Creating maximally-entangled state in quantum circuits using Qiskit

Question

I am trying to create a function in Qiskit that, given an integer n, returns a circuit of that size in which all qubits at the output are entangled together in a maximally-entangled state.

Some examples:

|001⟩ -> (|001⟩ + |110⟩)/√(2)

|010⟩ -> (|100⟩ + |011⟩)/√(2)

|100⟩ -> (|000⟩ - |111⟩)/√(2)

|101⟩ -> (|001⟩ - |110⟩)/√(2)

|111⟩ -> (|010⟩ - |101⟩)/√(2)

I have written the following function in Qiskit to build a basic maximally entangled circuit:

import qiskit

def maximally_entangled_state(n: int):

        qr = qiskit.QuantumRegister(n)
        #cr = qiskit.ClassicalRegister(6)
        circuit = qiskit.QuantumCircuit(qr)#, cr)

        circuit.h(qr[0])
        circuit.cx(qr[0], qr[1])

        if n>2:
          for item in range(2 , n):
             circuit.cx(qr[0], qr[item])

        return circuit

that returns such a circuit:

circuit = maximally_entangled_state(4)
circuit.draw()

I do not know how to investigate the examples and add relevant quantum gates to my code.