Iterations of the functor of naive A¹-connected components of varieties

For any sheaf of sets F on $Sm/k$, it is well known that the universal A¹-invariant quotient of F is given as the colimit of sheaves Sⁿ( F) where S(F) is the sheaf of naive A¹-connected components of F. We show that these infinite iterations of naive A¹-connected components in the construction of universal A¹-invariant quotient for a scheme are certainly required. For every n, we construct a variety Xₙ such that Sⁿ(Xₙ)≠ Sⁿ⁺¹(Xₙ).