





"""simple docstring"""
_snake_case	:						Any					=					[0.3_3, 0.4_4, 0.5_5, 0.4_4, 0.3_3]
_snake_case	:						List[Any]					=					3
_snake_case	:						str					=					5

# Buffer Space (with Parameters Space)
_snake_case	:						list[float]					=					[]
_snake_case	:						list[float]					=					[]

# Machine Time
_snake_case	:						Dict					=					0






def    A__							(     UpperCamelCase			):
							global buffer_space, params_space, machine_time, K, m, t

							# Choosing Dynamical Systems (All)
							for key, value in enumerate(UpperCamelCase			):
														# Evolution Parameter
														A						=    float(seed / value			)

														# Control Theory: Orbit Change
														A						=    (buffer_space[(key + 1) % m] + e) % 1

														# Control Theory: Trajectory Change
														A						=    (params_space[key] + e) % 1 + 3

														# Modification (Transition Function) - Jumps
														A						=    round(float(r * value * (1 - value)			)   ,    10			)
														A						=    r  # Saving to Parameters Space

							# Logistic Map
							assert max(UpperCamelCase			) < 1
							assert max(UpperCamelCase			) < 4

							# Machine Time
							machine_time += 1






def    A__							(     ):
							global buffer_space, params_space, machine_time, K, m, t

							# PRNG (Xorshift by George Marsaglia)
							def xorshift(UpperCamelCase   ,    UpperCamelCase			):
														x ^= y >> 13
														y ^= x << 17
														x ^= y >> 5
														return x

							# Choosing Dynamical Systems (Increment)
							A						=    machine_time % m

							# Evolution (Time Length)
							for _ in range(0   ,    UpperCamelCase			):
														# Variables (Position + Parameters)
														A						=    params_space[key]
														A						=    buffer_space[key]

														# Modification (Transition Function) - Flow
														A						=    round(float(r * value * (1 - value)			)   ,    10			)
														A						=    (machine_time * 0.01 + r * 1.01) % 1 + 3

							# Choosing Chaotic Data
							A						=    int(buffer_space[(key + 2) % m] * (10**10)			)
							A						=    int(buffer_space[(key - 2) % m] * (10**10)			)

							# Machine Time
							machine_time += 1

							return xorshift(UpperCamelCase   ,    UpperCamelCase			) % 0xF_F_F_F_F_F_F_F






def    A__							(     ):
							global buffer_space, params_space, machine_time, K, m, t

							A						=    K
							A						=    [0] * m
							A						=    0


if __name__ == "__main__":
		# Initialization
		reset()

		# Pushing Data (Input)
		import random

		_snake_case	:						Optional[int]					=					random.sample(range(0xffff_ffff), 100)
		for chunk in message:
				push(chunk)

		# for controlling
		_snake_case	:						int					=					''

		# Pulling Data (Output)
		while inp in ("e", "E"):
				print(F"""{format(pull(), '#04x')}""")
				print(buffer_space)
				print(params_space)
				_snake_case	:						List[str]					=					input('(e)exit? ').strip()









"""simple docstring"""
from __future__ import annotations

from queue import Queue






def    A__							(     UpperCamelCase   ,    UpperCamelCase			):
							a ^= b
							b ^= a
							a ^= b
							return a, b






def    A__							(     UpperCamelCase   ,    UpperCamelCase			):
							A						=    1
							while (1 << j) < max_node:
														for i in range(1   ,    max_node + 1			):
																					A						=    parent[j - 1][parent[j - 1][i]]
														j += 1
							return parent






def    A__							(     UpperCamelCase   ,    UpperCamelCase   ,    UpperCamelCase   ,    UpperCamelCase			):
							# u must be deeper in the tree than v
							if level[u] < level[v]:
														A,      A						=    swap(UpperCamelCase   ,    UpperCamelCase			)
							# making depth of u same as depth of v
							for i in range(18   ,    -1   ,    -1			):
														if level[u] - (1 << i) >= level[v]:
																					A						=    parent[i][u]
    # at the same depth if u==v that mean lca is found
							if u == v:
														return u
							# moving both nodes upwards till lca in found
							for i in range(18   ,    -1   ,    -1			):
														if parent[i][u] not in [0, parent[i][v]]:
																					A,      A						=    parent[i][u], parent[i][v]
    # returning longest common ancestor of u,v
							return parent[0][u]






def    A__							(     UpperCamelCase   ,    UpperCamelCase   ,    UpperCamelCase   ,    UpperCamelCase   ,    UpperCamelCase = 1   ,    ):
							A						=    0
							A						=    Queue(maxsize=UpperCamelCase			)
							q.put(UpperCamelCase			)
							while q.qsize() != 0:
														A						=    q.get()
														for v in graph[u]:
																					if level[v] == -1:
																												A						=    level[u] + 1
																												q.put(UpperCamelCase			)
																												A						=    u
							return level, parent






def    A__							(     ):
							A						=    13
							# initializing with 0
							A						=    [[0 for _ in range(max_node + 10			)] for _ in range(20			)]
							# initializing with -1 which means every node is unvisited
							A						=    [-1 for _ in range(max_node + 10			)]
							A						=    {
							    1: [2, 3, 4],
							    2: [5],
							    3: [6, 7],
							    4: [8],
							    5: [9, 10],
							    6: [11],
							    7: [],
							    8: [12, 13],
							    9: [],
							    10: [],
							    11: [],
							    12: [],
							    13: [],
							}
							A,      A						=    breadth_first_search(UpperCamelCase   ,    UpperCamelCase   ,    UpperCamelCase   ,    UpperCamelCase   ,    1			)
							A						=    create_sparse(UpperCamelCase   ,    UpperCamelCase			)
							print("LCA of node 1 and 3 is: "   ,    lowest_common_ancestor(1   ,    3   ,    UpperCamelCase   ,    UpperCamelCase			)			)
							print("LCA of node 5 and 6 is: "   ,    lowest_common_ancestor(5   ,    6   ,    UpperCamelCase   ,    UpperCamelCase			)			)
							print("LCA of node 7 and 11 is: "   ,    lowest_common_ancestor(7   ,    11   ,    UpperCamelCase   ,    UpperCamelCase			)			)
							print("LCA of node 6 and 7 is: "   ,    lowest_common_ancestor(6   ,    7   ,    UpperCamelCase   ,    UpperCamelCase			)			)
							print("LCA of node 4 and 12 is: "   ,    lowest_common_ancestor(4   ,    12   ,    UpperCamelCase   ,    UpperCamelCase			)			)
							print("LCA of node 8 and 8 is: "   ,    lowest_common_ancestor(8   ,    8   ,    UpperCamelCase   ,    UpperCamelCase			)			)


if __name__ == "__main__":
		main()


