code: def ll_op(left, right):
      """Perform a LL operation.
  
      A LL operation multiplies both left and right circuits
      with the dagger of the left circuit's leftmost gate, and
      the dagger is multiplied on the left side of both circuits.
  
      If a LL is possible, it returns the new gate rule as a
      2-tuple (LHS, RHS), where LHS is the left circuit and
      and RHS is the right circuit of the new rule.
      If a LL is not possible, None is returned.
  
      Parameters
      ==========
  
      left : Gate tuple
          The left circuit of a gate rule expression.
      right : Gate tuple
          The right circuit of a gate rule expression.
  
      Examples
      ========
  
      Generate a new gate rule using a LL operation:
  
      >>> from sympy.physics.quantum.identitysearch import ll_op
      >>> from sympy.physics.quantum.gate import X, Y, Z
      >>> x = X(0); y = Y(0); z = Z(0)
      >>> ll_op((x, y, z), ())
      ((Y(0), Z(0)), (X(0),))
  
      >>> ll_op((y, z), (x,))
      ((Z(0),), (Y(0), X(0)))
      """
  
      if len(left) > 0:
          ll_gate = left[0]
          ll_gate_is_unitary = is_scalar_matrix(
              (Dagger(ll_gate), ll_gate), _get_min_qubits(ll_gate), True
          )
  
      if len(left) > 0 and ll_gate_is_unitary:
          # Get the new left side w/o the leftmost gate
          new_left = left[1 : len(left)]
          # Add the leftmost gate to the left position on the right side
          new_right = (Dagger(ll_gate),) + right
          # Return the new gate rule
          return (new_left, new_right)
  
      return None
  
imports: from collections import deque
  from sympy.core.random import randint
  from sympy.external import import_module
  from sympy.core.basic import Basic
  from sympy.core.mul import Mul
  from sympy.core.numbers import Number, equal_valued
  from sympy.core.power import Pow
  from sympy.core.singleton import S
  from sympy.physics.quantum.represent import represent
  from sympy.physics.quantum.dagger import Dagger
label_desc: Use image node_id 4 for calling a global function with example usage: ll_op(left, right) and returns: None, new_left,  new_right