



"""simple docstring"""





import math

import numpy as np
import qiskit
from qiskit import Aer, ClassicalRegister, QuantumCircuit, QuantumRegister, execute
def      a__			(   lowerCAmelCase__ = 3   ):
      if isinstance(lowerCAmelCase__			,    lowerCAmelCase__   ):
            raise TypeError("number of qubits must be a integer."   )
      if number_of_qubits <= 0:
            raise ValueError("number of qubits must be > 0."   )
      if math.floor(lowerCAmelCase__   ) != number_of_qubits:
            raise ValueError("number of qubits must be exact integer."   )
      if number_of_qubits > 10:
            raise ValueError("number of qubits too large to simulate(>10)."   )

      UpperCAmelCase_    				=							QuantumRegister(lowerCAmelCase__			,    "qr"   )
      UpperCAmelCase_    				=							ClassicalRegister(lowerCAmelCase__			,    "cr"   )

      UpperCAmelCase_    				=							QuantumCircuit(lowerCAmelCase__			,    lowerCAmelCase__   )

      UpperCAmelCase_    				=							number_of_qubits

      for i in range(lowerCAmelCase__   ):
            quantum_circuit.h(number_of_qubits - i - 1   )
            counter -= 1
            for j in range(lowerCAmelCase__   ):
                  quantum_circuit.cp(np.pi / 2 ** (counter - j)			,    lowerCAmelCase__			,    lowerCAmelCase__   )

      for k in range(number_of_qubits // 2   ):
            quantum_circuit.swap(lowerCAmelCase__			,    number_of_qubits - k - 1   )

      # measure all the qubits
      quantum_circuit.measure(lowerCAmelCase__			,    lowerCAmelCase__   )
      # simulate with 10000 shots
      UpperCAmelCase_    				=							Aer.get_backend("qasm_simulator"   )
      UpperCAmelCase_    				=							execute(lowerCAmelCase__			,    lowerCAmelCase__			,    shots=10000   )

      return job.result().get_counts(lowerCAmelCase__   )


if __name__ == "__main__":
  print(
      F"Total count for quantum fourier transform state is: \
    {quantum_fourier_transform(3)}"
  )









"""simple docstring"""





from __future__ import annotations
def      a__			(   lowerCAmelCase__			,    lowerCAmelCase__			,    lowerCAmelCase__			,    lowerCAmelCase__   ):
      UpperCAmelCase_    				=							[]
      UpperCAmelCase_				,					UpperCAmelCase_    				=							input_list[low:mid], input_list[mid : high + 1]
      while left and right:
            result.append((left if left[0] <= right[0] else right).pop(0   )   )
      UpperCAmelCase_    				=							result + left + right
      return input_list
def      a__			(   lowerCAmelCase__   ):
      if len(lowerCAmelCase__   ) <= 1:
            return input_list
      UpperCAmelCase_    				=							list(lowerCAmelCase__   )

      # iteration for two-way merging
      UpperCAmelCase_    				=							2
      while p <= len(lowerCAmelCase__   ):
            # getting low, high and middle value for merge-sort of single list
            for i in range(0			,    len(lowerCAmelCase__   )			,    lowerCAmelCase__   ):
                  UpperCAmelCase_    				=							i
                  UpperCAmelCase_    				=							i + p - 1
                  UpperCAmelCase_    				=							(low + high + 1) // 2
                  UpperCAmelCase_    				=							merge(lowerCAmelCase__			,    lowerCAmelCase__			,    lowerCAmelCase__			,    lowerCAmelCase__   )
            # final merge of last two parts
            if p * 2 >= len(lowerCAmelCase__   ):
                  UpperCAmelCase_    				=							i
                  UpperCAmelCase_    				=							merge(lowerCAmelCase__			,    0			,    lowerCAmelCase__			,    len(lowerCAmelCase__   ) - 1   )
                  break
            p *= 2

      return input_list


if __name__ == "__main__":
  lowerCamelCase      =		input("""Enter numbers separated by a comma:\n""").strip()
  if user_input == "":
    lowerCamelCase      =		[]
  else:
    lowerCamelCase      =		[int(item.strip()) for item in user_input.split(""",""")]
  print(iter_merge_sort(unsorted))




