Short-term addresses
https://github.com/paritytech/polkadot-sdk/issues/4737.

- [x] Resolve benchmarking
I've digged into benchmarking mentioned
https://github.com/paritytech/polkadot-sdk/issues/4737#issuecomment-2155084660,
but it seemed to me that this code is different proof/path. @acatangiu
could you confirm? (btw, in this
[bench](https://github.com/paritytech/polkadot-sdk/blob/b65313e8

/bridges/modules/parachains/src/benchmarking.rs#L57),
where do you actually set the `fn parachains()` to a reasonable number?
i've only seen 1)
- [ ] Communicate to Snowfork team:
This seems to be the relevant code:
https://github.com/Snowfork/snowbridge/blob/1e18e010331777042aa7e8fff3c118094af856ba/relayer/cmd/parachain_head_proof.go#L95-L120
- [x] Is it preferred to iter() in some random order as suggested in
https://github.com/paritytech/polkadot-sdk/issues/4737#issuecomment-2155084660
or take lowest para ids instead as implemented here currently?
- [x] PRDoc

## Updating Polkadot and Kusama runtimes:

New weights need to be generated (`pallet_mmr`) and configs updated
similar to Rococo/Westend:
```patch
diff --git a/polkadot/runtime/rococo/src/lib.rs b/polkadot/runtime/rococo/src/lib.rs
index 5adffbd7422..c7da339b981 100644
--- a/polkadot/runtime/rococo/src/lib.rs
+++ b/polkadot/runtime/rococo/src/lib.rs
@@ -1307,9 +1307,11 @@ impl pallet_mmr::Config for Runtime {
        const INDEXING_PREFIX: &'static [u8] = mmr::INDEXING_PREFIX;
        type Hashing = Keccak256;
        type OnNewRoot = pallet_beefy_mmr::DepositBeefyDigest<Runtime>;
-       type WeightInfo = ();
        type LeafData = pallet_beefy_mmr::Pallet<Runtime>;
        type BlockHashProvider = pallet_mmr::DefaultBlockHashProvider<Runtime>;
+       type WeightInfo = weights::pallet_mmr::WeightInfo<Runtime>;
+       #[cfg(feature = "runtime-benchmarks")]
+       type BenchmarkHelper = parachains_paras::benchmarking::mmr_setup::MmrSetup<Runtime>;
 }

 parameter_types! {
@@ -1319,13 +1321,8 @@ parameter_types! {
 pub struct ParaHeadsRootProvider;
 impl BeefyDataProvider<H256> for ParaHeadsRootProvider {
        fn extra_data() -> H256 {
-               let mut para_heads: Vec<(u32, Vec<u8>)> = parachains_paras::Parachains::<Runtime>::get()
-                       .into_iter()
-                       .filter_map(|id| {
-                               parachains_paras::Heads::<Runtime>::get(&id).map(|head| (id.into(), head.0))
-                       })
-                       .collect();
-               para_heads.sort();
+               let para_heads: Vec<(u32, Vec<u8>)> =
+                       parachains_paras::Pallet::<Runtime>::sorted_para_heads();
                binary_merkle_tree::merkle_root::<mmr::Hashing, _>(
                        para_heads.into_iter().map(|pair| pair.encode()),
                )
@@ -1746,6 +1743,7 @@ mod benches {
                [pallet_identity, Identity]
                [pallet_indices, Indices]
                [pallet_message_queue, MessageQueue]
+               [pallet_mmr, Mmr]
                [pallet_multisig, Multisig]
                [pallet_parameters, Parameters]
                [pallet_preimage, Preimage]
```

---------

Co-authored-by: Adrian Catangiu <adrian@parity.io>