next generation
+        population.generate()
+
+        # calc fitness
+        population.calc_fitness()
+
+    print(population.best_genome.grid)
+    print("Fitness of the best: ", population.best_genome.fitness)
+
+    export_map(population.best_genome.grid)
 
 
 if __name__ == '__main__':

algorithms/genetic/map_importer_exporter.py

@@ -2,22 +2,24 @@ import json
 import random
 import string
 from datetime import datetime
-
+from pathlib import Path
 import numpy
 import numpy.typing as npt
 from os import listdir
 from os.path import isfile, join
 
 
-
 # Save map to file
 def export_map(grid: npt.NDArray):
     json_data = {"map": grid.tolist()}
 
     now = datetime.now()
     file_name = "map_" + now.strftime("%Y_%m_%d_%H_%M_%S") + ".json"
+    path = Path("../../resources/maps/")
+    file_to_open = path / file_name
 
-    with open("resources/maps/" + file_name, "w") as write_file:
+    print(file_to_open)
+    with open(file_to_open, "w+") as write_file:
         json.dump(json_data, write_file)
     print("Saved map to file " + file_name)
 
@@ -30,9 +32,10 @@ def import_random_map() -> object:
 
 
 # Read map from file
-def import_map(file: string) -> object:
+def import_map(file_name: string) -> object:
-    with open("resources/maps/" + file, "r") as read_file:
+    file_to_open = "resources/maps/" + file_name
-        print("Reading map from file " + file)
+    with open(file_to_open, "r") as read_file:
+        print("Reading map from file " + file_name)
         decoded_json = json.load(read_file)
 
         decoded_grid = numpy.asarray(decoded_json["map"])

algorithms/genetic/population.py

@@ -0,0 +1,81 @@
+import random
+from typing import List
+
+import numpy as np
+import numpy.typing as npt
+
+from genome import Genome
+
+
+class Population:
+    population: List[Genome] = []  # array to hold the current population
+    mating_pool: List[Genome] = []  # array which we will use for our "mating pool"
+    generations: int = 0  # number of generations
+    finished: bool = False  # are we finished evolving?
+    mutation_rate: float
+    perfect_score: int
+    best_genome: Genome
+
+    def __init__(self, mutation_rate, population_size, perfect_score=20):
+        self.mutation_rate = mutation_rate
+        self.perfect_score = perfect_score
+
+        for i in range(0, population_size):
+            new_genome = Genome()
+            new_genome.calc_fitness()
+            self.population.append(new_genome)
+
+    # create a new generation
+    def generate(self):
+        max_fitness = 0
+        for genome in self.population:
+            if genome.fitness > max_fitness:
+                max_fitness = genome.fitness
+
+        print("Max fitness of generation " + str(self.generations) + " = " + str(max_fitness))
+
+        # refill the population with children from the mating pool
+        new_population = []
+        for genome in self.population:
+            partner_a = self.accept_reject(max_fitness)
+            partner_b = self.accept_reject(max_fitness)
+            child = partner_a.crossover(partner_b)
+            child.mutate(self.mutation_rate)
+            new_population.append(child)
+
+        self.population = new_population
+        self.generations += 1
+
+    # select random with correct probability from population
+    def accept_reject(self, max_fitness: int):
+        safe_flag = 0
+
+        while safe_flag < 10000:
+            partner = random.choice(self.population)
+            r = random.randint(0, max_fitness)
+
+            if r < partner.fitness:
+                return partner
+
+            safe_flag += 1
+
+    # compute the current "most fit" member of the population
+    def evaluate(self):
+        record = 0
+        best_index = 0
+
+        for index in range(len(self.population)):
+            genome = self.population[index]
+            if genome.fitness > record:
+                record = genome.fitness
+                best_index = index
+
+        self.best_genome = self.population[best_index]
+        if record >= self.perfect_score:
+            self.finished = True
+
+        return self.finished
+
+    def calc_fitness(self):
+        for genome in self.population:
+            genome.calc_fitness()

resources/maps/map_2022_05_31_00_41_36.json

@@ -1 +0,0 @@
-{"map": [[0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 1, 4, 2, 3, 0, 0, 3, 3, 0, 3, 4, 0, 0], [0, 3, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 1, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 2, 0, 1, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 2, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 3, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0], [3, 0, 0, 0, 0, 0, 0, 0, 0, 5, 5, 3, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, 0, 0, 0, 0, 3, 5, 5, 0, 0, 0, 0, 1, 0, 1, 3, 0, 0, 7, 0, 0], [2, 0, 3, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 3, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0], [6, 6, 1, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 6, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 3, 0, 2, 2, 0, 2, 0, 3, 0, 0, 7, 0], [0, 0, 3, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0], [3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0], [1, 0, 3, 0, 0, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0], [0, 2, 2, 0, 3, 0, 0, 0, 0, 0, 0, 0, 3, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0], [1, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}

resources/maps/map_2022_05_31_00_41_47.json

@@ -1 +0,0 @@
-{"map": [[0, 0, 0, 2, 0, 0, 0, 0, 3, 0, 0, 0, 0, 3, 3, 0, 0, 0, 3, 0, 0, 3, 0, 0], [0, 0, 0, 1, 0, 0, 0, 1, 0, 4, 0, 0, 0, 0, 2, 1, 2, 3, 0, 3, 0, 0, 0, 0], [3, 1, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 1, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 1, 3, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 1, 0, 0, 0, 0, 0, 3, 0, 0], [0, 6, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 3, 0, 0, 7, 7], [0, 0, 3, 2, 0, 0, 0, 0, 0, 5, 5, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, 0, 0, 0, 0, 1, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0], [0, 0, 6, 1, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 1, 2, 2, 0, 0, 0, 3, 0, 7, 0], [0, 6, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 2, 0, 1, 0, 0, 0], [0, 3, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], [3, 0, 0, 0, 0, 0, 0, 0, 3, 0, 2, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 7, 0, 0], [0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 1, 3, 0, 2, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 3, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0], [0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 2, 0, 0, 3, 0, 0, 2, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 3, 3, 0, 3, 0, 0, 0, 0, 0, 0, 2, 0, 0, 3, 0, 0, 3, 0, 0, 0, 3, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}

resources/maps/map_2022_05_31_00_41_51.json

@@ -1 +0,0 @@
-{"map": [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 3, 3, 0], [1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 3, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0], [0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 2, 0, 0, 0, 0, 1, 0, 0, 0], [2, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 1, 3, 0, 0, 0, 0, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 2, 0], [0, 1, 0, 0, 3, 0, 0, 1, 0, 0, 3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0], [6, 0, 0, 0, 1, 2, 0, 0, 0, 5, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 3, 0, 0, 0, 5, 5, 0, 0, 0, 0, 3, 0, 3, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 2, 2, 0, 2, 0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 7, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 3, 0, 0, 0], [6, 2, 6, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 3, 3, 0, 0, 7, 0, 7], [0, 3, 6, 2, 0, 3, 0, 0, 0, 1, 0, 0, 3, 0, 0, 0, 2, 0, 0, 3, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0, 0, 2, 0, 0, 3, 3, 0, 0, 0, 4, 0, 0, 0, 3, 1, 0, 0, 0], [0, 3, 2, 3, 0, 2, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 4, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0], [0, 0, 0, 0, 0, 0, 3, 3, 0, 0, 3, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]}

resources/maps/map_2022_06_02_00_36_19.json

@@ -0,0 +1 @@
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resources/maps/map_2022_06_02_00_38_31.json

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resources/maps/map_2022_06_02_00_42_44.json

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+{"map": [[0, 3, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 0, 0, 2, 3, 0, 0, 0, 0], [0, 0, 0, 0, 0, 6, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 3, 0], [0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0], [2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 3, 0, 1], [0, 0, 0, 6, 0, 0, 0, 6, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 3, 5, 5, 0, 3, 2, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 6, 3, 0, 0, 0, 0, 0, 0, 5, 5, 3, 2, 0, 0, 0, 0, 0, 0, 0, 7, 7], [3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 7, 7, 0, 0], [0, 0, 0, 0, 1, 0, 3, 0, 0, 3, 3, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0], [0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0], [0, 0, 2, 0, 3, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 6, 0], [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [0, 0, 3, 1, 0, 0, 0, 0, 0, 0, 2, 0, 3, 0, 0, 3, 0, 0, 3, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 3, 0, 0, 2, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0], [3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0]]}