ethereum.forks.constantinople.forkethereum.forks.istanbul.fork

Ethereum Specification.

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

Introduction

Entry point for the Ethereum specification.

BLOCK_REWARD

64
BLOCK_REWARD = U256(2 * 10**18)

MINIMUM_DIFFICULTY

65
MINIMUM_DIFFICULTY = Uint(131072)

MAX_OMMER_DEPTH

66
MAX_OMMER_DEPTH = Uint(6)

BOMB_DELAY_BLOCKS

67
BOMB_DELAY_BLOCKS = 5000000

EMPTY_OMMER_HASH

68
EMPTY_OMMER_HASH = keccak256(rlp.encode([]))

BlockChain

History and current state of the block chain.

71
@dataclass
class BlockChain:

blocks

77
    blocks: List[Block]

state

78
    state: State

chain_id

79
    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:
83
    <snip>
102
    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]:
106
    <snip>
126
    recent_blocks = chain.blocks[-255:]
127
    # TODO: This function has not been tested rigorously
128
    if len(recent_blocks) == 0:
129
        return []
130
131
    recent_block_hashes = []
132
133
    for block in recent_blocks:
134
        prev_block_hash = block.header.parent_hash
135
        recent_block_hashes.append(prev_block_hash)
136
137
    # We are computing the hash only for the most recent block and not for
138
    # the rest of the blocks as they have successors which have the hash of
139
    # the current block as parent hash.
140
    most_recent_block_hash = keccak256(rlp.encode(recent_blocks[-1].header))
141
    recent_block_hashes.append(most_recent_block_hash)
142
143
    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:
147
    <snip>
169
    validate_header(chain, block.header)
170
    validate_ommers(block.ommers, block.header, chain)
171
172
    block_state = BlockState(pre_state=chain.state)
173
174
    block_env = vm.BlockEnvironment(
175
        chain_id=chain.chain_id,
176
        state=block_state,
177
        block_gas_limit=block.header.gas_limit,
178
        block_hashes=get_last_256_block_hashes(chain),
179
        coinbase=block.header.coinbase,
180
        number=block.header.number,
181
        time=block.header.timestamp,
182
        difficulty=block.header.difficulty,
183
    )
184
185
    block_output = apply_body(
186
        block_env=block_env,
187
        transactions=block.transactions,
188
        ommers=block.ommers,
189
    )
190
    block_diff = extract_block_diff(block_state)
191
    block_state_root, _ = chain.state.compute_state_root_and_trie_changes(
192
        block_diff.account_changes,
193
        block_diff.storage_changes,
194
        block_diff.storage_clears,
195
    )
196
    transactions_root = root(block_output.transactions_trie)
197
    receipt_root = root(block_output.receipts_trie)
198
    block_logs_bloom = logs_bloom(block_output.block_logs)
199
200
    if block_output.block_gas_used != block.header.gas_used:
201
        raise InvalidBlock(
202
            f"{block_output.block_gas_used} != {block.header.gas_used}"
203
        )
204
    if transactions_root != block.header.transactions_root:
205
        raise InvalidBlock
206
    if block_state_root != block.header.state_root:
207
        raise InvalidBlock
208
    if receipt_root != block.header.receipt_root:
209
        raise InvalidBlock
210
    if block_logs_bloom != block.header.bloom:
211
        raise InvalidBlock
212
213
    apply_changes_to_state(chain.state, block_diff)
214
    chain.blocks.append(block)
215
    if len(chain.blocks) > 255:
216
        # Real clients have to store more blocks to deal with reorgs, but the
217
        # protocol only requires the last 255
218
        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:
222
    <snip>
240
    if header.number < Uint(1):
241
        raise InvalidBlock
242
    parent_header_number = header.number - Uint(1)
243
    first_block_number = chain.blocks[0].header.number
244
    last_block_number = chain.blocks[-1].header.number
245
246
    if (
247
        parent_header_number < first_block_number
248
        or parent_header_number > last_block_number
249
    ):
250
        raise InvalidBlock
251
252
    parent_header = chain.blocks[
253
        parent_header_number - first_block_number
254
    ].header
255
256
    if header.gas_used > header.gas_limit:
257
        raise InvalidBlock
258
259
    parent_has_ommers = parent_header.ommers_hash != EMPTY_OMMER_HASH
260
    if header.timestamp <= parent_header.timestamp:
261
        raise InvalidBlock
262
    if header.number != parent_header.number + Uint(1):
263
        raise InvalidBlock
264
    if not check_gas_limit(header.gas_limit, parent_header.gas_limit):
265
        raise InvalidBlock
266
    if len(header.extra_data) > 32:
267
        raise InvalidBlock
268
269
    block_difficulty = calculate_block_difficulty(
270
        header.number,
271
        header.timestamp,
272
        parent_header.timestamp,
273
        parent_header.difficulty,
274
        parent_has_ommers,
275
    )
276
    if header.difficulty != block_difficulty:
277
        raise InvalidBlock
278
279
    block_parent_hash = keccak256(rlp.encode(parent_header))
280
    if header.parent_hash != block_parent_hash:
281
        raise InvalidBlock
282
283
    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:
287
    <snip>
310
    header_data_without_pow_artefacts = (
311
        header.parent_hash,
312
        header.ommers_hash,
313
        header.coinbase,
314
        header.state_root,
315
        header.transactions_root,
316
        header.receipt_root,
317
        header.bloom,
318
        header.difficulty,
319
        header.number,
320
        header.gas_limit,
321
        header.gas_used,
322
        header.timestamp,
323
        header.extra_data,
324
    )
325
326
    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:
330
    <snip>
345
    header_hash = generate_header_hash_for_pow(header)
346
    # TODO: Memoize this somewhere and read from that data instead of
347
    # calculating cache for every block validation.
348
    cache = generate_cache(header.number)
349
    mix_digest, result = hashimoto_light(
350
        header_hash, header.nonce, cache, dataset_size(header.number)
351
    )
352
    if mix_digest != header.mix_digest:
353
        raise InvalidBlock
354
355
    limit = Uint(U256.MAX_VALUE) + Uint(1)
356
    if Uint.from_be_bytes(result) > (limit // header.difficulty):
357
        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.constantinople.vm.BlockEnvironmentethereum.forks.istanbul.vm.BlockEnvironment, ​​block_output: ethereum.forks.constantinople.vm.BlockOutputethereum.forks.istanbul.vm.BlockOutput, ​​tx: Transaction, ​​tx_state: TransactionState) -> Address:
366
    <snip>
397
    gas_available = block_env.block_gas_limit - block_output.block_gas_used
398
    if tx.gas > gas_available:
399
        raise GasUsedExceedsLimitError("gas used exceeds limit")
400
    sender_address = recover_sender(block_env.chain_id, tx)
401
    sender_account = get_account(tx_state, sender_address)
402
403
    max_gas_fee = tx.gas * tx.gas_price
404
405
    if sender_account.nonce > Uint(tx.nonce):
406
        raise NonceMismatchError("nonce too low")
407
    elif sender_account.nonce < Uint(tx.nonce):
408
        raise NonceMismatchError("nonce too high")
409
    if Uint(sender_account.balance) < max_gas_fee + Uint(tx.value):
410
        raise InsufficientBalanceError("insufficient sender balance")
411
    if sender_account.code_hash != EMPTY_CODE_HASH:
412
        raise InvalidSenderError("not EOA")
413
414
    return sender_address

make_receipt

Make the receipt for a transaction that was executed.

Parameters

error : Error in the top level frame of the transaction, if any. 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(error: Optional[EthereumException], ​​cumulative_gas_used: Uint, ​​logs: Tuple[Log, ...]) -> Receipt:
422
    <snip>
441
    receipt = Receipt(
442
        succeeded=error is None,
443
        cumulative_gas_used=cumulative_gas_used,
444
        bloom=logs_bloom(logs),
445
        logs=logs,
446
    )
447
448
    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.constantinople.vm.BlockEnvironmentethereum.forks.istanbul.vm.BlockEnvironment, ​​transactions: Tuple[Transaction, ...], ​​ommers: Tuple[Header, ...]) -> ethereum.forks.constantinople.vm.BlockOutputethereum.forks.istanbul.vm.BlockOutput:
456
    <snip>
482
    block_output = vm.BlockOutput()
483
484
    for i, tx in enumerate(transactions):
485
        process_transaction(block_env, block_output, tx, Uint(i))
486
487
    pay_rewards(block_env, ommers)
488
489
    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:
495
    <snip>
517
    block_hash = keccak256(rlp.encode(block_header))
518
    if keccak256(rlp.encode(ommers)) != block_header.ommers_hash:
519
        raise InvalidBlock
520
521
    if len(ommers) == 0:
522
        # Nothing to validate
523
        return
524
525
    # Check that each ommer satisfies the constraints of a header
526
    for ommer in ommers:
527
        if Uint(1) > ommer.number or ommer.number >= block_header.number:
528
            raise InvalidBlock
529
        validate_header(chain, ommer)
530
    if len(ommers) > 2:
531
        raise InvalidBlock
532
533
    ommers_hashes = [keccak256(rlp.encode(ommer)) for ommer in ommers]
534
    if len(ommers_hashes) != len(set(ommers_hashes)):
535
        raise InvalidBlock
536
537
    recent_canonical_blocks = chain.blocks[-(MAX_OMMER_DEPTH + Uint(1)) :]
538
    recent_canonical_block_hashes = {
539
        keccak256(rlp.encode(block.header))
540
        for block in recent_canonical_blocks
541
    }
542
    recent_ommers_hashes: Set[Hash32] = set()
543
    for block in recent_canonical_blocks:
544
        recent_ommers_hashes = recent_ommers_hashes.union(
545
            {keccak256(rlp.encode(ommer)) for ommer in block.ommers}
546
        )
547
548
    for ommer_index, ommer in enumerate(ommers):
549
        ommer_hash = ommers_hashes[ommer_index]
550
        if ommer_hash == block_hash:
551
            raise InvalidBlock
552
        if ommer_hash in recent_canonical_block_hashes:
553
            raise InvalidBlock
554
        if ommer_hash in recent_ommers_hashes:
555
            raise InvalidBlock
556
557
        # Ommer age with respect to the current block. For example, an age of
558
        # 1 indicates that the ommer is a sibling of previous block.
559
        ommer_age = block_header.number - ommer.number
560
        if Uint(1) > ommer_age or ommer_age > MAX_OMMER_DEPTH:
561
            raise InvalidBlock
562
        if ommer.parent_hash not in recent_canonical_block_hashes:
563
            raise InvalidBlock
564
        if ommer.parent_hash == block_header.parent_hash:
565
            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.constantinople.vm.BlockEnvironmentethereum.forks.istanbul.vm.BlockEnvironment, ​​ommers: Tuple[Header, ...]) -> None:
572
    <snip>
594
    rewards_state = TransactionState(parent=block_env.state)
595
    ommer_count = U256(len(ommers))
596
    miner_reward = BLOCK_REWARD + (ommer_count * (BLOCK_REWARD // U256(32)))
597
    create_ether(rewards_state, block_env.coinbase, miner_reward)
598
599
    for ommer in ommers:
600
        # Ommer age with respect to the current block.
601
        ommer_age = U256(block_env.number - ommer.number)
602
        ommer_miner_reward = ((U256(8) - ommer_age) * BLOCK_REWARD) // U256(8)
603
        create_ether(rewards_state, ommer.coinbase, ommer_miner_reward)
604
605
    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.constantinople.vm.BlockEnvironmentethereum.forks.istanbul.vm.BlockEnvironment, ​​block_output: ethereum.forks.constantinople.vm.BlockOutputethereum.forks.istanbul.vm.BlockOutput, ​​tx: Transaction, ​​index: Uint) -> None:
614
    <snip>
638
    tx_state = TransactionState(parent=block_env.state)
639
640
    trie_set(block_output.transactions_trie, rlp.encode(Uint(index)), tx)
641
    intrinsic_gas = validate_transaction(tx)
642
643
    sender = check_transaction(
644
        block_env=block_env,
645
        block_output=block_output,
646
        tx=tx,
647
        tx_state=tx_state,
648
    )
649
650
    sender_account = get_account(tx_state, sender)
651
652
    gas = tx.gas - intrinsic_gas
653
    increment_nonce(tx_state, sender)
654
655
    gas_fee = tx.gas * tx.gas_price
656
    sender_balance_after_gas_fee = Uint(sender_account.balance) - gas_fee
657
    set_account_balance(tx_state, sender, U256(sender_balance_after_gas_fee))
658
659
    tx_env = vm.TransactionEnvironment(
660
        origin=sender,
661
        gas_price=tx.gas_price,
662
        gas=gas,
663
        state=tx_state,
664
        index_in_block=index,
665
        tx_hash=get_transaction_hash(tx),
666
    )
667
668
    message = prepare_message(block_env, tx_env, tx)
669
670
    tx_output = process_message_call(message)
671
672
    tx_gas_used_before_refund = tx.gas - tx_output.gas_left
673
    tx_gas_refund = min(
674
        tx_gas_used_before_refund // Uint(2), Uint(tx_output.refund_counter)
675
    )
676
    tx_gas_used_after_refund = tx_gas_used_before_refund - tx_gas_refund
677
    tx_gas_left = tx.gas - tx_gas_used_after_refund
678
    gas_refund_amount = tx_gas_left * tx.gas_price
679
680
    transaction_fee = tx_gas_used_after_refund * tx.gas_price
681
682
    # refund gas
683
    sender_balance_after_refund = get_account(tx_state, sender).balance + U256(
684
        gas_refund_amount
685
    )
686
    set_account_balance(tx_state, sender, sender_balance_after_refund)
687
688
    # transfer miner fees
689
    coinbase_balance_after_mining_fee = get_account(
690
        tx_state, block_env.coinbase
691
    ).balance + U256(transaction_fee)
692
    if coinbase_balance_after_mining_fee != 0:
693
        set_account_balance(
694
            tx_state,
695
            block_env.coinbase,
696
            coinbase_balance_after_mining_fee,
697
        )
698
    elif account_exists_and_is_empty(tx_state, block_env.coinbase):
699
        destroy_account(tx_state, block_env.coinbase)
700
701
    for address in tx_output.accounts_to_delete:
702
        destroy_account(tx_state, address)
703
704
    destroy_touched_empty_accounts(tx_state, tx_output.touched_accounts)
705
706
    block_output.block_gas_used += tx_gas_used_after_refund
707
708
    receipt = make_receipt(
709
        tx_output.error, block_output.block_gas_used, tx_output.logs
710
    )
711
712
    receipt_key = rlp.encode(Uint(index))
713
    block_output.receipt_keys += (receipt_key,)
714
715
    trie_set(
716
        block_output.receipts_trie,
717
        receipt_key,
718
        receipt,
719
    )
720
721
    block_output.block_logs += tx_output.logs
722
723
    incorporate_tx_into_block(tx_state)

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. Therefore, if the gas limit that is passed passed through as a parameter is greater than or equal to the through as a parameter is greater than or equal to the sum of of the the parent's gas and the adjustment delta then the limit for gas is tooparent's gas and the adjustment delta then the limit for gas is too high high and fails this function's check. Similarly, if the limit is lessand fails this function's check. Similarly, if the limit is less than or than or equal to the equal to the difference of the parent's gas and the adjustment of the parent's gas and the adjustment delta or delta or the predefined the predefined LIMIT_MINIMUM then this function's then this function's check fails because check fails because the gas limit doesn't allow for a sufficient orthe gas limit doesn't allow for a sufficient or reasonable amount of gas to reasonable amount of gas to be used on a block.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:
727
    <snip>
755
    max_adjustment_delta = parent_gas_limit // GasCosts.LIMIT_ADJUSTMENT_FACTOR
756
    if gas_limit >= parent_gas_limit + max_adjustment_delta:
757
        return False
758
    if gas_limit <= parent_gas_limit - max_adjustment_delta:
759
        return False
760
    if gas_limit < GasCosts.LIMIT_MINIMUM:
761
        return False
762
763
    return True

calculate_block_difficulty

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

The difficulty is determined by the time the block was created after its parent. The offset is calculated using the parent block's difficulty, parent_difficulty, and the timestamp between blocks. This offset is then added to the parent difficulty and is stored as the difficulty variable. If the time between the block and its parent is too short, the offset will result in a positive number thus making the sum of 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. parent_has_ommers: does the parent have ommers.

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, ​​parent_has_ommers: bool) -> Uint:
773
    <snip>
812
    offset = (
813
        int(parent_difficulty)
814
        // 2048
815
        * max(
816
            (2 if parent_has_ommers else 1)
817
            - int(block_timestamp - parent_timestamp) // 9,
818
            -99,
819
        )
820
    )
821
    difficulty = int(parent_difficulty) + offset
822
    # Historical Note: The difficulty bomb was not present in Ethereum at the
823
    # start of Frontier, but was added shortly after launch. However since the
824
    # bomb has no effect prior to block 200000 we pretend it existed from
825
    # genesis.
826
    # See https://github.com/ethereum/go-ethereum/pull/1588
827
    num_bomb_periods = ((int(block_number) - BOMB_DELAY_BLOCKS) // 100000) - 2
828
    if num_bomb_periods >= 0:
829
        difficulty += 2**num_bomb_periods
830
831
    # Some clients raise the difficulty to `MINIMUM_DIFFICULTY` prior to adding
832
    # the bomb. This bug does not matter because the difficulty is always much
833
    # greater than `MINIMUM_DIFFICULTY` on Mainnet.
834
    return Uint(max(difficulty, int(MINIMUM_DIFFICULTY)))