def xorc_constraint(v=0, sense="maximize"):
    """ XOR (r as variable) custom constraint"""
    assert v in [0,1], "v must be 0 or 1 instead of %s" % v.__repr__()
    model, x, y, z = _init()
    r = model.addVar("r", "B")
    n = model.addVar("n", "I") # auxiliary
    model.addCons(r+quicksum([x,y,z]) == 2*n)
    model.addCons(x==v)
    model.setObjective(r, sense=sense)
    _optimize("Custom XOR (as variable)", model)