How much length of a very thin wire is required to obtain a solenoid of length  l0 and inductance L

Suppose solenoid has N turns, each of radius r and length of wire is l. It’s self inductance  L=μ0N2Al0=μ0N2πr2l0 .... (i)Also length of the wire  l=N×2πr⇒N2r2=l24π2.... (ii)From equation (i) and (ii)  l=4πLloμo