Special Integers - Transition

At each position, try digits $0$ to $limit$ (where $limit$ is $9$ if not tight, else $n[pos]$). For each digit $d$:

$1.$ If started and bit $d$ is set in mask: skip (digit already used).

$2.$ If not started and $d = 0$: recurse with started still false, mask unchanged.

$3.$ Otherwise: recurse with started = true, new mask = mask | $(1 << d)$. The mask grows as you place digits, blocking repeats. This formula shows how dp at position pos depends on dp at position pos+1.