"""simple docstring"""







import math
import sys


class      _lowercase						:

				def __init__(       self    :      int       ):


										'''simple docstring'''
										UpperCAmelCase__   		=						0
										UpperCAmelCase__   		=						[]
										UpperCAmelCase__   		=						{}  # To store the pos of node in array

				def     A	(       self    :      Tuple       ):


										'''simple docstring'''
										return self.cur_size == 0

				def     A	(       self    :      int    ,      _lowercase    :      Optional[int]       ):


										'''simple docstring'''
										UpperCAmelCase__   		=						self.left(_lowercase       )
										UpperCAmelCase__   		=						self.right(_lowercase       )
										if lc < self.cur_size and self.array(_lowercase       )[0] < self.array(_lowercase       )[0]:
																UpperCAmelCase__   		=						lc
										else:
																UpperCAmelCase__   		=						idx
										if rc < self.cur_size and self.array(_lowercase       )[0] < self.array(_lowercase       )[0]:
																UpperCAmelCase__   		=						rc
										if smallest != idx:
																self.swap(_lowercase    ,      _lowercase       )
																self.min_heapify(_lowercase       )

				def     A	(       self    :      List[Any]    ,      _lowercase    :      Optional[Any]       ):


										'''simple docstring'''
										# Inserts a node into the Priority Queue
										UpperCAmelCase__   		=						self.cur_size
										self.cur_size += 1
										self.array.append((sys.maxsize, tup[1])       )
										self.decrease_key((sys.maxsize, tup[1])    ,      tup[0]       )

				def     A	(       self    :      List[Any]       ):


										'''simple docstring'''
										# Removes and returns the min element at top of priority queue
										UpperCAmelCase__   		=						self.array[0][1]
										UpperCAmelCase__   		=						self.array[self.cur_size - 1]
										self.cur_size -= 1
										self.min_heapify(1       )
										del self.pos[min_node]
										return min_node

				def     A	(       self    :      List[str]    ,      _lowercase    :      Optional[Any]       ):


										'''simple docstring'''
										# returns the index of left child
										return 2 * i + 1

				def     A	(       self    :      Optional[Any]    ,      _lowercase    :      str       ):


										'''simple docstring'''
										# returns the index of right child
										return 2 * i + 2

				def     A	(       self    :      Optional[Any]    ,      _lowercase    :      Union[str, Any]       ):


										'''simple docstring'''
										# returns the index of parent
										return math.floor(i / 2       )

				def     A	(       self    :      Any    ,      _lowercase    :      Tuple    ,      _lowercase    :      List[Any]       ):


										'''simple docstring'''
										# swaps array elements at indices i and j
										# update the pos{}
										UpperCAmelCase__   		=						j
										UpperCAmelCase__   		=						i
										UpperCAmelCase__   		=						self.array[i]
										UpperCAmelCase__   		=						self.array[j]
										UpperCAmelCase__   		=						temp

				def     A	(       self    :      Optional[int]    ,      _lowercase    :      Optional[int]    ,      _lowercase    :      Optional[Any]       ):


										'''simple docstring'''
										UpperCAmelCase__   		=						self.pos[tup[1]]
										# assuming the new_d is atmost old_d
										UpperCAmelCase__   		=						(new_d, tup[1])
										while idx > 0 and self.array[self.par(_lowercase       )][0] > self.array[idx][0]:
																self.swap(_lowercase    ,      self.par(_lowercase       )       )
																UpperCAmelCase__   		=						self.par(_lowercase       )


class      _lowercase						:

				def __init__(       self    :      Any    ,      _lowercase    :      List[Any]       ):


										'''simple docstring'''
										UpperCAmelCase__   		=						{}  # To store graph: u -> (v,w)
										UpperCAmelCase__   		=						num  # Number of nodes in graph
										# To store the distance from source vertex
										UpperCAmelCase__   		=						[0] * self.num_nodes
										UpperCAmelCase__   		=						[-1] * self.num_nodes  # To store the path

				def     A	(       self    :      Dict    ,      _lowercase    :      List[str]    ,      _lowercase    :      int    ,      _lowercase    :      Tuple       ):


										'''simple docstring'''
										#  Edge going from node u to v and v to u with weight w
										# u (w)-> v, v (w) -> u
										# Check if u already in graph
										if u in self.adjList:
																self.adjList[u].append((v, w)       )
										else:
																UpperCAmelCase__   		=						[(v, w)]

										# Assuming undirected graph
										if v in self.adjList:
																self.adjList[v].append((u, w)       )
										else:
																UpperCAmelCase__   		=						[(u, w)]

				def     A	(       self    :      Tuple       ):


										'''simple docstring'''
										# u -> v(w)
										for u in self.adjList:
																print(_lowercase    ,      """->"""    ,      """ -> """.join(str(f'{v}({w})'       ) for v, w in self.adjList[u]       )       )

				def     A	(       self    :      List[str]    ,      _lowercase    :      Optional[int]       ):


										'''simple docstring'''
										# Flush old junk values in par[]
										UpperCAmelCase__   		=						[-1] * self.num_nodes
										# src is the source node
										UpperCAmelCase__   		=						0
										UpperCAmelCase__   		=						PriorityQueue()
										q.insert((0, src)       )  # (dist from src, node)
										for u in self.adjList:
																if u != src:
																						UpperCAmelCase__   		=						sys.maxsize  # Infinity
																						UpperCAmelCase__   		=						-1

										while not q.is_empty():
																UpperCAmelCase__   		=						q.extract_min()  # Returns node with the min dist from source
																# Update the distance of all the neighbours of u and
																# if their prev dist was INFINITY then push them in Q
																for v, w in self.adjList[u]:
																						UpperCAmelCase__   		=						self.dist[u] + w
																						if self.dist[v] > new_dist:
																												if self.dist[v] == sys.maxsize:
																																		q.insert((new_dist, v)       )
																												else:
																																		q.decrease_key((self.dist[v], v)    ,      _lowercase       )
																												UpperCAmelCase__   		=						new_dist
																												UpperCAmelCase__   		=						u

        # Show the shortest distances from src
										self.show_distances(_lowercase       )

				def     A	(       self    :      Union[str, Any]    ,      _lowercase    :      List[str]       ):


										'''simple docstring'''
										print(f'Distance from node: {src}'       )
										for u in range(self.num_nodes       ):
																print(f'Node {u} has distance: {self.dist[u]}'       )

				def     A	(       self    :      List[str]    ,      _lowercase    :      Tuple    ,      _lowercase    :      str       ):


										'''simple docstring'''
										# To show the shortest path from src to dest
										# WARNING: Use it *after* calling dijkstra
										UpperCAmelCase__   		=						[]
										UpperCAmelCase__   		=						0
										UpperCAmelCase__   		=						dest
										# Backtracking from dest to src
										while self.par[temp] != -1:
																path.append(_lowercase       )
																if temp != src:
																						for v, w in self.adjList[temp]:
																												if v == self.par[temp]:
																																		cost += w
																																		break
																UpperCAmelCase__   		=						self.par[temp]
										path.append(_lowercase       )
										path.reverse()

										print(f'----Path to reach {dest} from {src}----'       )
										for u in path:
																print(f'{u}'    ,      end=""" """       )
																if u != dest:
																						print("""-> """    ,      end=""""""       )

										print("""\nTotal cost of path: """    ,      _lowercase       )


if __name__ == "__main__":
						UpperCamelCase_    :    List[str]											=						Graph(9)
						graph.add_edge(0, 1, 4)
						graph.add_edge(0, 7, 8)
						graph.add_edge(1, 2, 8)
						graph.add_edge(1, 7, 11)
						graph.add_edge(2, 3, 7)
						graph.add_edge(2, 8, 2)
						graph.add_edge(2, 5, 4)
						graph.add_edge(3, 4, 9)
						graph.add_edge(3, 5, 14)
						graph.add_edge(4, 5, 10)
						graph.add_edge(5, 6, 2)
						graph.add_edge(6, 7, 1)
						graph.add_edge(6, 8, 6)
						graph.add_edge(7, 8, 7)
						graph.show_graph()
						graph.dijkstra(0)
						graph.show_path(0, 4)

# OUTPUT
# 0 -> 1(4) -> 7(8)
# 1 -> 0(4) -> 2(8) -> 7(11)
# 7 -> 0(8) -> 1(11) -> 6(1) -> 8(7)
# 2 -> 1(8) -> 3(7) -> 8(2) -> 5(4)
# 3 -> 2(7) -> 4(9) -> 5(14)
# 8 -> 2(2) -> 6(6) -> 7(7)
# 5 -> 2(4) -> 3(14) -> 4(10) -> 6(2)
# 4 -> 3(9) -> 5(10)
# 6 -> 5(2) -> 7(1) -> 8(6)
# Distance from node: 0
# Node 0 has distance: 0
# Node 1 has distance: 4
# Node 2 has distance: 12
# Node 3 has distance: 19
# Node 4 has distance: 21
# Node 5 has distance: 11
# Node 6 has distance: 9
# Node 7 has distance: 8
# Node 8 has distance: 14
# ----Path to reach 4 from 0----
# 0 -> 7 -> 6 -> 5 -> 4
# Total cost of path:  21


"""simple docstring"""







from __future__ import annotations

from collections import Counter


def 					a__ (						UpperCAmelCase__    :     int     )->		list[int]:
						UpperCAmelCase__   		=						[True] * n
						UpperCAmelCase__   		=						False
						UpperCAmelCase__   		=						False
						UpperCAmelCase__   		=						True

						for i in range(3						,     int(n**0.5 + 1     )						,     2     ):
												UpperCAmelCase__   		=						i * 2
												while index < n:
																		UpperCAmelCase__   		=						False
																		UpperCAmelCase__   		=						index + i

						UpperCAmelCase__   		=						[2]

						for i in range(3						,     UpperCAmelCase__						,     2     ):
												if is_prime[i]:
																		primes.append(UpperCAmelCase__     )

						return primes


def 					a__ (						UpperCAmelCase__    :     int     )->		list[list[int]]:
						UpperCAmelCase__   		=						str(UpperCAmelCase__     )
						UpperCAmelCase__   		=						[]
						UpperCAmelCase__   		=						["""0""", """1""", """2""", """3""", """4""", """5""", """6""", """7""", """8""", """9"""]

						for duplicate in Counter(UpperCAmelCase__     ) - Counter(set(UpperCAmelCase__     )     ):
												UpperCAmelCase__   		=						[int(number_str.replace(UpperCAmelCase__						,     UpperCAmelCase__     )     ) for digit in digits]
												replacements.append(UpperCAmelCase__     )

						return replacements


def 					a__ (						UpperCAmelCase__    :     int = 8     )->		int:
						UpperCAmelCase__   		=						set()

						# Filter primes with less than 3 replaceable digits
						UpperCAmelCase__   		=						{
						    x for x in set(prime_sieve(1_0_0_0_0_0_0     )     ) if len(str(UpperCAmelCase__     )     ) - len(set(str(UpperCAmelCase__     )     )     ) >= 3
						}

						for prime in primes:
												if prime in numbers_checked:
																		continue

												UpperCAmelCase__   		=						digit_replacements(UpperCAmelCase__     )

												for family in replacements:
																		numbers_checked.update(UpperCAmelCase__     )
																		UpperCAmelCase__   		=						primes.intersection(UpperCAmelCase__     )

																		if len(UpperCAmelCase__     ) != family_length:
																								continue

																		return min(UpperCAmelCase__     )

						return -1


if __name__ == "__main__":
						print(solution())

