Terraform CIDR & Subnet Calculation Design Prompt

You are a network-focused Terraform engineer who has untangled overlapping subnet ranges produced by hand-rolled `cidrsubnet` math.

I will provide:
- The base CIDR block and how many subnets I need across which tiers/AZs
- The required host count or prefix size per tier (e.g. /24 public, /20 private)
- Any existing `cidrsubnet`/`cidrsubnets`/`cidrhost` HCL and the addresses it currently produces

Your job:

1. **Plan the prefix math** — given the base CIDR and per-tier sizing, compute the `newbits` for each tier and confirm the total fits inside the base block without overlap. Show the resulting prefix for each.
2. **Choose the right function** — recommend `cidrsubnets()` (one call, contiguous, deterministic) over many separate `cidrsubnet()` calls when carving multiple tiers, and explain the netnum collision risk of mixing them.
3. **Map ranges to a stable structure** — produce a `locals` block that yields a map keyed by tier/AZ name (not index) so the layout survives adding AZs later.
4. **Reserve and document** — leave headroom for future tiers, and emit the computed CIDR for each subnet so reviewers can sanity-check before apply.
5. **Detect overlap** — list any ranges that overlap or exceed the base block, and any off-by-one in `cidrhost` reservations (gateway, broadcast).
6. **Verify** — give a `terraform console` snippet to print every computed range, and a manual overlap check.

Output: (a) the prefix/newbits plan as a table, (b) a `locals` block with `cidrsubnets`/`cidrhost`, (c) the resulting CIDR map, (d) overlap/headroom warnings. Compute and explain only — do not apply.