


'''simple docstring'''






import os






def 	_A				(lowerCAmelCase__  :Any		)   ->  List[str]:




     '''simple docstring'''



     _a			      =							len(grid[0]		)
     _a			      =							len(lowerCAmelCase__		)

     _a			      =							0
     _a			      =							0
     _a			      =							0

     # Check vertically, horizontally, diagonally at the same time (only works
     # for nxn grid)
     for i in range(lowerCAmelCase__		):
          for j in range(n_rows - 3		):
               _a			      =							grid[j][i] * grid[j + 1][i] * grid[j + 2][i] * grid[j + 3][i]
               _a			      =							grid[i][j] * grid[i][j + 1] * grid[i][j + 2] * grid[i][j + 3]

               # Left-to-right diagonal (\) product
               if i < n_columns - 3:
                    _a			      =							(
                        grid[i][j]
                        * grid[i + 1][j + 1]
                        * grid[i + 2][j + 2]
                        * grid[i + 3][j + 3]
                    )

               # Right-to-left diagonal(/) product
               if i > 2:
                    _a			      =							(
                        grid[i][j]
                        * grid[i - 1][j + 1]
                        * grid[i - 2][j + 2]
                        * grid[i - 3][j + 3]
                    )

               _a			      =							max(
                   lowerCAmelCase__				,						lowerCAmelCase__				,						lowerCAmelCase__				,						lowerCAmelCase__		)
               if max_product > largest:
                    _a			      =							max_product

     return largest






def 	_A				()   ->  List[Any]:




     '''simple docstring'''



     _a			      =							[]
     with open(os.path.dirname(lowerCAmelCase__		) + '/grid.txt'		) as file:
          for line in file:
               grid.append(line.strip('\n'		).split(' '		)		)

     _a			      =							[[int(lowerCAmelCase__		) for i in grid[j]] for j in range(len(lowerCAmelCase__		)		)]

     return largest_product(lowerCAmelCase__		)


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





'''simple docstring'''






import numpy as np
import qiskit






def 	_A				(lowerCAmelCase__  :int = 8				,						lowerCAmelCase__  :int | None = None		)   ->  str:




     '''simple docstring'''



     _a			      =							np.random.default_rng(seed=lowerCAmelCase__		)

     # Roughly 25% of the qubits will contribute to the key.
     # So we take more than we need.
     _a			      =							6 * key_len
     # Measurement basis for Alice's qubits.
     _a			      =							rng.integers(2				,						size=lowerCAmelCase__		)
     # The set of states Alice will prepare.
     _a			      =							rng.integers(2				,						size=lowerCAmelCase__		)
     # Measurement basis for Bob's qubits.
     _a			      =							rng.integers(2				,						size=lowerCAmelCase__		)

     # Quantum Circuit to simulate BB84
     _a			      =							qiskit.QuantumCircuit(lowerCAmelCase__				,						name='BB84'		)

     # Alice prepares her qubits according to rules above.
     for index, _ in enumerate(lowerCAmelCase__		):
          if alice_state[index] == 1:
               bbaa_circ.x(lowerCAmelCase__		)
          if alice_basis[index] == 1:
               bbaa_circ.h(lowerCAmelCase__		)
     bbaa_circ.barrier()

     # Bob measures the received qubits according to rules above.
     for index, _ in enumerate(lowerCAmelCase__		):
          if bob_basis[index] == 1:
               bbaa_circ.h(lowerCAmelCase__		)

     bbaa_circ.barrier()
     bbaa_circ.measure_all()

     # Simulate the quantum circuit.
     _a			      =							qiskit.Aer.get_backend('aer_simulator'		)
     # We only need to run one shot because the key is unique.
     # Multiple shots will produce the same key.
     _a			      =							qiskit.execute(lowerCAmelCase__				,						lowerCAmelCase__				,						shots=1				,						seed_simulator=lowerCAmelCase__		)
     # Returns the result of measurement.
     _a			      =							job.result().get_counts(lowerCAmelCase__		).most_frequent()

     # Extracting the generated key from the simulation results.
     # Only keep measurement results where Alice and Bob chose the same basis.
     _a			      =							''.join(
         [
             result_bit
             for alice_basis_bit, bob_basis_bit, result_bit in zip(
                 lowerCAmelCase__				,						lowerCAmelCase__				,						lowerCAmelCase__		)
             if alice_basis_bit == bob_basis_bit
         ]		)

     # Get final key. Pad with 0 if too short, otherwise truncate.
     _a			      =							gen_key[:key_len] if len(lowerCAmelCase__		) >= key_len else gen_key.ljust(lowerCAmelCase__				,						'0'		)
     return key


if __name__ == "__main__":
 print(f'''The generated key is : {bbaa(8, seed=0)}''')
 from doctest import testmod

 testmod()

