ethereum.forks.frontier.forkethereum.forks.homestead.fork

Ethereum Specification.

.. contents:: Table of Contents :backlinks: none :local:

Introduction

Entry point for the Ethereum specification.

BLOCK_REWARD

62
BLOCK_REWARD = U256(5 * 10**18)

MINIMUM_DIFFICULTY

63
MINIMUM_DIFFICULTY = Uint(131072)

MAX_OMMER_DEPTH

64
MAX_OMMER_DEPTH = Uint(6)

BlockChain

History and current state of the block chain.

67
@final
68
@dataclass
class BlockChain:

blocks

74
    blocks: List[Block]

state

75
    state: State

chain_id

76
    chain_id: U64

apply_fork

Transforms the state from the previous hard fork (old) into the block chain object for this hard fork and returns it.

When forks need to implement an irregular state transition, this function is used to handle the irregularity. See the :ref:DAO Fork <dao-fork> for an example.

Parameters

old : Previous block chain object.

Returns

new : BlockChain Upgraded block chain object for this hard fork.

def apply_fork(old: BlockChain) -> BlockChain:
80
    <snip>
99
    return old

get_last_256_block_hashes

Obtain the list of hashes of the previous 256 blocks in order of increasing block number.

This function will return less hashes for the first 256 blocks.

The BLOCKHASH opcode needs to access the latest hashes on the chain, therefore this function retrieves them.

Parameters

chain : History and current state.

Returns

recent_block_hashes : List[Hash32] Hashes of the recent 256 blocks in order of increasing block number.

def get_last_256_block_hashes(chain: BlockChain) -> List[Hash32]:
103
    <snip>
123
    recent_blocks = chain.blocks[-255:]
124
    # TODO: This function has not been tested rigorously
125
    if len(recent_blocks) == 0:
126
        return []
127
128
    recent_block_hashes = []
129
130
    for block in recent_blocks:
131
        prev_block_hash = block.header.parent_hash
132
        recent_block_hashes.append(prev_block_hash)
133
134
    # We are computing the hash only for the most recent block and not for
135
    # the rest of the blocks as they have successors which have the hash of
136
    # the current block as parent hash.
137
    most_recent_block_hash = keccak256(rlp.encode(recent_blocks[-1].header))
138
    recent_block_hashes.append(most_recent_block_hash)
139
140
    return recent_block_hashes

state_transition

Attempts to apply a block to an existing block chain.

All parts of the block's contents need to be verified before being added to the chain. Blocks are verified by ensuring that the contents of the block make logical sense with the contents of the parent block. The information in the block's header must also match the corresponding information in the block.

To implement Ethereum, in theory clients are only required to store the most recent 255 blocks of the chain since as far as execution is concerned, only those blocks are accessed. Practically, however, clients should store more blocks to handle reorgs.

Parameters

chain : History and current state. block : Block to apply to chain.

def state_transition(chain: BlockChain, ​​block: Block) -> None:
144
    <snip>
166
    validate_header(chain, block.header)
167
    validate_ommers(block.ommers, block.header, chain)
168
169
    block_state = BlockState(pre_state=chain.state)
170
171
    block_env = vm.BlockEnvironment(
172
        chain_id=chain.chain_id,
173
        state=block_state,
174
        block_gas_limit=block.header.gas_limit,
175
        block_hashes=get_last_256_block_hashes(chain),
176
        coinbase=block.header.coinbase,
177
        number=block.header.number,
178
        time=block.header.timestamp,
179
        difficulty=block.header.difficulty,
180
    )
181
182
    block_output = apply_body(
183
        block_env=block_env,
184
        transactions=block.transactions,
185
        ommers=block.ommers,
186
    )
187
    block_diff = extract_block_diff(block_state)
188
    block_state_root, _ = chain.state.compute_state_root_and_trie_changes(
189
        block_diff.account_changes,
190
        block_diff.storage_changes,
191
        block_diff.storage_clears,
192
    )
193
    transactions_root = root(block_output.transactions_trie)
194
    receipt_root = root(block_output.receipts_trie)
195
    block_logs_bloom = logs_bloom(block_output.block_logs)
196
197
    if block_output.block_gas_used != block.header.gas_used:
198
        raise InvalidBlock(
199
            f"{block_output.block_gas_used} != {block.header.gas_used}"
200
        )
201
    if transactions_root != block.header.transactions_root:
202
        raise InvalidBlock
203
    if block_state_root != block.header.state_root:
204
        raise InvalidBlock
205
    if receipt_root != block.header.receipt_root:
206
        raise InvalidBlock
207
    if block_logs_bloom != block.header.bloom:
208
        raise InvalidBlock
209
210
    apply_changes_to_state(chain.state, block_diff)
211
    chain.blocks.append(block)
212
    if len(chain.blocks) > 255:
213
        # Real clients have to store more blocks to deal with reorgs, but the
214
        # protocol only requires the last 255
215
        chain.blocks = chain.blocks[-255:]

validate_header

Verifies a block header.

In order to consider a block's header valid, the logic for the quantities in the header should match the logic for the block itself. For example the header timestamp should be greater than the block's parent timestamp because the block was created after the parent block. Additionally, the block's number should be directly following the parent block's number since it is the next block in the sequence.

Parameters

chain : History and current state. header : Header to check for correctness.

def validate_header(chain: BlockChain, ​​header: Header) -> None:
219
    <snip>
237
    if header.number < Uint(1):
238
        raise InvalidBlock
239
    parent_header_number = header.number - Uint(1)
240
    first_block_number = chain.blocks[0].header.number
241
    last_block_number = chain.blocks[-1].header.number
242
243
    if (
244
        parent_header_number < first_block_number
245
        or parent_header_number > last_block_number
246
    ):
247
        raise InvalidBlock
248
249
    parent_header = chain.blocks[
250
        parent_header_number - first_block_number
251
    ].header
252
253
    if header.gas_used > header.gas_limit:
254
        raise InvalidBlock
255
256
    if header.timestamp <= parent_header.timestamp:
257
        raise InvalidBlock
258
    if header.number != parent_header.number + Uint(1):
259
        raise InvalidBlock
260
    if not check_gas_limit(header.gas_limit, parent_header.gas_limit):
261
        raise InvalidBlock
262
    if len(header.extra_data) > 32:
263
        raise InvalidBlock
264
265
    block_difficulty = calculate_block_difficulty(
266
        header.number,
267
        header.timestamp,
268
        parent_header.timestamp,
269
        parent_header.difficulty,
270
    )
271
    if header.difficulty != block_difficulty:
272
        raise InvalidBlock
273
274
    block_parent_hash = keccak256(rlp.encode(parent_header))
275
    if header.parent_hash != block_parent_hash:
276
        raise InvalidBlock
277
278
    validate_proof_of_work(header)

generate_header_hash_for_pow

Generate rlp hash of the header which is to be used for Proof-of-Work verification.

In other words, the PoW artefacts mix_digest and nonce are ignored while calculating this hash.

A particular PoW is valid for a single hash, that hash is computed by this function. The nonce and mix_digest are omitted from this hash because they are being changed by miners in their search for a sufficient proof-of-work.

Parameters

header : The header object for which the hash is to be generated.

Returns

hash : Hash32 The PoW valid rlp hash of the passed in header.

def generate_header_hash_for_pow(header: Header) -> Hash32:
282
    <snip>
305
    header_data_without_pow_artefacts = (
306
        header.parent_hash,
307
        header.ommers_hash,
308
        header.coinbase,
309
        header.state_root,
310
        header.transactions_root,
311
        header.receipt_root,
312
        header.bloom,
313
        header.difficulty,
314
        header.number,
315
        header.gas_limit,
316
        header.gas_used,
317
        header.timestamp,
318
        header.extra_data,
319
    )
320
321
    return keccak256(rlp.encode(header_data_without_pow_artefacts))

validate_proof_of_work

Validates the Proof of Work constraints.

In order to verify that a miner's proof-of-work is valid for a block, a mix-digest and result are calculated using the hashimoto_light hash function. The mix digest is a hash of the header and the nonce that is passed through and it confirms whether or not proof-of-work was done on the correct block. The result is the actual hash value of the block.

Parameters

header : Header of interest.

def validate_proof_of_work(header: Header) -> None:
325
    <snip>
340
    header_hash = generate_header_hash_for_pow(header)
341
    # TODO: Memoize this somewhere and read from that data instead of
342
    # calculating cache for every block validation.
343
    cache = generate_cache(header.number)
344
    mix_digest, result = hashimoto_light(
345
        header_hash, header.nonce, cache, dataset_size(header.number)
346
    )
347
    if mix_digest != header.mix_digest:
348
        raise InvalidBlock
349
350
    limit = Uint(U256.MAX_VALUE) + Uint(1)
351
    if Uint.from_be_bytes(result) > (limit // header.difficulty):
352
        raise InvalidBlock

check_transaction

Check if the transaction is includable in the block.

Parameters

block_env : The block scoped environment. block_output : The block output for the current block. tx : The transaction. tx_state : The transaction state tracker.

Returns

sender_address : The sender of the transaction.

Raises

GasUsedExceedsLimitError : If the gas used by the transaction exceeds the block's gas limit. NonceMismatchError : If the nonce of the transaction is not equal to the sender's nonce. InsufficientBalanceError : If the sender's balance is not enough to pay for the transaction. InvalidSenderError : If the transaction is from an address that does not exist anymore.

def check_transaction(block_env: ethereum.forks.frontier.vm.BlockEnvironmentethereum.forks.homestead.vm.BlockEnvironment, ​​block_output: ethereum.forks.frontier.vm.BlockOutputethereum.forks.homestead.vm.BlockOutput, ​​tx: Transaction, ​​tx_state: TransactionState) -> Address:
361
    <snip>
392
    gas_available = block_env.block_gas_limit - block_output.block_gas_used
393
    if tx.gas > gas_available:
394
        raise GasUsedExceedsLimitError("gas used exceeds limit")
395
    sender_address = recover_sender(tx)
396
    sender_account = get_account(tx_state, sender_address)
397
398
    max_gas_fee = tx.gas * tx.gas_price
399
400
    if sender_account.nonce > Uint(tx.nonce):
401
        raise NonceMismatchError("nonce too low")
402
    elif sender_account.nonce < Uint(tx.nonce):
403
        raise NonceMismatchError("nonce too high")
404
    if Uint(sender_account.balance) < max_gas_fee + Uint(tx.value):
405
        raise InsufficientBalanceError("insufficient sender balance")
406
    if sender_account.code_hash != EMPTY_CODE_HASH:
407
        raise InvalidSenderError("not EOA")
408
409
    return sender_address

make_receipt

Make the receipt for a transaction that was executed.

Parameters

post_state : The state root immediately after this transaction. cumulative_gas_used : The total gas used so far in the block after the transaction was executed. logs : The logs produced by the transaction.

Returns

receipt : The receipt for the transaction.

def make_receipt(post_state: Bytes32, ​​cumulative_gas_used: Uint, ​​logs: Tuple[Log, ...]) -> Receipt:
417
    <snip>
436
    receipt = Receipt(
437
        post_state=post_state,
438
        cumulative_gas_used=cumulative_gas_used,
439
        bloom=logs_bloom(logs),
440
        logs=logs,
441
    )
442
443
    return receipt

apply_body

Executes a block.

Many of the contents of a block are stored in data structures called tries. There is a transactions trie which is similar to a ledger of the transactions stored in the current block. There is also a receipts trie which stores the results of executing a transaction, like the post state and gas used. This function creates and executes the block that is to be added to the chain.

Parameters

block_env : The block scoped environment. transactions : Transactions included in the block. ommers : Headers of ancestor blocks which are not direct parents (formerly uncles.)

Returns

block_output : The block output for the current block.

def apply_body(block_env: ethereum.forks.frontier.vm.BlockEnvironmentethereum.forks.homestead.vm.BlockEnvironment, ​​transactions: Tuple[Transaction, ...], ​​ommers: Tuple[Header, ...]) -> ethereum.forks.frontier.vm.BlockOutputethereum.forks.homestead.vm.BlockOutput:
451
    <snip>
477
    block_output = vm.BlockOutput()
478
479
    for i, tx in enumerate(transactions):
480
        process_transaction(block_env, block_output, tx, Uint(i))
481
482
    pay_rewards(block_env, ommers)
483
484
    return block_output

validate_ommers

Validates the ommers mentioned in the block.

An ommer block is a block that wasn't canonically added to the blockchain because it wasn't validated as fast as the canonical block but was mined at the same time.

To be considered valid, the ommers must adhere to the rules defined in the Ethereum protocol. The maximum amount of ommers is 2 per block and there cannot be duplicate ommers in a block. Many of the other ommer constraints are listed in the in-line comments of this function.

Parameters

ommers : List of ommers mentioned in the current block. block_header: The header of current block. chain : History and current state.

def validate_ommers(ommers: Tuple[Header, ...], ​​block_header: Header, ​​chain: BlockChain) -> None:
490
    <snip>
512
    block_hash = keccak256(rlp.encode(block_header))
513
    if keccak256(rlp.encode(ommers)) != block_header.ommers_hash:
514
        raise InvalidBlock
515
516
    if len(ommers) == 0:
517
        # Nothing to validate
518
        return
519
520
    # Check that each ommer satisfies the constraints of a header
521
    for ommer in ommers:
522
        if Uint(1) > ommer.number or ommer.number >= block_header.number:
523
            raise InvalidBlock
524
        validate_header(chain, ommer)
525
    if len(ommers) > 2:
526
        raise InvalidBlock
527
528
    ommers_hashes = [keccak256(rlp.encode(ommer)) for ommer in ommers]
529
    if len(ommers_hashes) != len(set(ommers_hashes)):
530
        raise InvalidBlock
531
532
    recent_canonical_blocks = chain.blocks[-(MAX_OMMER_DEPTH + Uint(1)) :]
533
    recent_canonical_block_hashes = {
534
        keccak256(rlp.encode(block.header))
535
        for block in recent_canonical_blocks
536
    }
537
    recent_ommers_hashes: Set[Hash32] = set()
538
    for block in recent_canonical_blocks:
539
        recent_ommers_hashes = recent_ommers_hashes.union(
540
            {keccak256(rlp.encode(ommer)) for ommer in block.ommers}
541
        )
542
543
    for ommer_index, ommer in enumerate(ommers):
544
        ommer_hash = ommers_hashes[ommer_index]
545
        if ommer_hash == block_hash:
546
            raise InvalidBlock
547
        if ommer_hash in recent_canonical_block_hashes:
548
            raise InvalidBlock
549
        if ommer_hash in recent_ommers_hashes:
550
            raise InvalidBlock
551
552
        # Ommer age with respect to the current block. For example, an age of
553
        # 1 indicates that the ommer is a sibling of previous block.
554
        ommer_age = block_header.number - ommer.number
555
        if Uint(1) > ommer_age or ommer_age > MAX_OMMER_DEPTH:
556
            raise InvalidBlock
557
        if ommer.parent_hash not in recent_canonical_block_hashes:
558
            raise InvalidBlock
559
        if ommer.parent_hash == block_header.parent_hash:
560
            raise InvalidBlock

pay_rewards

Pay rewards to the block miner as well as the ommers miners.

The miner of the canonical block is rewarded with the predetermined block reward, BLOCK_REWARD, plus a variable award based off of the number of ommer blocks that were mined around the same time, and included in the canonical block's header. An ommer block is a block that wasn't added to the canonical blockchain because it wasn't validated as fast as the accepted block but was mined at the same time. Although not all blocks that are mined are added to the canonical chain, miners are still paid a reward for their efforts. This reward is called an ommer reward and is calculated based on the number associated with the ommer block that they mined.

Parameters

block_env : The block scoped environment. ommers : List of ommers mentioned in the current block.

def pay_rewards(block_env: ethereum.forks.frontier.vm.BlockEnvironmentethereum.forks.homestead.vm.BlockEnvironment, ​​ommers: Tuple[Header, ...]) -> None:
567
    <snip>
589
    rewards_state = TransactionState(parent=block_env.state)
590
    ommer_count = U256(len(ommers))
591
    miner_reward = BLOCK_REWARD + (ommer_count * (BLOCK_REWARD // U256(32)))
592
    create_ether(rewards_state, block_env.coinbase, miner_reward)
593
594
    for ommer in ommers:
595
        # Ommer age with respect to the current block.
596
        ommer_age = U256(block_env.number - ommer.number)
597
        ommer_miner_reward = ((U256(8) - ommer_age) * BLOCK_REWARD) // U256(8)
598
        create_ether(rewards_state, ommer.coinbase, ommer_miner_reward)
599
600
    incorporate_tx_into_block(rewards_state)

process_transaction

Execute a transaction against the provided environment.

This function processes the actions needed to execute a transaction. It decrements the sender's account balance after calculating the gas fee and refunds them the proper amount after execution. Calling contracts, deploying code, and incrementing nonces are all examples of actions that happen within this function or from a call made within this function.

Accounts that are marked for deletion are processed and destroyed after execution.

Parameters

block_env : Environment for the Ethereum Virtual Machine. block_output : The block output for the current block. tx : Transaction to execute. index: Index of the transaction in the block.

def process_transaction(block_env: ethereum.forks.frontier.vm.BlockEnvironmentethereum.forks.homestead.vm.BlockEnvironment, ​​block_output: ethereum.forks.frontier.vm.BlockOutputethereum.forks.homestead.vm.BlockOutput, ​​tx: Transaction, ​​index: Uint) -> None:
609
    <snip>
633
    tx_state = TransactionState(parent=block_env.state)
634
635
    trie_set(block_output.transactions_trie, rlp.encode(Uint(index)), tx)
636
    intrinsic_gas = validate_transaction(tx)
637
638
    sender = check_transaction(
639
        block_env=block_env,
640
        block_output=block_output,
641
        tx=tx,
642
        tx_state=tx_state,
643
    )
644
645
    sender_account = get_account(tx_state, sender)
646
647
    gas = tx.gas - intrinsic_gas
648
    increment_nonce(tx_state, sender)
649
650
    gas_fee = tx.gas * tx.gas_price
651
    sender_balance_after_gas_fee = Uint(sender_account.balance) - gas_fee
652
    set_account_balance(tx_state, sender, U256(sender_balance_after_gas_fee))
653
654
    tx_env = vm.TransactionEnvironment(
655
        origin=sender,
656
        gas_price=tx.gas_price,
657
        gas=gas,
658
        state=tx_state,
659
        index_in_block=index,
660
        tx_hash=get_transaction_hash(tx),
661
    )
662
663
    message = prepare_message(block_env, tx_env, tx)
664
665
    tx_output = process_message_call(message)
666
667
    tx_gas_used_before_refund = tx.gas - tx_output.gas_left
668
    tx_gas_refund = min(
669
        tx_gas_used_before_refund // Uint(2), Uint(tx_output.refund_counter)
670
    )
671
    tx_gas_used_after_refund = tx_gas_used_before_refund - tx_gas_refund
672
    tx_gas_left = tx.gas - tx_gas_used_after_refund
673
    gas_refund_amount = tx_gas_left * tx.gas_price
674
675
    transaction_fee = tx_gas_used_after_refund * tx.gas_price
676
677
    # refund gas
678
    create_ether(tx_state, sender, U256(gas_refund_amount))
679
680
    # transfer miner fees
681
    create_ether(tx_state, block_env.coinbase, U256(transaction_fee))
682
683
    for address in tx_output.accounts_to_delete:
684
        destroy_account(tx_state, address)
685
686
    block_output.block_gas_used += tx_gas_used_after_refund
687
688
    incorporate_tx_into_block(tx_state)
689
690
    block_state = block_env.state
691
    block_diff = extract_block_diff(block_state)
692
    intermediate_state_root, _ = (
693
        block_state.pre_state.compute_state_root_and_trie_changes(
694
            block_diff.account_changes,
695
            block_diff.storage_changes,
696
            block_diff.storage_clears,
697
        )
698
    )
699
700
    receipt = make_receipt(
701
        intermediate_state_root,
702
        block_output.block_gas_used,
703
        tx_output.logs,
704
    )
705
706
    receipt_key = rlp.encode(Uint(index))
707
    block_output.receipt_keys += (receipt_key,)
708
709
    trie_set(
710
        block_output.receipts_trie,
711
        receipt_key,
712
        receipt,
713
    )
714
715
    block_output.block_logs += tx_output.logs

check_gas_limit

Validates the gas limit for a block.

The bounds of the gas limit, max_adjustment_delta, is set as the quotient of the parent block's gas limit and the LIMIT_ADJUSTMENT_FACTOR. Therefore, if the gas limit that is passed. Therefore, if the gas limit that is through as a parameter is greater than or equal to the passed through as a parameter is greater than or equal to the sum of the of parent's gas and the adjustment delta then the limit for gas is too highthe parent's gas and the adjustment delta then the limit for gas is too and fails this function's check. Similarly, if the limit is less than orhigh and fails this function's check. Similarly, if the limit is less equal to the than or equal to the difference of the parent's gas and the adjustment delta of the parent's gas and the adjustment delta or the predefined LIMIT_MINIMUM then this function's the predefined LIMIT_MINIMUM then this function's check fails becausecheck fails because the gas limit doesn't allow for a sufficient or the gas limit doesn't allow for a sufficient or reasonable amount of gas to be used on a block.reasonable amount of gas to be used on a block.

Parameters

gas_limit : Gas limit to validate.

parent_gas_limit : Gas limit of the parent block.

Returns

check : bool True if gas limit constraints are satisfied, False otherwise.

def check_gas_limit(gas_limit: Uint, ​​parent_gas_limit: Uint) -> bool:
719
    <snip>
747
    max_adjustment_delta = parent_gas_limit // GasCosts.LIMIT_ADJUSTMENT_FACTOR
748
    if gas_limit >= parent_gas_limit + max_adjustment_delta:
749
        return False
750
    if gas_limit <= parent_gas_limit - max_adjustment_delta:
751
        return False
752
    if gas_limit < GasCosts.LIMIT_MINIMUM:
753
        return False
754
755
    return True

calculate_block_difficulty

Computes difficulty of a block using its header and parent header.

The difficulty of a block is determined by the time the block was createdThe difficulty is determined by the time the block was created after its after its parent. If a block's timestamp is more than 13 seconds after itsparent. The offset is calculated using the parent block's difficulty, parent block then its difficulty is set as the difference between theparent_difficulty, and the timestamp between blocks. This offset is parent's difficulty and the then added to the parent difficulty and is stored as the max_adjustment_deltadifficulty. Otherwise, if the time between parent and child blocks is too small (under 13 seconds) then,variable. If the time between the block and its parent is too short, the to avoid mass forking, the block's difficulty is set to the sum of theoffset will result in a positive number thus making the sum of delta and the parent's difficulty.parent_difficulty and offset to be a greater value in order to avoid mass forking. But, if the time is long enough, then the offset results in a negative value making the block less difficult than its parent.

The base standard for a block's difficulty is the predefined value set for the genesis block since it has no parent. So, a block can't be less difficult than the genesis block, therefore each block's difficulty is set to the maximum value between the calculated difficulty and the MINIMUM_DIFFICULTY.

Parameters

block_number : Block number of the block. block_timestamp : Timestamp of the block. parent_timestamp : Timestamp of the parent block. parent_difficulty : difficulty of the parent block.

Returns

difficulty : ethereum.base_types.Uint Computed difficulty for a block.

def calculate_block_difficulty(block_number: Uint, ​​block_timestamp: U256, ​​parent_timestamp: U256, ​​parent_difficulty: Uint) -> Uint:
764
    <snip>
792
    max_adjustment_delta = parent_difficulty // Uint(2048)
793
    if block_timestamp < parent_timestamp + U256(13):
794
        difficulty = parent_difficulty + max_adjustment_delta
795
    else:  # block_timestamp >= parent_timestamp + 13
796
        difficulty = parent_difficulty - max_adjustment_delta
797
801
    offset = (
802
        int(parent_difficulty)
803
        // 2048
804
        * max(1 - int(block_timestamp - parent_timestamp) // 10, -99)
805
    )
806
    difficulty = int(parent_difficulty) + offset
807
    # Historical Note: The difficulty bomb was not present in Ethereum at the
808
    # start of Frontier, but was added shortly after launch. However since the
809
    # bomb has no effect prior to block 200000 we pretend it existed from
810
    # genesis.
811
    # See https://github.com/ethereum/go-ethereum/pull/1588
812
    num_bomb_periods = (int(block_number) // 100000) - 2
813
    if num_bomb_periods >= 0:
805
        difficulty += Uint(2**num_bomb_periods)
814
        difficulty += 2**num_bomb_periods
815
816
    # Some clients raise the difficulty to `MINIMUM_DIFFICULTY` prior to adding
817
    # the bomb. This bug does not matter because the difficulty is always much
818
    # greater than `MINIMUM_DIFFICULTY` on Mainnet.
810
    return max(difficulty, MINIMUM_DIFFICULTY)
819
    return Uint(max(difficulty, int(MINIMUM_DIFFICULTY)))