sp_staking/
lib.rs

1// This file is part of Substrate.
2
3// Copyright (C) Parity Technologies (UK) Ltd.
4// SPDX-License-Identifier: Apache-2.0
5
6// Licensed under the Apache License, Version 2.0 (the "License");
7// you may not use this file except in compliance with the License.
8// You may obtain a copy of the License at
9//
10// 	http://www.apache.org/licenses/LICENSE-2.0
11//
12// Unless required by applicable law or agreed to in writing, software
13// distributed under the License is distributed on an "AS IS" BASIS,
14// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
15// See the License for the specific language governing permissions and
16// limitations under the License.
17
18#![cfg_attr(not(feature = "std"), no_std)]
19
20//! A crate which contains primitives that are useful for implementation that uses staking
21//! approaches in general. Definitions related to sessions, slashing, etc go here.
22
23extern crate alloc;
24
25use crate::currency_to_vote::CurrencyToVote;
26use alloc::{collections::btree_map::BTreeMap, vec, vec::Vec};
27use codec::{Decode, Encode, FullCodec, HasCompact, MaxEncodedLen};
28use core::ops::Sub;
29use scale_info::TypeInfo;
30use sp_runtime::{
31	traits::{AtLeast32BitUnsigned, Zero},
32	DispatchError, DispatchResult, Perbill, RuntimeDebug, Saturating,
33};
34
35pub mod offence;
36
37pub mod currency_to_vote;
38
39/// Simple index type with which we can count sessions.
40pub type SessionIndex = u32;
41
42/// Counter for the number of eras that have passed.
43pub type EraIndex = u32;
44
45/// Type for identifying a page.
46pub type Page = u32;
47/// Representation of a staking account, which may be a stash or controller account.
48///
49/// Note: once the controller is completely deprecated, this enum can also be deprecated in favor of
50/// the stash account. Tracking issue: <https://github.com/paritytech/substrate/issues/6927>.
51#[derive(Clone, Debug)]
52pub enum StakingAccount<AccountId> {
53	Stash(AccountId),
54	Controller(AccountId),
55}
56
57#[cfg(feature = "std")]
58impl<AccountId> From<AccountId> for StakingAccount<AccountId> {
59	fn from(account: AccountId) -> Self {
60		StakingAccount::Stash(account)
61	}
62}
63
64/// Representation of the status of a staker.
65#[derive(RuntimeDebug, TypeInfo)]
66#[cfg_attr(feature = "serde", derive(serde::Serialize, serde::Deserialize, PartialEq, Eq, Clone))]
67pub enum StakerStatus<AccountId> {
68	/// Chilling.
69	Idle,
70	/// Declaring desire in validate, i.e author blocks.
71	Validator,
72	/// Declaring desire to nominate, delegate, or generally approve of the given set of others.
73	Nominator(Vec<AccountId>),
74}
75
76/// A struct that reflects stake that an account has in the staking system. Provides a set of
77/// methods to operate on it's properties. Aimed at making `StakingInterface` more concise.
78#[derive(RuntimeDebug, Clone, Copy, Eq, PartialEq, Default)]
79pub struct Stake<Balance> {
80	/// The total stake that `stash` has in the staking system. This includes the
81	/// `active` stake, and any funds currently in the process of unbonding via
82	/// [`StakingInterface::unbond`].
83	///
84	/// # Note
85	///
86	/// This is only guaranteed to reflect the amount locked by the staking system. If there are
87	/// non-staking locks on the bonded pair's balance this amount is going to be larger in
88	/// reality.
89	pub total: Balance,
90	/// The total amount of the stash's balance that will be at stake in any forthcoming
91	/// rounds.
92	pub active: Balance,
93}
94
95/// A generic staking event listener.
96///
97/// Note that the interface is designed in a way that the events are fired post-action, so any
98/// pre-action data that is needed needs to be passed to interface methods. The rest of the data can
99/// be retrieved by using `StakingInterface`.
100#[impl_trait_for_tuples::impl_for_tuples(10)]
101pub trait OnStakingUpdate<AccountId, Balance> {
102	/// Fired when the stake amount of someone updates.
103	///
104	/// This is effectively any changes to the bond amount, such as bonding more funds, and
105	/// unbonding.
106	fn on_stake_update(_who: &AccountId, _prev_stake: Option<Stake<Balance>>) {}
107
108	/// Fired when someone sets their intention to nominate.
109	///
110	/// This should never be fired for existing nominators.
111	fn on_nominator_add(_who: &AccountId) {}
112
113	/// Fired when an existing nominator updates their nominations.
114	///
115	/// Note that this is not fired when a nominator changes their stake. For that,
116	/// `on_stake_update` should be used, followed by querying whether `who` was a validator or a
117	/// nominator.
118	fn on_nominator_update(_who: &AccountId, _prev_nominations: Vec<AccountId>) {}
119
120	/// Fired when someone removes their intention to nominate, either due to chill or validating.
121	///
122	/// The set of nominations at the time of removal is provided as it can no longer be fetched in
123	/// any way.
124	fn on_nominator_remove(_who: &AccountId, _nominations: Vec<AccountId>) {}
125
126	/// Fired when someone sets their intention to validate.
127	///
128	/// Note validator preference changes are not communicated, but could be added if needed.
129	fn on_validator_add(_who: &AccountId) {}
130
131	/// Fired when an existing validator updates their preferences.
132	///
133	/// Note validator preference changes are not communicated, but could be added if needed.
134	fn on_validator_update(_who: &AccountId) {}
135
136	/// Fired when someone removes their intention to validate, either due to chill or nominating.
137	fn on_validator_remove(_who: &AccountId) {}
138
139	/// Fired when someone is fully unstaked.
140	fn on_unstake(_who: &AccountId) {}
141
142	/// Fired when a staker is slashed.
143	///
144	/// * `stash` - The stash of the staker whom the slash was applied to.
145	/// * `slashed_active` - The new bonded balance of the staker after the slash was applied.
146	/// * `slashed_unlocking` - A map of slashed eras, and the balance of that unlocking chunk after
147	///   the slash is applied. Any era not present in the map is not affected at all.
148	/// * `slashed_total` - The aggregated balance that was lost due to the slash.
149	fn on_slash(
150		_stash: &AccountId,
151		_slashed_active: Balance,
152		_slashed_unlocking: &BTreeMap<EraIndex, Balance>,
153		_slashed_total: Balance,
154	) {
155	}
156
157	/// Fired when a portion of a staker's balance has been withdrawn.
158	fn on_withdraw(_stash: &AccountId, _amount: Balance) {}
159}
160
161/// A generic representation of a staking implementation.
162///
163/// This interface uses the terminology of NPoS, but it is aims to be generic enough to cover other
164/// implementations as well.
165pub trait StakingInterface {
166	/// Balance type used by the staking system.
167	type Balance: Sub<Output = Self::Balance>
168		+ Ord
169		+ PartialEq
170		+ Default
171		+ Copy
172		+ MaxEncodedLen
173		+ FullCodec
174		+ TypeInfo
175		+ Saturating;
176
177	/// AccountId type used by the staking system.
178	type AccountId: Clone + core::fmt::Debug;
179
180	/// Means of converting Currency to VoteWeight.
181	type CurrencyToVote: CurrencyToVote<Self::Balance>;
182
183	/// The minimum amount required to bond in order to set nomination intentions. This does not
184	/// necessarily mean the nomination will be counted in an election, but instead just enough to
185	/// be stored as a nominator. In other words, this is the minimum amount to register the
186	/// intention to nominate.
187	fn minimum_nominator_bond() -> Self::Balance;
188
189	/// The minimum amount required to bond in order to set validation intentions.
190	fn minimum_validator_bond() -> Self::Balance;
191
192	/// Return a stash account that is controlled by a `controller`.
193	///
194	/// ## Note
195	///
196	/// The controller abstraction is not permanent and might go away. Avoid using this as much as
197	/// possible.
198	fn stash_by_ctrl(controller: &Self::AccountId) -> Result<Self::AccountId, DispatchError>;
199
200	/// Number of eras that staked funds must remain bonded for.
201	fn bonding_duration() -> EraIndex;
202
203	/// The current era index.
204	///
205	/// This should be the latest planned era that the staking system knows about.
206	fn current_era() -> EraIndex;
207
208	/// Returns the [`Stake`] of `who`.
209	fn stake(who: &Self::AccountId) -> Result<Stake<Self::Balance>, DispatchError>;
210
211	/// Total stake of a staker, `Err` if not a staker.
212	fn total_stake(who: &Self::AccountId) -> Result<Self::Balance, DispatchError> {
213		Self::stake(who).map(|s| s.total)
214	}
215
216	/// Total active portion of a staker's [`Stake`], `Err` if not a staker.
217	fn active_stake(who: &Self::AccountId) -> Result<Self::Balance, DispatchError> {
218		Self::stake(who).map(|s| s.active)
219	}
220
221	/// Returns whether a staker is unbonding, `Err` if not a staker at all.
222	fn is_unbonding(who: &Self::AccountId) -> Result<bool, DispatchError> {
223		Self::stake(who).map(|s| s.active != s.total)
224	}
225
226	/// Returns whether a staker is FULLY unbonding, `Err` if not a staker at all.
227	fn fully_unbond(who: &Self::AccountId) -> DispatchResult {
228		Self::unbond(who, Self::stake(who)?.active)
229	}
230
231	/// Bond (lock) `value` of `who`'s balance, while forwarding any rewards to `payee`.
232	fn bond(who: &Self::AccountId, value: Self::Balance, payee: &Self::AccountId)
233		-> DispatchResult;
234
235	/// Have `who` nominate `validators`.
236	fn nominate(who: &Self::AccountId, validators: Vec<Self::AccountId>) -> DispatchResult;
237
238	/// Chill `who`.
239	fn chill(who: &Self::AccountId) -> DispatchResult;
240
241	/// Bond some extra amount in `who`'s free balance against the active bonded balance of
242	/// the account. The amount extra actually bonded will never be more than `who`'s free
243	/// balance.
244	fn bond_extra(who: &Self::AccountId, extra: Self::Balance) -> DispatchResult;
245
246	/// Schedule a portion of the active bonded balance to be unlocked at era
247	/// [Self::current_era] + [`Self::bonding_duration`].
248	///
249	/// Once the unlock era has been reached, [`Self::withdraw_unbonded`] can be called to unlock
250	/// the funds.
251	///
252	/// The amount of times this can be successfully called is limited based on how many distinct
253	/// eras funds are schedule to unlock in. Calling [`Self::withdraw_unbonded`] after some unlock
254	/// schedules have reached their unlocking era should allow more calls to this function.
255	fn unbond(stash: &Self::AccountId, value: Self::Balance) -> DispatchResult;
256
257	/// Set the reward destination for the ledger associated with the stash.
258	fn set_payee(stash: &Self::AccountId, reward_acc: &Self::AccountId) -> DispatchResult;
259
260	/// Unlock any funds schedule to unlock before or at the current era.
261	///
262	/// Returns whether the stash was killed because of this withdraw or not.
263	fn withdraw_unbonded(
264		stash: Self::AccountId,
265		num_slashing_spans: u32,
266	) -> Result<bool, DispatchError>;
267
268	/// The ideal number of active validators.
269	fn desired_validator_count() -> u32;
270
271	/// Whether or not there is an ongoing election.
272	fn election_ongoing() -> bool;
273
274	/// Force a current staker to become completely unstaked, immediately.
275	fn force_unstake(who: Self::AccountId) -> DispatchResult;
276
277	/// Checks whether an account `staker` has been exposed in an era.
278	fn is_exposed_in_era(who: &Self::AccountId, era: &EraIndex) -> bool;
279
280	/// Return the status of the given staker, `Err` if not staked at all.
281	fn status(who: &Self::AccountId) -> Result<StakerStatus<Self::AccountId>, DispatchError>;
282
283	/// Checks whether or not this is a validator account.
284	fn is_validator(who: &Self::AccountId) -> bool {
285		Self::status(who).map(|s| matches!(s, StakerStatus::Validator)).unwrap_or(false)
286	}
287
288	/// Checks whether the staker is a virtual account.
289	///
290	/// A virtual staker is an account whose locks are not managed by the [`StakingInterface`]
291	/// implementation but by an external pallet. See [`StakingUnchecked::virtual_bond`] for more
292	/// details.
293	fn is_virtual_staker(who: &Self::AccountId) -> bool;
294
295	/// Get the nominations of a stash, if they are a nominator, `None` otherwise.
296	fn nominations(who: &Self::AccountId) -> Option<Vec<Self::AccountId>> {
297		match Self::status(who) {
298			Ok(StakerStatus::Nominator(t)) => Some(t),
299			_ => None,
300		}
301	}
302
303	/// Returns the fraction of the slash to be rewarded to reporter.
304	fn slash_reward_fraction() -> Perbill;
305
306	#[cfg(feature = "runtime-benchmarks")]
307	fn max_exposure_page_size() -> Page;
308
309	#[cfg(feature = "runtime-benchmarks")]
310	fn add_era_stakers(
311		current_era: &EraIndex,
312		stash: &Self::AccountId,
313		exposures: Vec<(Self::AccountId, Self::Balance)>,
314	);
315
316	#[cfg(feature = "runtime-benchmarks")]
317	fn set_current_era(era: EraIndex);
318}
319
320/// Set of low level apis to manipulate staking ledger.
321///
322/// These apis bypass some or all safety checks and should only be used if you know what you are
323/// doing.
324pub trait StakingUnchecked: StakingInterface {
325	/// Migrate an existing staker to a virtual staker.
326	///
327	/// It would release all funds held by the implementation pallet.
328	fn migrate_to_virtual_staker(who: &Self::AccountId);
329
330	/// Book-keep a new bond for `keyless_who` without applying any locks (hence virtual).
331	///
332	/// It is important that `keyless_who` is a keyless account and therefore cannot interact with
333	/// staking pallet directly. Caller is responsible for ensuring the passed amount is locked and
334	/// valid.
335	fn virtual_bond(
336		keyless_who: &Self::AccountId,
337		value: Self::Balance,
338		payee: &Self::AccountId,
339	) -> DispatchResult;
340
341	/// Migrate a virtual staker to a direct staker.
342	///
343	/// Only used for testing.
344	#[cfg(feature = "runtime-benchmarks")]
345	fn migrate_to_direct_staker(who: &Self::AccountId);
346}
347
348/// The amount of exposure for an era that an individual nominator has (susceptible to slashing).
349#[derive(PartialEq, Eq, PartialOrd, Ord, Clone, Encode, Decode, RuntimeDebug, TypeInfo)]
350pub struct IndividualExposure<AccountId, Balance: HasCompact> {
351	/// The stash account of the nominator in question.
352	pub who: AccountId,
353	/// Amount of funds exposed.
354	#[codec(compact)]
355	pub value: Balance,
356}
357
358/// A snapshot of the stake backing a single validator in the system.
359#[derive(PartialEq, Eq, PartialOrd, Ord, Clone, Encode, Decode, RuntimeDebug, TypeInfo)]
360pub struct Exposure<AccountId, Balance: HasCompact> {
361	/// The total balance backing this validator.
362	#[codec(compact)]
363	pub total: Balance,
364	/// The validator's own stash that is exposed.
365	#[codec(compact)]
366	pub own: Balance,
367	/// The portions of nominators stashes that are exposed.
368	pub others: Vec<IndividualExposure<AccountId, Balance>>,
369}
370
371impl<AccountId, Balance: Default + HasCompact> Default for Exposure<AccountId, Balance> {
372	fn default() -> Self {
373		Self { total: Default::default(), own: Default::default(), others: vec![] }
374	}
375}
376
377impl<
378		AccountId: Clone,
379		Balance: HasCompact + AtLeast32BitUnsigned + Copy + codec::MaxEncodedLen,
380	> Exposure<AccountId, Balance>
381{
382	/// Splits an `Exposure` into `PagedExposureMetadata` and multiple chunks of
383	/// `IndividualExposure` with each chunk having maximum of `page_size` elements.
384	pub fn into_pages(
385		self,
386		page_size: Page,
387	) -> (PagedExposureMetadata<Balance>, Vec<ExposurePage<AccountId, Balance>>) {
388		let individual_chunks = self.others.chunks(page_size as usize);
389		let mut exposure_pages: Vec<ExposurePage<AccountId, Balance>> =
390			Vec::with_capacity(individual_chunks.len());
391
392		for chunk in individual_chunks {
393			let mut page_total: Balance = Zero::zero();
394			let mut others: Vec<IndividualExposure<AccountId, Balance>> =
395				Vec::with_capacity(chunk.len());
396			for individual in chunk.iter() {
397				page_total.saturating_accrue(individual.value);
398				others.push(IndividualExposure {
399					who: individual.who.clone(),
400					value: individual.value,
401				})
402			}
403
404			exposure_pages.push(ExposurePage { page_total, others });
405		}
406
407		(
408			PagedExposureMetadata {
409				total: self.total,
410				own: self.own,
411				nominator_count: self.others.len() as u32,
412				page_count: exposure_pages.len() as Page,
413			},
414			exposure_pages,
415		)
416	}
417}
418
419/// A snapshot of the stake backing a single validator in the system.
420#[derive(PartialEq, Eq, PartialOrd, Ord, Clone, Encode, Decode, RuntimeDebug, TypeInfo)]
421pub struct ExposurePage<AccountId, Balance: HasCompact> {
422	/// The total balance of this chunk/page.
423	#[codec(compact)]
424	pub page_total: Balance,
425	/// The portions of nominators stashes that are exposed.
426	pub others: Vec<IndividualExposure<AccountId, Balance>>,
427}
428
429impl<A, B: Default + HasCompact> Default for ExposurePage<A, B> {
430	fn default() -> Self {
431		ExposurePage { page_total: Default::default(), others: vec![] }
432	}
433}
434
435/// Metadata for Paged Exposure of a validator such as total stake across pages and page count.
436///
437/// In combination with the associated `ExposurePage`s, it can be used to reconstruct a full
438/// `Exposure` set of a validator. This is useful for cases where we want to query full set of
439/// `Exposure` as one page (for backward compatibility).
440#[derive(
441	PartialEq,
442	Eq,
443	PartialOrd,
444	Ord,
445	Clone,
446	Encode,
447	Decode,
448	RuntimeDebug,
449	TypeInfo,
450	Default,
451	MaxEncodedLen,
452)]
453pub struct PagedExposureMetadata<Balance: HasCompact + codec::MaxEncodedLen> {
454	/// The total balance backing this validator.
455	#[codec(compact)]
456	pub total: Balance,
457	/// The validator's own stash that is exposed.
458	#[codec(compact)]
459	pub own: Balance,
460	/// Number of nominators backing this validator.
461	pub nominator_count: u32,
462	/// Number of pages of nominators.
463	pub page_count: Page,
464}
465
466/// A type that belongs only in the context of an `Agent`.
467///
468/// `Agent` is someone that manages delegated funds from [`Delegator`] accounts. It can
469/// then use these funds to participate in the staking system. It can never use its own funds to
470/// stake. They instead (virtually bond)[`StakingUnchecked::virtual_bond`] into the staking system
471/// and are also called `Virtual Stakers`.
472///
473/// The `Agent` is also responsible for managing rewards and slashing for all the `Delegators` that
474/// have delegated funds to it.
475#[derive(Clone, Debug)]
476pub struct Agent<T>(T);
477impl<T> From<T> for Agent<T> {
478	fn from(acc: T) -> Self {
479		Agent(acc)
480	}
481}
482
483impl<T> Agent<T> {
484	pub fn get(self) -> T {
485		self.0
486	}
487}
488
489/// A type that belongs only in the context of a `Delegator`.
490///
491/// `Delegator` is someone that delegates funds to an `Agent`, allowing them to pool funds
492/// along with other delegators and participate in the staking system.
493#[derive(Clone, Debug)]
494pub struct Delegator<T>(T);
495impl<T> From<T> for Delegator<T> {
496	fn from(acc: T) -> Self {
497		Delegator(acc)
498	}
499}
500
501impl<T> Delegator<T> {
502	pub fn get(self) -> T {
503		self.0
504	}
505}
506
507/// Trait to provide delegation functionality for stakers.
508pub trait DelegationInterface {
509	/// Balance type used by the staking system.
510	type Balance: Sub<Output = Self::Balance>
511		+ Ord
512		+ PartialEq
513		+ Default
514		+ Copy
515		+ MaxEncodedLen
516		+ FullCodec
517		+ TypeInfo
518		+ Saturating;
519
520	/// AccountId type used by the staking system.
521	type AccountId: Clone + core::fmt::Debug;
522
523	/// Returns effective balance of the `Agent` account. `None` if not an `Agent`.
524	///
525	/// This takes into account any pending slashes to `Agent` against the delegated balance.
526	fn agent_balance(agent: Agent<Self::AccountId>) -> Option<Self::Balance>;
527
528	/// Returns the total amount of funds that is unbonded and can be withdrawn from the `Agent`
529	/// account. `None` if not an `Agent`.
530	fn agent_transferable_balance(agent: Agent<Self::AccountId>) -> Option<Self::Balance>;
531
532	/// Returns the total amount of funds delegated. `None` if not a `Delegator`.
533	fn delegator_balance(delegator: Delegator<Self::AccountId>) -> Option<Self::Balance>;
534
535	/// Register `Agent` such that it can accept delegation.
536	fn register_agent(
537		agent: Agent<Self::AccountId>,
538		reward_account: &Self::AccountId,
539	) -> DispatchResult;
540
541	/// Removes `Agent` registration.
542	///
543	/// This should only be allowed if the agent has no staked funds.
544	fn remove_agent(agent: Agent<Self::AccountId>) -> DispatchResult;
545
546	/// Add delegation to the `Agent`.
547	fn delegate(
548		delegator: Delegator<Self::AccountId>,
549		agent: Agent<Self::AccountId>,
550		amount: Self::Balance,
551	) -> DispatchResult;
552
553	/// Withdraw or revoke delegation to `Agent`.
554	///
555	/// If there are `Agent` funds upto `amount` available to withdraw, then those funds would
556	/// be released to the `delegator`
557	fn withdraw_delegation(
558		delegator: Delegator<Self::AccountId>,
559		agent: Agent<Self::AccountId>,
560		amount: Self::Balance,
561		num_slashing_spans: u32,
562	) -> DispatchResult;
563
564	/// Returns pending slashes posted to the `Agent` account. None if not an `Agent`.
565	///
566	/// Slashes to `Agent` account are not immediate and are applied lazily. Since `Agent`
567	/// has an unbounded number of delegators, immediate slashing is not possible.
568	fn pending_slash(agent: Agent<Self::AccountId>) -> Option<Self::Balance>;
569
570	/// Apply a pending slash to an `Agent` by slashing `value` from `delegator`.
571	///
572	/// A reporter may be provided (if one exists) in order for the implementor to reward them,
573	/// if applicable.
574	fn delegator_slash(
575		agent: Agent<Self::AccountId>,
576		delegator: Delegator<Self::AccountId>,
577		value: Self::Balance,
578		maybe_reporter: Option<Self::AccountId>,
579	) -> DispatchResult;
580}
581
582/// Trait to provide functionality for direct stakers to migrate to delegation agents.
583/// See [`DelegationInterface`] for more details on delegation.
584pub trait DelegationMigrator {
585	/// Balance type used by the staking system.
586	type Balance: Sub<Output = Self::Balance>
587		+ Ord
588		+ PartialEq
589		+ Default
590		+ Copy
591		+ MaxEncodedLen
592		+ FullCodec
593		+ TypeInfo
594		+ Saturating;
595
596	/// AccountId type used by the staking system.
597	type AccountId: Clone + core::fmt::Debug;
598
599	/// Migrate an existing `Nominator` to `Agent` account.
600	///
601	/// The implementation should ensure the `Nominator` account funds are moved to an escrow
602	/// from which `Agents` can later release funds to its `Delegators`.
603	fn migrate_nominator_to_agent(
604		agent: Agent<Self::AccountId>,
605		reward_account: &Self::AccountId,
606	) -> DispatchResult;
607
608	/// Migrate `value` of delegation to `delegator` from a migrating agent.
609	///
610	/// When a direct `Nominator` migrates to `Agent`, the funds are kept in escrow. This function
611	/// allows the `Agent` to release the funds to the `delegator`.
612	fn migrate_delegation(
613		agent: Agent<Self::AccountId>,
614		delegator: Delegator<Self::AccountId>,
615		value: Self::Balance,
616	) -> DispatchResult;
617
618	/// Drop the `Agent` account and its associated delegators.
619	///
620	/// Also removed from [`StakingUnchecked`] as a Virtual Staker. Useful for testing.
621	#[cfg(feature = "runtime-benchmarks")]
622	fn migrate_to_direct_staker(agent: Agent<Self::AccountId>);
623}
624
625sp_core::generate_feature_enabled_macro!(runtime_benchmarks_enabled, feature = "runtime-benchmarks", $);