Contract Address Details

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.24;

import "@openzeppelin/contracts/utils/cryptography/ECDSA.sol";
import "src/shared/common/EssentialContract.sol";
import "src/shared/libs/LibStrings.sol";
import "../automata-attestation/interfaces/IAttestation.sol";
import "../automata-attestation/lib/QuoteV3Auth/V3Struct.sol";
import "../based/ITaikoInbox.sol";
import "./LibPublicInput.sol";
import "./IVerifier.sol";

/// @title SgxVerifier
/// @notice This contract is the implementation of verifying SGX signature proofs
/// onchain.
/// @dev Please see references below:
/// - Reference #1: https://ethresear.ch/t/2fa-zk-rollups-using-sgx/14462
/// - Reference #2: https://github.com/gramineproject/gramine/discussions/1579
/// @custom:security-contact security@taiko.xyz
contract SgxVerifier is EssentialContract, IVerifier {
    /// @dev Each public-private key pair (Ethereum address) is generated within
    /// the SGX program when it boots up. The off-chain remote attestation
    /// ensures the validity of the program hash and has the capability of
    /// bootstrapping the network with trustworthy instances.
    struct Instance {
        address addr;
        uint64 validSince;
    }

    /// @notice The expiry time for the SGX instance.
    uint64 public constant INSTANCE_EXPIRY = 365 days;

    /// @notice A security feature, a delay until an instance is enabled when using onchain RA
    /// verification
    uint64 public constant INSTANCE_VALIDITY_DELAY = 0;

    uint64 public immutable taikoChainId;
    address public immutable taikoInbox;
    address public immutable taikoProofVerifier;
    address public immutable automataDcapAttestation;

    /// @dev For gas savings, we shall assign each SGX instance with an id that when we need to
    /// set a new pub key, just write storage once.
    /// Slot 1.
    uint256 public nextInstanceId;

    /// @dev One SGX instance is uniquely identified (on-chain) by it's ECDSA public key
    /// (or rather ethereum address). Once that address is used (by proof verification) it has to be
    /// overwritten by a new one (representing the same instance). This is due to side-channel
    /// protection. Also this public key shall expire after some time
    /// (for now it is a long enough 6 months setting).
    /// Slot 2.
    mapping(uint256 instanceId => Instance instance) public instances;

    /// @dev One address shall be registered (during attestation) only once, otherwise it could
    /// bypass this contract's expiry check by always registering with the same attestation and
    /// getting multiple valid instanceIds. While during proving, it is technically possible to
    /// register the old addresses, it is less of a problem, because the instanceId would be the
    /// same for those addresses and if deleted - the attestation cannot be reused anyways.
    /// Slot 3.
    mapping(address instanceAddress => bool alreadyAttested) public addressRegistered;

    uint256[47] private __gap;

    /// @notice Emitted when a new SGX instance is added to the registry, or replaced.
    /// @param id The ID of the SGX instance.
    /// @param instance The address of the SGX instance.
    /// @param replaced The address of the SGX instance that was replaced. If it is the first
    /// instance, this value is zero address.
    /// @param validSince The time since the instance is valid.
    event InstanceAdded(
        uint256 indexed id, address indexed instance, address indexed replaced, uint256 validSince
    );

    /// @notice Emitted when an SGX instance is deleted from the registry.
    /// @param id The ID of the SGX instance.
    /// @param instance The address of the SGX instance.
    event InstanceDeleted(uint256 indexed id, address indexed instance);

    error SGX_ALREADY_ATTESTED();
    error SGX_INVALID_ATTESTATION();
    error SGX_INVALID_INSTANCE();
    error SGX_INVALID_PROOF();

    constructor(
        uint64 _taikoChainId,
        address _taikoInbox,
        address _taikoProofVerifier,
        address _automataDcapAttestation
    )
        EssentialContract(address(0))
    {
        taikoChainId = _taikoChainId;
        taikoInbox = _taikoInbox;
        taikoProofVerifier = _taikoProofVerifier;
        automataDcapAttestation = _automataDcapAttestation;
    }

    /// @notice Initializes the contract.
    /// @param _owner The owner of this contract. msg.sender will be used if this value is zero.
    function init(address _owner) external initializer {
        __Essential_init(_owner);
    }

    /// @notice Adds trusted SGX instances to the registry.
    /// @param _instances The address array of trusted SGX instances.
    /// @return The respective instanceId array per addresses.
    function addInstances(address[] calldata _instances)
        external
        onlyOwner
        returns (uint256[] memory)
    {
        return _addInstances(_instances, true);
    }

    /// @notice Deletes SGX instances from the registry.
    /// @param _ids The ids array of SGX instances.
    function deleteInstances(uint256[] calldata _ids) external onlyOwner {
        uint256 size = _ids.length;
        for (uint256 i; i < size; ++i) {
            uint256 idx = _ids[i];

            require(instances[idx].addr != address(0), SGX_INVALID_INSTANCE());

            emit InstanceDeleted(idx, instances[idx].addr);

            delete instances[idx];
        }
    }

    /// @notice Adds an SGX instance after the attestation is verified
    /// @param _attestation The parsed attestation quote.
    /// @return The respective instanceId
    function registerInstance(V3Struct.ParsedV3QuoteStruct calldata _attestation)
        external
        returns (uint256)
    {
        (bool verified,) = IAttestation(automataDcapAttestation).verifyParsedQuote(_attestation);
        require(verified, SGX_INVALID_ATTESTATION());

        address[] memory addresses = new address[](1);
        addresses[0] = address(bytes20(_attestation.localEnclaveReport.reportData));

        return _addInstances(addresses, false)[0];
    }

    /// @inheritdoc IVerifier
    function verifyProof(
        Context[] calldata _ctxs,
        bytes calldata _proof
    )
        external
        onlyFromEither(taikoInbox, taikoProofVerifier)
    {
        // Size is: 109 bytes
        // 4 bytes + 20 bytes + 20 bytes + 65 bytes (signature) = 109
        require(_proof.length == 109, SGX_INVALID_PROOF());

        address oldInstance = address(bytes20(_proof[4:24]));
        address newInstance = address(bytes20(_proof[24:44]));

        // Collect public inputs
        uint256 size = _ctxs.length;
        bytes32[] memory publicInputs = new bytes32[](size + 2);
        // First public input is the current instance public key
        publicInputs[0] = bytes32(uint256(uint160(oldInstance)));
        publicInputs[1] = bytes32(uint256(uint160(newInstance)));

        // All other inputs are the block program public inputs (a single 32 byte value)
        for (uint256 i; i < size; ++i) {
            // TODO(Yue): For now this assumes the new instance public key to remain the same
            publicInputs[i + 2] = LibPublicInput.hashPublicInputs(
                _ctxs[i].transition, address(this), newInstance, _ctxs[i].metaHash, taikoChainId
            );
        }

        bytes32 signatureHash = keccak256(abi.encodePacked(publicInputs));
        // Verify the blocks
        bytes memory signature = _proof[44:];
        require(oldInstance == ECDSA.recover(signatureHash, signature), SGX_INVALID_PROOF());

        uint32 id = uint32(bytes4(_proof[:4]));
        require(_isInstanceValid(id, oldInstance), SGX_INVALID_INSTANCE());

        if (newInstance != oldInstance && newInstance != address(0)) {
            _replaceInstance(id, oldInstance, newInstance);
        }
    }

    function _addInstances(
        address[] memory _instances,
        bool instantValid
    )
        private
        returns (uint256[] memory ids)
    {
        uint256 size = _instances.length;
        ids = new uint256[](size);

        uint64 validSince = uint64(block.timestamp);

        if (!instantValid) {
            validSince += INSTANCE_VALIDITY_DELAY;
        }

        for (uint256 i; i < size; ++i) {
            require(!addressRegistered[_instances[i]], SGX_ALREADY_ATTESTED());

            addressRegistered[_instances[i]] = true;

            require(_instances[i] != address(0), SGX_INVALID_INSTANCE());

            instances[nextInstanceId] = Instance(_instances[i], validSince);
            ids[i] = nextInstanceId;

            emit InstanceAdded(nextInstanceId, _instances[i], address(0), validSince);

            ++nextInstanceId;
        }
    }

    function _replaceInstance(uint256 id, address oldInstance, address newInstance) private {
        // Replacing an instance means, it went through a cooldown (if added by on-chain RA) so no
        // need to have a cooldown
        instances[id] = Instance(newInstance, uint64(block.timestamp));
        emit InstanceAdded(id, newInstance, oldInstance, block.timestamp);
    }

    function _isInstanceValid(uint256 id, address instance) private view returns (bool) {
        require(instance != address(0), SGX_INVALID_INSTANCE());
        require(instance == instances[id].addr, SGX_INVALID_INSTANCE());
        return instances[id].validSince <= block.timestamp
            && block.timestamp <= instances[id].validSince + INSTANCE_EXPIRY;
    }
}
        

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts v4.4.1 (proxy/beacon/IBeacon.sol)

pragma solidity ^0.8.0;

/**
 * @dev This is the interface that {BeaconProxy} expects of its beacon.
 */
interface IBeacon {
    /**
     * @dev Must return an address that can be used as a delegate call target.
     *
     * {BeaconProxy} will check that this address is a contract.
     */
    function implementation() external view returns (address);
}
          

//SPDX-License-Identifier: MIT
pragma solidity ^0.8.24;

import "../lib/QuoteV3Auth/V3Struct.sol";

/// @title IAttestation
/// @custom:security-contact security@taiko.xyz
interface IAttestation {
    function verifyAttestation(bytes calldata data) external returns (bool);
    function verifyParsedQuote(V3Struct.ParsedV3QuoteStruct calldata v3quote)
        external
        returns (bool success, bytes memory retData);
}
          

//SPDX-License-Identifier: MIT
pragma solidity ^0.8.24;

/// @title V3Struct
/// @custom:security-contact security@taiko.xyz
library V3Struct {
    struct Header {
        bytes2 version;
        bytes2 attestationKeyType;
        bytes4 teeType;
        bytes2 qeSvn;
        bytes2 pceSvn;
        bytes16 qeVendorId;
        bytes20 userData;
    }

    struct EnclaveReport {
        bytes16 cpuSvn;
        bytes4 miscSelect;
        bytes28 reserved1;
        bytes16 attributes;
        bytes32 mrEnclave;
        bytes32 reserved2;
        bytes32 mrSigner;
        bytes reserved3; // 96 bytes
        uint16 isvProdId;
        uint16 isvSvn;
        bytes reserved4; // 60 bytes
        bytes reportData; // 64 bytes - For QEReports, this contains the hash of the concatenation
            // of attestation key and QEAuthData
    }

    struct QEAuthData {
        uint16 parsedDataSize;
        bytes data;
    }

    struct CertificationData {
        uint16 certType;
        // TODO(Yue): In encoded path, we need to calculate the size of certDataArray
        // certDataSize = len(join((BEGIN_CERT, certArray[i], END_CERT) for i in 0..3))
        // But for plain bytes path, we don't need that.
        uint32 certDataSize;
        bytes[3] decodedCertDataArray; // base64 decoded cert bytes array
    }

    struct ECDSAQuoteV3AuthData {
        bytes ecdsa256BitSignature; // 64 bytes
        bytes ecdsaAttestationKey; // 64 bytes
        EnclaveReport pckSignedQeReport; // 384 bytes
        bytes qeReportSignature; // 64 bytes
        QEAuthData qeAuthData;
        CertificationData certification;
    }

    struct ParsedV3QuoteStruct {
        Header header;
        EnclaveReport localEnclaveReport;
        ECDSAQuoteV3AuthData v3AuthData;
    }
}
          

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.24;

import "src/shared/based/LibSharedData.sol";

/// @title TaikoInbox
/// @notice Acts as the inbox for the Taiko Alethia protocol, a simplified version of the
/// original Taiko-Based Contestable Rollup (BCR). The tier-based proof system and
/// contestation mechanisms have been removed.
///
/// Key assumptions of this protocol:
/// - Block proposals and proofs are asynchronous. Proofs are not available at proposal time,
///   unlike Taiko Gwyneth, which assumes synchronous composability.
/// - Proofs are presumed error-free and thoroughly validated, with proof type management
///   delegated to IVerifier contracts.
///
/// @dev Registered in the address resolver as "taiko".
/// @custom:security-contact security@taiko.xyz
interface ITaikoInbox {
    struct BlockParams {
        // the max number of transactions in this block. Note that if there are not enough
        // transactions in calldata or blobs, the block will contains as many transactions as
        // possible.
        uint16 numTransactions;
        // The time difference (in seconds) between the timestamp of this block and
        // the timestamp of the parent block in the same batch. For the first block in a batch,
        // there is not parent block in the same batch, so the time shift should be 0.
        uint8 timeShift;
        // Signals sent on L1 and need to sync to this L2 block.
        bytes32[] signalSlots;
    }

    struct BlobParams {
        // The hashes of the blob. Note that if this array is not empty.  `firstBlobIndex` and
        // `numBlobs` must be 0.
        bytes32[] blobHashes;
        // The index of the first blob in this batch.
        uint8 firstBlobIndex;
        // The number of blobs in this batch. Blobs are initially concatenated and subsequently
        // decompressed via Zlib.
        uint8 numBlobs;
        // The byte offset of the blob in the batch.
        uint32 byteOffset;
        // The byte size of the blob.
        uint32 byteSize;
        // The block number when the blob was created.
        uint64 createdIn;
    }

    struct BatchParams {
        address proposer;
        address coinbase;
        bytes32 parentMetaHash;
        uint64 anchorBlockId;
        uint64 lastBlockTimestamp;
        bool revertIfNotFirstProposal;
        // Specifies the number of blocks to be generated from this batch.
        BlobParams blobParams;
        BlockParams[] blocks;
    }

    /// @dev This struct holds batch information essential for constructing blocks offchain, but it
    /// does not include data necessary for batch proving.
    struct BatchInfo {
        bytes32 txsHash;
        // Data to build L2 blocks
        BlockParams[] blocks;
        bytes32[] blobHashes;
        bytes32 extraData;
        address coinbase;
        uint64 proposedIn; // Used by node/client
        uint64 blobCreatedIn;
        uint32 blobByteOffset;
        uint32 blobByteSize;
        uint32 gasLimit;
        uint64 lastBlockId;
        uint64 lastBlockTimestamp;
        // Data for the L2 anchor transaction, shared by all blocks in the batch
        uint64 anchorBlockId;
        // corresponds to the `_anchorStateRoot` parameter in the anchor transaction.
        // The batch's validity proof shall verify the integrity of these two values.
        bytes32 anchorBlockHash;
        LibSharedData.BaseFeeConfig baseFeeConfig;
    }

    /// @dev This struct holds batch metadata essential for proving the batch.
    struct BatchMetadata {
        bytes32 infoHash;
        address proposer;
        uint64 batchId;
        uint64 proposedAt; // Used by node/client
    }

    /// @notice Struct representing transition to be proven.
    struct Transition {
        bytes32 parentHash;
        bytes32 blockHash;
        bytes32 stateRoot;
    }

    //  @notice Struct representing transition storage
    /// @notice 4 slots used.
    struct TransitionState {
        bytes32 parentHash;
        bytes32 blockHash;
        bytes32 stateRoot;
        address prover;
        bool inProvingWindow;
        uint48 createdAt;
    }

    /// @notice 3 slots used.
    struct Batch {
        bytes32 metaHash; // slot 1
        uint64 lastBlockId; // slot 2
        uint96 reserved3;
        uint96 livenessBond;
        uint64 batchId; // slot 3
        uint64 lastBlockTimestamp;
        uint64 anchorBlockId;
        uint24 nextTransitionId;
        uint8 reserved4;
        // The ID of the transaction that is used to verify this batch. However, if this batch is
        // not verified as the last one in a transaction, verifiedTransitionId will remain zero.
        uint24 verifiedTransitionId;
    }

    /// @notice Forge is only able to run coverage in case the contracts by default capable of
    /// compiling without any optimization (neither optimizer runs, no compiling --via-ir flag).
    struct Stats1 {
        uint64 genesisHeight;
        uint64 __reserved2;
        uint64 lastSyncedBatchId;
        uint64 lastSyncedAt;
    }

    struct Stats2 {
        uint64 numBatches;
        uint64 lastVerifiedBatchId;
        bool paused;
        uint56 lastProposedIn;
        uint64 lastUnpausedAt;
    }

    struct ForkHeights {
        uint64 ontake; // measured with block number.
        uint64 pacaya; // measured with the batch Id, not block number.
        uint64 shasta; // measured with the batch Id, not block number.
        uint64 unzen; // measured with the batch Id, not block number.
    }

    /// @notice Struct holding Taiko configuration parameters. See {TaikoConfig}.
    struct Config {
        /// @notice The chain ID of the network where Taiko contracts are deployed.
        uint64 chainId;
        /// @notice The maximum number of unverified batches the protocol supports.
        uint64 maxUnverifiedBatches;
        /// @notice Size of the batch ring buffer, allowing extra space for proposals.
        uint64 batchRingBufferSize;
        /// @notice The maximum number of verifications allowed when a batch is proposed or proved.
        uint64 maxBatchesToVerify;
        /// @notice The maximum gas limit allowed for a block.
        uint32 blockMaxGasLimit;
        /// @notice The amount of Taiko token as a prover liveness bond per batch.
        uint96 livenessBondBase;
        /// @notice The amount of Taiko token as a prover liveness bond per block.
        uint96 livenessBondPerBlock;
        /// @notice The number of batches between two L2-to-L1 state root sync.
        uint8 stateRootSyncInternal;
        /// @notice The max differences of the anchor height and the current block number.
        uint64 maxAnchorHeightOffset;
        /// @notice Base fee configuration
        LibSharedData.BaseFeeConfig baseFeeConfig;
        /// @notice The proving window in seconds.
        uint16 provingWindow;
        /// @notice The time required for a transition to be used for verifying a batch.
        uint24 cooldownWindow;
        /// @notice The maximum number of signals to be received by TaikoL2.
        uint8 maxSignalsToReceive;
        /// @notice The maximum number of blocks per batch.
        uint16 maxBlocksPerBatch;
        /// @notice Historical heights of the forks.
        ForkHeights forkHeights;
    }

    /// @notice Struct holding the state variables for the {Taiko} contract.
    struct State {
        // Ring buffer for proposed batches and a some recent verified batches.
        mapping(uint256 batchId_mod_batchRingBufferSize => Batch batch) batches;
        // Indexing to transition ids (ring buffer not possible)
        mapping(uint256 batchId => mapping(bytes32 parentHash => uint24 transitionId)) transitionIds;
        // Ring buffer for transitions
        mapping(
            uint256 batchId_mod_batchRingBufferSize
                => mapping(uint24 transitionId => TransitionState ts)
        ) transitions;
        bytes32 __reserve1; // slot 4 - was used as a ring buffer for Ether deposits
        Stats1 stats1; // slot 5
        Stats2 stats2; // slot 6
        mapping(address account => uint256 bond) bondBalance;
        uint256[43] __gap;
    }

    /// @notice Emitted when tokens are deposited into a user's bond balance.
    /// @param user The address of the user who deposited the tokens.
    /// @param amount The amount of tokens deposited.
    event BondDeposited(address indexed user, uint256 amount);

    /// @notice Emitted when tokens are withdrawn from a user's bond balance.
    /// @param user The address of the user who withdrew the tokens.
    /// @param amount The amount of tokens withdrawn.
    event BondWithdrawn(address indexed user, uint256 amount);

    /// @notice Emitted when a token is credited back to a user's bond balance.
    /// @param user The address of the user whose bond balance is credited.
    /// @param amount The amount of tokens credited.
    event BondCredited(address indexed user, uint256 amount);

    /// @notice Emitted when a token is debited from a user's bond balance.
    /// @param user The address of the user whose bond balance is debited.
    /// @param amount The amount of tokens debited.
    event BondDebited(address indexed user, uint256 amount);

    /// @notice Emitted when a batch is synced.
    /// @param stats1 The Stats1 data structure.
    event Stats1Updated(Stats1 stats1);

    /// @notice Emitted when some state variable values changed.
    /// @param stats2 The Stats2 data structure.
    event Stats2Updated(Stats2 stats2);

    /// @notice Emitted when a batch is proposed.
    /// @param info The info of the proposed batch.
    /// @param meta The metadata of the proposed batch.
    /// @param txList The tx list in calldata.
    event BatchProposed(BatchInfo info, BatchMetadata meta, bytes txList);

    /// @notice Emitted when multiple transitions are proved.
    /// @param verifier The address of the verifier.
    /// @param transitions The transitions data.
    event BatchesProved(address verifier, uint64[] batchIds, Transition[] transitions);

    /// @notice Emitted when a transition is overwritten by a conflicting one with the same parent
    /// hash but different block hash or state root.
    /// @param batchId The batch ID.
    /// @param oldTran The old transition overwritten.
    /// @param newTran The new transition.
    event ConflictingProof(uint64 batchId, TransitionState oldTran, Transition newTran);

    /// @notice Emitted when a batch is verified.
    /// @param batchId The ID of the verified batch.
    /// @param blockHash The hash of the verified batch.
    event BatchesVerified(uint64 batchId, bytes32 blockHash);

    error AnchorBlockIdSmallerThanParent();
    error AnchorBlockIdTooLarge();
    error AnchorBlockIdTooSmall();
    error ArraySizesMismatch();
    error BatchNotFound();
    error BatchVerified();
    error BeyondCurrentFork();
    error BlobNotFound();
    error BlockNotFound();
    error BlobNotSpecified();
    error ContractPaused();
    error CustomProposerMissing();
    error CustomProposerNotAllowed();
    error EtherNotPaidAsBond();
    error FirstBlockTimeShiftNotZero();
    error ForkNotActivated();
    error InsufficientBond();
    error InvalidBlobCreatedIn();
    error InvalidBlobParams();
    error InvalidGenesisBlockHash();
    error InvalidParams();
    error InvalidTransitionBlockHash();
    error InvalidTransitionParentHash();
    error InvalidTransitionStateRoot();
    error MetaHashMismatch();
    error MsgValueNotZero();
    error NoBlocksToProve();
    error NotFirstProposal();
    error NotInboxWrapper();
    error ParentMetaHashMismatch();
    error SameTransition();
    error SignalNotSent();
    error TimestampSmallerThanParent();
    error TimestampTooLarge();
    error TimestampTooSmall();
    error TooManyBatches();
    error TooManyBlocks();
    error TooManySignals();
    error TransitionNotFound();
    error ZeroAnchorBlockHash();

    /// @notice Proposes a batch of blocks.
    /// @param _params ABI-encoded parameters.
    /// @param _txList The transaction list in calldata. If the txList is empty, blob will be used
    /// for data availability.
    /// @return info_ The info of the proposed batch.
    /// @return meta_ The metadata of the proposed batch.
    function proposeBatch(
        bytes calldata _params,
        bytes calldata _txList
    )
        external
        returns (ITaikoInbox.BatchInfo memory info_, ITaikoInbox.BatchMetadata memory meta_);

    /// @notice Proves state transitions for multiple batches with a single aggregated proof.
    /// @param _params ABI-encoded parameter containing:
    /// - metas: Array of metadata for each batch being proved.
    /// - transitions: Array of batch transitions to be proved.
    /// @param _proof The aggregated cryptographic proof proving the batches transitions.
    function proveBatches(bytes calldata _params, bytes calldata _proof) external;

    /// @notice Deposits TAIKO tokens into the contract to be used as liveness bond.
    /// @param _amount The amount of TAIKO tokens to deposit.
    function depositBond(uint256 _amount) external payable;

    /// @notice Withdraws a specified amount of TAIKO tokens from the contract.
    /// @param _amount The amount of TAIKO tokens to withdraw.
    function withdrawBond(uint256 _amount) external;

    /// @notice Returns the TAIKO token balance of a specific user.
    /// @param _user The address of the user.
    /// @return The TAIKO token balance of the user.
    function bondBalanceOf(address _user) external view returns (uint256);

    /// @notice Retrieves the Bond token address. If Ether is used as bond, this function returns
    /// address(0).
    /// @return The Bond token address.
    function bondToken() external view returns (address);

    /// @notice Retrieves the first set of protocol statistics.
    /// @return Stats1 structure containing the statistics.
    function getStats1() external view returns (Stats1 memory);

    /// @notice Retrieves the second set of protocol statistics.
    /// @return Stats2 structure containing the statistics.
    function getStats2() external view returns (Stats2 memory);

    /// @notice Retrieves data about a specific batch.
    /// @param _batchId The ID of the batch to retrieve.
    /// @return batch_ The batch data.
    function getBatch(uint64 _batchId) external view returns (Batch memory batch_);

    /// @notice Retrieves a specific transition by batch ID and transition ID. This function may
    /// revert if the transition is not found.
    /// @param _batchId The batch ID.
    /// @param _tid The transition ID.
    /// @return The specified transition state.
    function getTransitionById(
        uint64 _batchId,
        uint24 _tid
    )
        external
        view
        returns (ITaikoInbox.TransitionState memory);

    /// @notice Retrieves a specific transition by batch ID and parent Hash. This function may
    /// revert if the transition is not found.
    /// @param _batchId The batch ID.
    /// @param _parentHash The parent hash.
    /// @return The specified transition state.
    function getTransitionByParentHash(
        uint64 _batchId,
        bytes32 _parentHash
    )
        external
        view
        returns (ITaikoInbox.TransitionState memory);

    /// @notice Retrieves the transition used for the last verified batch.
    /// @return batchId_ The batch ID of the last verified transition.
    /// @return blockId_ The block ID of the last verified block.
    /// @return ts_ The last verified transition.
    function getLastVerifiedTransition()
        external
        view
        returns (uint64 batchId_, uint64 blockId_, TransitionState memory ts_);

    /// @notice Retrieves the transition used for the last synced batch.
    /// @return batchId_ The batch ID of the last synced transition.
    /// @return blockId_ The block ID of the last synced block.
    /// @return ts_ The last synced transition.
    function getLastSyncedTransition()
        external
        view
        returns (uint64 batchId_, uint64 blockId_, TransitionState memory ts_);

    /// @notice Retrieves the transition used for verifying a batch.
    /// @param _batchId The batch ID.
    /// @return The transition used for verifying the batch.
    function getBatchVerifyingTransition(uint64 _batchId)
        external
        view
        returns (TransitionState memory);

    /// @notice Retrieves the current protocol configuration.
    /// @return The current configuration.
    function pacayaConfig() external view returns (Config memory);
}
          

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.24;

import "../based/ITaikoInbox.sol";

/// @title IVerifier
/// @notice Defines the function that handles proof verification.
/// @custom:security-contact security@taiko.xyz
interface IVerifier {
    struct Context {
        uint64 batchId;
        bytes32 metaHash;
        ITaikoInbox.Transition transition;
    }

    /// @notice Verifies multiple proofs. This function must throw if the proof cannot be verified.
    /// @param _ctxs The array of contexts for the proof verifications.
    /// @param _proof The batch proof to verify.
    function verifyProof(Context[] calldata _ctxs, bytes calldata _proof) external;
}
          

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.24;

import "../../layer1/based/ITaikoInbox.sol";

/// @title LibPublicInput
/// @notice A library for handling hashing the so-called public input hash, used by sgx and zk
/// proofs.
/// @custom:security-contact security@taiko.xyz
library LibPublicInput {
    /// @notice Hashes the public input for the proof verification.
    /// @param _transition The transition to verify.
    /// @param _verifierContract The contract address which as current verifier.
    /// @param _newInstance The new instance address. For SGX it is the new signer address, for ZK
    /// this variable is not used and must have value address(0).
    /// @param _metaHash The meta hash.
    /// @param _chainId The chain id.
    /// @return The public input hash.
    function hashPublicInputs(
        ITaikoInbox.Transition memory _transition,
        address _verifierContract,
        address _newInstance,
        bytes32 _metaHash,
        uint64 _chainId
    )
        internal
        pure
        returns (bytes32)
    {
        return keccak256(
            abi.encode(
                "VERIFY_PROOF", _chainId, _verifierContract, _transition, _newInstance, _metaHash
            )
        );
    }
}
          

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.24;

library LibSharedData {
    /// @dev Struct that represents L2 basefee configurations
    struct BaseFeeConfig {
        uint8 adjustmentQuotient;
        uint8 sharingPctg;
        uint32 gasIssuancePerSecond;
        uint64 minGasExcess;
        uint32 maxGasIssuancePerBlock;
    }
}
          

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.24;

import "@openzeppelin/contracts/proxy/utils/UUPSUpgradeable.sol";
import "@openzeppelin/contracts-upgradeable/access/Ownable2StepUpgradeable.sol";
import "./IResolver.sol";

/// @title EssentialContract
/// @custom:security-contact security@taiko.xyz
abstract contract EssentialContract is UUPSUpgradeable, Ownable2StepUpgradeable {
    uint8 internal constant _FALSE = 1;
    uint8 internal constant _TRUE = 2;

    address private immutable __resolver;
    uint256[50] private __gapFromOldAddressResolver;

    /// @dev Slot 1.
    uint8 internal __reentry;
    uint8 internal __paused;

    uint256[49] private __gap;

    /// @notice Emitted when the contract is paused.
    /// @param account The account that paused the contract.
    event Paused(address account);

    /// @notice Emitted when the contract is unpaused.
    /// @param account The account that unpaused the contract.
    event Unpaused(address account);

    error INVALID_PAUSE_STATUS();
    error FUNC_NOT_IMPLEMENTED();
    error REENTRANT_CALL();
    error ACCESS_DENIED();
    error RESOLVER_NOT_FOUND();
    error ZERO_ADDRESS();
    error ZERO_VALUE();

    /// @dev Modifier that ensures the caller is the owner or resolved address of a given name.
    /// @param _name The name to check against.
    modifier onlyFromOwnerOrNamed(bytes32 _name) {
        require(msg.sender == owner() || msg.sender == resolve(_name, true), ACCESS_DENIED());
        _;
    }

    /// @dev Modifier that ensures the caller is either the owner or a specified address.
    /// @param _addr The address to check against.
    modifier onlyFromOwnerOr(address _addr) {
        require(msg.sender == owner() || msg.sender == _addr, ACCESS_DENIED());
        _;
    }

    /// @dev Modifier that reverts the function call, indicating it is not implemented.
    modifier notImplemented() {
        revert FUNC_NOT_IMPLEMENTED();
        _;
    }

    /// @dev Modifier that prevents reentrant calls to a function.
    modifier nonReentrant() {
        require(_loadReentryLock() != _TRUE, REENTRANT_CALL());
        _storeReentryLock(_TRUE);
        _;
        _storeReentryLock(_FALSE);
    }

    /// @dev Modifier that allows function execution only when the contract is paused.
    modifier whenPaused() {
        require(paused(), INVALID_PAUSE_STATUS());
        _;
    }

    /// @dev Modifier that allows function execution only when the contract is not paused.
    modifier whenNotPaused() {
        require(!paused(), INVALID_PAUSE_STATUS());
        _;
    }

    /// @dev Modifier that ensures the provided address is not the zero address.
    /// @param _addr The address to check.
    modifier nonZeroAddr(address _addr) {
        require(_addr != address(0), ZERO_ADDRESS());
        _;
    }

    /// @dev Modifier that ensures the provided value is not zero.
    /// @param _value The value to check.
    modifier nonZeroValue(uint256 _value) {
        require(_value != 0, ZERO_VALUE());
        _;
    }

    /// @dev Modifier that ensures the provided bytes32 value is not zero.
    /// @param _value The bytes32 value to check.
    modifier nonZeroBytes32(bytes32 _value) {
        require(_value != 0, ZERO_VALUE());
        _;
    }

    /// @dev Modifier that ensures the caller is the resolved address of a given
    /// name.
    /// @param _name The name to check against.
    modifier onlyFromNamed(bytes32 _name) {
        require(msg.sender == resolve(_name, true), ACCESS_DENIED());
        _;
    }

    /// @dev Modifier that ensures the caller is the resolved address of a given
    /// name, if the name is set.
    /// @param _name The name to check against.
    modifier onlyFromOptionalNamed(bytes32 _name) {
        address addr = resolve(_name, true);
        require(addr == address(0) || msg.sender == addr, ACCESS_DENIED());
        _;
    }

    /// @dev Modifier that ensures the caller is a resolved address to either _name1 or _name2
    /// name.
    /// @param _name1 The first name to check against.
    /// @param _name2 The second name to check against.
    modifier onlyFromNamedEither(bytes32 _name1, bytes32 _name2) {
        require(
            msg.sender == resolve(_name1, true) || msg.sender == resolve(_name2, true),
            ACCESS_DENIED()
        );
        _;
    }

    /// @dev Modifier that ensures the caller is either of the two specified addresses.
    /// @param _addr1 The first address to check against.
    /// @param _addr2 The second address to check against.
    modifier onlyFromEither(address _addr1, address _addr2) {
        require(msg.sender == _addr1 || msg.sender == _addr2, ACCESS_DENIED());
        _;
    }

    /// @dev Modifier that ensures the caller is the specified address.
    /// @param _addr The address to check against.
    modifier onlyFrom(address _addr) {
        require(msg.sender == _addr, ACCESS_DENIED());
        _;
    }

    /// @dev Modifier that ensures the caller is the specified address.
    /// @param _addr The address to check against.
    modifier onlyFromOptional(address _addr) {
        require(_addr == address(0) || msg.sender == _addr, ACCESS_DENIED());
        _;
    }

    constructor(address _resolver) {
        __resolver = _resolver;
        _disableInitializers();
    }

    /// @notice Pauses the contract.
    function pause() public whenNotPaused {
        _pause();
        emit Paused(msg.sender);
        // We call the authorize function here to avoid:
        // Warning (5740): Unreachable code.
        _authorizePause(msg.sender, true);
    }

    /// @notice Unpauses the contract.
    function unpause() public whenPaused {
        _unpause();
        emit Unpaused(msg.sender);
        // We call the authorize function here to avoid:
        // Warning (5740): Unreachable code.
        _authorizePause(msg.sender, false);
    }

    function impl() public view returns (address) {
        return _getImplementation();
    }

    /// @notice Returns true if the contract is paused, and false otherwise.
    /// @return true if paused, false otherwise.
    function paused() public view virtual returns (bool) {
        return __paused == _TRUE;
    }

    function inNonReentrant() public view returns (bool) {
        return _loadReentryLock() == _TRUE;
    }

    /// @notice Returns the address of this contract.
    /// @return The address of this contract.
    function resolver() public view virtual returns (address) {
        return __resolver;
    }

    /// @notice Resolves a name to an address on a specific chain
    /// @param _chainId The chain ID to resolve the name on
    /// @param _name The name to resolve
    /// @param _allowZeroAddress Whether to allow resolving to the zero address
    /// @return The resolved address
    function resolve(
        uint64 _chainId,
        bytes32 _name,
        bool _allowZeroAddress
    )
        internal
        view
        returns (address)
    {
        return IResolver(resolver()).resolve(_chainId, _name, _allowZeroAddress);
    }

    /// @notice Resolves a name to an address on the current chain
    /// @param _name The name to resolve
    /// @param _allowZeroAddress Whether to allow resolving to the zero address
    /// @return The resolved address
    function resolve(bytes32 _name, bool _allowZeroAddress) internal view returns (address) {
        return IResolver(resolver()).resolve(block.chainid, _name, _allowZeroAddress);
    }

    /// @notice Initializes the contract.
    /// @param _owner The owner of this contract. msg.sender will be used if this value is zero.
    function __Essential_init(address _owner) internal virtual onlyInitializing {
        __Context_init();
        _transferOwnership(_owner == address(0) ? msg.sender : _owner);
        __paused = _FALSE;
    }

    function _pause() internal virtual {
        __paused = _TRUE;
    }

    function _unpause() internal virtual {
        __paused = _FALSE;
    }

    function _authorizeUpgrade(address) internal virtual override onlyOwner { }

    function _authorizePause(address, bool) internal virtual onlyOwner { }

    // Stores the reentry lock
    function _storeReentryLock(uint8 _reentry) internal virtual {
        __reentry = _reentry;
    }

    // Loads the reentry lock
    function _loadReentryLock() internal view virtual returns (uint8 reentry_) {
        reentry_ = __reentry;
    }
}
          

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.24;

/// @title IResolver
/// @notice This contract acts as a bridge for name-to-address resolution.
/// @custom:security-contact security@taiko.xyz
interface IResolver {
    error RESOLVED_TO_ZERO_ADDRESS();

    /// @notice Resolves a name to its address deployed on a specified chain.
    /// @param _chainId The chainId of interest.
    /// @param _name Name whose address is to be resolved.
    /// @param _allowZeroAddress If set to true, does not throw if the resolved
    /// address is `address(0)`.
    /// @return Address associated with the given name on the specified
    /// chain.
    function resolve(
        uint256 _chainId,
        bytes32 _name,
        bool _allowZeroAddress
    )
        external
        view
        returns (address);
}
          

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (proxy/utils/UUPSUpgradeable.sol)

pragma solidity ^0.8.0;

import "../../interfaces/draft-IERC1822.sol";
import "../ERC1967/ERC1967Upgrade.sol";

/**
 * @dev An upgradeability mechanism designed for UUPS proxies. The functions included here can perform an upgrade of an
 * {ERC1967Proxy}, when this contract is set as the implementation behind such a proxy.
 *
 * A security mechanism ensures that an upgrade does not turn off upgradeability accidentally, although this risk is
 * reinstated if the upgrade retains upgradeability but removes the security mechanism, e.g. by replacing
 * `UUPSUpgradeable` with a custom implementation of upgrades.
 *
 * The {_authorizeUpgrade} function must be overridden to include access restriction to the upgrade mechanism.
 *
 * _Available since v4.1._
 */
abstract contract UUPSUpgradeable is IERC1822Proxiable, ERC1967Upgrade {
    /// @custom:oz-upgrades-unsafe-allow state-variable-immutable state-variable-assignment
    address private immutable __self = address(this);

    /**
     * @dev Check that the execution is being performed through a delegatecall call and that the execution context is
     * a proxy contract with an implementation (as defined in ERC1967) pointing to self. This should only be the case
     * for UUPS and transparent proxies that are using the current contract as their implementation. Execution of a
     * function through ERC1167 minimal proxies (clones) would not normally pass this test, but is not guaranteed to
     * fail.
     */
    modifier onlyProxy() {
        require(address(this) != __self, "Function must be called through delegatecall");
        require(_getImplementation() == __self, "Function must be called through active proxy");
        _;
    }

    /**
     * @dev Check that the execution is not being performed through a delegate call. This allows a function to be
     * callable on the implementing contract but not through proxies.
     */
    modifier notDelegated() {
        require(address(this) == __self, "UUPSUpgradeable: must not be called through delegatecall");
        _;
    }

    /**
     * @dev Implementation of the ERC1822 {proxiableUUID} function. This returns the storage slot used by the
     * implementation. It is used to validate the implementation's compatibility when performing an upgrade.
     *
     * IMPORTANT: A proxy pointing at a proxiable contract should not be considered proxiable itself, because this risks
     * bricking a proxy that upgrades to it, by delegating to itself until out of gas. Thus it is critical that this
     * function revert if invoked through a proxy. This is guaranteed by the `notDelegated` modifier.
     */
    function proxiableUUID() external view virtual override notDelegated returns (bytes32) {
        return _IMPLEMENTATION_SLOT;
    }

    /**
     * @dev Upgrade the implementation of the proxy to `newImplementation`.
     *
     * Calls {_authorizeUpgrade}.
     *
     * Emits an {Upgraded} event.
     *
     * @custom:oz-upgrades-unsafe-allow-reachable delegatecall
     */
    function upgradeTo(address newImplementation) public virtual onlyProxy {
        _authorizeUpgrade(newImplementation);
        _upgradeToAndCallUUPS(newImplementation, new bytes(0), false);
    }

    /**
     * @dev Upgrade the implementation of the proxy to `newImplementation`, and subsequently execute the function call
     * encoded in `data`.
     *
     * Calls {_authorizeUpgrade}.
     *
     * Emits an {Upgraded} event.
     *
     * @custom:oz-upgrades-unsafe-allow-reachable delegatecall
     */
    function upgradeToAndCall(address newImplementation, bytes memory data) public payable virtual onlyProxy {
        _authorizeUpgrade(newImplementation);
        _upgradeToAndCallUUPS(newImplementation, data, true);
    }

    /**
     * @dev Function that should revert when `msg.sender` is not authorized to upgrade the contract. Called by
     * {upgradeTo} and {upgradeToAndCall}.
     *
     * Normally, this function will use an xref:access.adoc[access control] modifier such as {Ownable-onlyOwner}.
     *
     * ```solidity
     * function _authorizeUpgrade(address) internal override onlyOwner {}
     * ```
     */
    function _authorizeUpgrade(address newImplementation) internal virtual;
}
          

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (utils/Address.sol)

pragma solidity ^0.8.1;

/**
 * @dev Collection of functions related to the address type
 */
library Address {
    /**
     * @dev Returns true if `account` is a contract.
     *
     * [IMPORTANT]
     * ====
     * It is unsafe to assume that an address for which this function returns
     * false is an externally-owned account (EOA) and not a contract.
     *
     * Among others, `isContract` will return false for the following
     * types of addresses:
     *
     *  - an externally-owned account
     *  - a contract in construction
     *  - an address where a contract will be created
     *  - an address where a contract lived, but was destroyed
     *
     * Furthermore, `isContract` will also return true if the target contract within
     * the same transaction is already scheduled for destruction by `SELFDESTRUCT`,
     * which only has an effect at the end of a transaction.
     * ====
     *
     * [IMPORTANT]
     * ====
     * You shouldn't rely on `isContract` to protect against flash loan attacks!
     *
     * Preventing calls from contracts is highly discouraged. It breaks composability, breaks support for smart wallets
     * like Gnosis Safe, and does not provide security since it can be circumvented by calling from a contract
     * constructor.
     * ====
     */
    function isContract(address account) internal view returns (bool) {
        // This method relies on extcodesize/address.code.length, which returns 0
        // for contracts in construction, since the code is only stored at the end
        // of the constructor execution.

        return account.code.length > 0;
    }

    /**
     * @dev Replacement for Solidity's `transfer`: sends `amount` wei to
     * `recipient`, forwarding all available gas and reverting on errors.
     *
     * https://eips.ethereum.org/EIPS/eip-1884[EIP1884] increases the gas cost
     * of certain opcodes, possibly making contracts go over the 2300 gas limit
     * imposed by `transfer`, making them unable to receive funds via
     * `transfer`. {sendValue} removes this limitation.
     *
     * https://consensys.net/diligence/blog/2019/09/stop-using-soliditys-transfer-now/[Learn more].
     *
     * IMPORTANT: because control is transferred to `recipient`, care must be
     * taken to not create reentrancy vulnerabilities. Consider using
     * {ReentrancyGuard} or the
     * https://solidity.readthedocs.io/en/v0.8.0/security-considerations.html#use-the-checks-effects-interactions-pattern[checks-effects-interactions pattern].
     */
    function sendValue(address payable recipient, uint256 amount) internal {
        require(address(this).balance >= amount, "Address: insufficient balance");

        (bool success, ) = recipient.call{value: amount}("");
        require(success, "Address: unable to send value, recipient may have reverted");
    }

    /**
     * @dev Performs a Solidity function call using a low level `call`. A
     * plain `call` is an unsafe replacement for a function call: use this
     * function instead.
     *
     * If `target` reverts with a revert reason, it is bubbled up by this
     * function (like regular Solidity function calls).
     *
     * Returns the raw returned data. To convert to the expected return value,
     * use https://solidity.readthedocs.io/en/latest/units-and-global-variables.html?highlight=abi.decode#abi-encoding-and-decoding-functions[`abi.decode`].
     *
     * Requirements:
     *
     * - `target` must be a contract.
     * - calling `target` with `data` must not revert.
     *
     * _Available since v3.1._
     */
    function functionCall(address target, bytes memory data) internal returns (bytes memory) {
        return functionCallWithValue(target, data, 0, "Address: low-level call failed");
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`], but with
     * `errorMessage` as a fallback revert reason when `target` reverts.
     *
     * _Available since v3.1._
     */
    function functionCall(
        address target,
        bytes memory data,
        string memory errorMessage
    ) internal returns (bytes memory) {
        return functionCallWithValue(target, data, 0, errorMessage);
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but also transferring `value` wei to `target`.
     *
     * Requirements:
     *
     * - the calling contract must have an ETH balance of at least `value`.
     * - the called Solidity function must be `payable`.
     *
     * _Available since v3.1._
     */
    function functionCallWithValue(address target, bytes memory data, uint256 value) internal returns (bytes memory) {
        return functionCallWithValue(target, data, value, "Address: low-level call with value failed");
    }

    /**
     * @dev Same as {xref-Address-functionCallWithValue-address-bytes-uint256-}[`functionCallWithValue`], but
     * with `errorMessage` as a fallback revert reason when `target` reverts.
     *
     * _Available since v3.1._
     */
    function functionCallWithValue(
        address target,
        bytes memory data,
        uint256 value,
        string memory errorMessage
    ) internal returns (bytes memory) {
        require(address(this).balance >= value, "Address: insufficient balance for call");
        (bool success, bytes memory returndata) = target.call{value: value}(data);
        return verifyCallResultFromTarget(target, success, returndata, errorMessage);
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but performing a static call.
     *
     * _Available since v3.3._
     */
    function functionStaticCall(address target, bytes memory data) internal view returns (bytes memory) {
        return functionStaticCall(target, data, "Address: low-level static call failed");
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-string-}[`functionCall`],
     * but performing a static call.
     *
     * _Available since v3.3._
     */
    function functionStaticCall(
        address target,
        bytes memory data,
        string memory errorMessage
    ) internal view returns (bytes memory) {
        (bool success, bytes memory returndata) = target.staticcall(data);
        return verifyCallResultFromTarget(target, success, returndata, errorMessage);
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but performing a delegate call.
     *
     * _Available since v3.4._
     */
    function functionDelegateCall(address target, bytes memory data) internal returns (bytes memory) {
        return functionDelegateCall(target, data, "Address: low-level delegate call failed");
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-string-}[`functionCall`],
     * but performing a delegate call.
     *
     * _Available since v3.4._
     */
    function functionDelegateCall(
        address target,
        bytes memory data,
        string memory errorMessage
    ) internal returns (bytes memory) {
        (bool success, bytes memory returndata) = target.delegatecall(data);
        return verifyCallResultFromTarget(target, success, returndata, errorMessage);
    }

    /**
     * @dev Tool to verify that a low level call to smart-contract was successful, and revert (either by bubbling
     * the revert reason or using the provided one) in case of unsuccessful call or if target was not a contract.
     *
     * _Available since v4.8._
     */
    function verifyCallResultFromTarget(
        address target,
        bool success,
        bytes memory returndata,
        string memory errorMessage
    ) internal view returns (bytes memory) {
        if (success) {
            if (returndata.length == 0) {
                // only check isContract if the call was successful and the return data is empty
                // otherwise we already know that it was a contract
                require(isContract(target), "Address: call to non-contract");
            }
            return returndata;
        } else {
            _revert(returndata, errorMessage);
        }
    }

    /**
     * @dev Tool to verify that a low level call was successful, and revert if it wasn't, either by bubbling the
     * revert reason or using the provided one.
     *
     * _Available since v4.3._
     */
    function verifyCallResult(
        bool success,
        bytes memory returndata,
        string memory errorMessage
    ) internal pure returns (bytes memory) {
        if (success) {
            return returndata;
        } else {
            _revert(returndata, errorMessage);
        }
    }

    function _revert(bytes memory returndata, string memory errorMessage) private pure {
        // Look for revert reason and bubble it up if present
        if (returndata.length > 0) {
            // The easiest way to bubble the revert reason is using memory via assembly
            /// @solidity memory-safe-assembly
            assembly {
                let returndata_size := mload(returndata)
                revert(add(32, returndata), returndata_size)
            }
        } else {
            revert(errorMessage);
        }
    }
}
          

// SPDX-License-Identifier: MIT
pragma solidity ^0.8.24;

/// @title LibStrings
/// @custom:security-contact security@taiko.xyz
library LibStrings {
    bytes32 internal constant B_AUTOMATA_DCAP_ATTESTATION = bytes32("automata_dcap_attestation");
    bytes32 internal constant B_SGX_GETH_AUTOMATA = bytes32("sgx_geth_automata");
    bytes32 internal constant B_BOND_TOKEN = bytes32("bond_token");
    bytes32 internal constant B_BRIDGE = bytes32("bridge");
    bytes32 internal constant B_BRIDGE_WATCHDOG = bytes32("bridge_watchdog");
    bytes32 internal constant B_BRIDGED_ERC1155 = bytes32("bridged_erc1155");
    bytes32 internal constant B_BRIDGED_ERC20 = bytes32("bridged_erc20");
    bytes32 internal constant B_BRIDGED_ERC721 = bytes32("bridged_erc721");
    bytes32 internal constant B_CHAIN_WATCHDOG = bytes32("chain_watchdog");
    bytes32 internal constant B_ERC1155_VAULT = bytes32("erc1155_vault");
    bytes32 internal constant B_ERC20_VAULT = bytes32("erc20_vault");
    bytes32 internal constant B_ERC721_VAULT = bytes32("erc721_vault");
    bytes32 internal constant B_FORCED_INCLUSION_STORE = bytes32("forced_inclusion_store");
    bytes32 internal constant B_PRECONF_WHITELIST = bytes32("preconf_whitelist");
    bytes32 internal constant B_PRECONF_WHITELIST_OWNER = bytes32("preconf_whitelist_owner");
    bytes32 internal constant B_PRECONF_ROUTER = bytes32("preconf_router");
    bytes32 internal constant B_TAIKO_WRAPPER = bytes32("taiko_wrapper");
    bytes32 internal constant B_PROOF_VERIFIER = bytes32("proof_verifier");
    bytes32 internal constant B_SGX_RETH_VERIFIER = bytes32("sgx_reth_verifier");
    bytes32 internal constant B_SGX_GETH_VERIFIER = bytes32("sgx_geth_verifier");
    bytes32 internal constant B_RISC0_RETH_VERIFIER = bytes32("risc0_reth_verifier");
    bytes32 internal constant B_SP1_RETH_VERIFIER = bytes32("sp1_reth_verifier");
    bytes32 internal constant B_PROVER_SET = bytes32("prover_set");
    bytes32 internal constant B_QUOTA_MANAGER = bytes32("quota_manager");
    bytes32 internal constant B_SIGNAL_SERVICE = bytes32("signal_service");
    bytes32 internal constant B_TAIKO = bytes32("taiko");
    bytes32 internal constant B_TAIKO_TOKEN = bytes32("taiko_token");
    bytes32 internal constant B_WITHDRAWER = bytes32("withdrawer");
    bytes32 internal constant H_SIGNAL_ROOT = keccak256("SIGNAL_ROOT");
    bytes32 internal constant H_STATE_ROOT = keccak256("STATE_ROOT");
}
          

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (access/Ownable2Step.sol)

pragma solidity ^0.8.0;

import "./OwnableUpgradeable.sol";
import {Initializable} from "../proxy/utils/Initializable.sol";

/**
 * @dev Contract module which provides access control mechanism, where
 * there is an account (an owner) that can be granted exclusive access to
 * specific functions.
 *
 * By default, the owner account will be the one that deploys the contract. This
 * can later be changed with {transferOwnership} and {acceptOwnership}.
 *
 * This module is used through inheritance. It will make available all functions
 * from parent (Ownable).
 */
abstract contract Ownable2StepUpgradeable is Initializable, OwnableUpgradeable {
    address private _pendingOwner;

    event OwnershipTransferStarted(address indexed previousOwner, address indexed newOwner);

    function __Ownable2Step_init() internal onlyInitializing {
        __Ownable_init_unchained();
    }

    function __Ownable2Step_init_unchained() internal onlyInitializing {
    }
    /**
     * @dev Returns the address of the pending owner.
     */
    function pendingOwner() public view virtual returns (address) {
        return _pendingOwner;
    }

    /**
     * @dev Starts the ownership transfer of the contract to a new account. Replaces the pending transfer if there is one.
     * Can only be called by the current owner.
     */
    function transferOwnership(address newOwner) public virtual override onlyOwner {
        _pendingOwner = newOwner;
        emit OwnershipTransferStarted(owner(), newOwner);
    }

    /**
     * @dev Transfers ownership of the contract to a new account (`newOwner`) and deletes any pending owner.
     * Internal function without access restriction.
     */
    function _transferOwnership(address newOwner) internal virtual override {
        delete _pendingOwner;
        super._transferOwnership(newOwner);
    }

    /**
     * @dev The new owner accepts the ownership transfer.
     */
    function acceptOwnership() public virtual {
        address sender = _msgSender();
        require(pendingOwner() == sender, "Ownable2Step: caller is not the new owner");
        _transferOwnership(sender);
    }

    /**
     * @dev This empty reserved space is put in place to allow future versions to add new
     * variables without shifting down storage in the inheritance chain.
     * See https://docs.openzeppelin.com/contracts/4.x/upgradeable#storage_gaps
     */
    uint256[49] private __gap;
}
          

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (access/Ownable.sol)

pragma solidity ^0.8.0;

import "../utils/ContextUpgradeable.sol";
import {Initializable} from "../proxy/utils/Initializable.sol";

/**
 * @dev Contract module which provides a basic access control mechanism, where
 * there is an account (an owner) that can be granted exclusive access to
 * specific functions.
 *
 * By default, the owner account will be the one that deploys the contract. This
 * can later be changed with {transferOwnership}.
 *
 * This module is used through inheritance. It will make available the modifier
 * `onlyOwner`, which can be applied to your functions to restrict their use to
 * the owner.
 */
abstract contract OwnableUpgradeable is Initializable, ContextUpgradeable {
    address private _owner;

    event OwnershipTransferred(address indexed previousOwner, address indexed newOwner);

    /**
     * @dev Initializes the contract setting the deployer as the initial owner.
     */
    function __Ownable_init() internal onlyInitializing {
        __Ownable_init_unchained();
    }

    function __Ownable_init_unchained() internal onlyInitializing {
        _transferOwnership(_msgSender());
    }

    /**
     * @dev Throws if called by any account other than the owner.
     */
    modifier onlyOwner() {
        _checkOwner();
        _;
    }

    /**
     * @dev Returns the address of the current owner.
     */
    function owner() public view virtual returns (address) {
        return _owner;
    }

    /**
     * @dev Throws if the sender is not the owner.
     */
    function _checkOwner() internal view virtual {
        require(owner() == _msgSender(), "Ownable: caller is not the owner");
    }

    /**
     * @dev Leaves the contract without owner. It will not be possible to call
     * `onlyOwner` functions. Can only be called by the current owner.
     *
     * NOTE: Renouncing ownership will leave the contract without an owner,
     * thereby disabling any functionality that is only available to the owner.
     */
    function renounceOwnership() public virtual onlyOwner {
        _transferOwnership(address(0));
    }

    /**
     * @dev Transfers ownership of the contract to a new account (`newOwner`).
     * Can only be called by the current owner.
     */
    function transferOwnership(address newOwner) public virtual onlyOwner {
        require(newOwner != address(0), "Ownable: new owner is the zero address");
        _transferOwnership(newOwner);
    }

    /**
     * @dev Transfers ownership of the contract to a new account (`newOwner`).
     * Internal function without access restriction.
     */
    function _transferOwnership(address newOwner) internal virtual {
        address oldOwner = _owner;
        _owner = newOwner;
        emit OwnershipTransferred(oldOwner, newOwner);
    }

    /**
     * @dev This empty reserved space is put in place to allow future versions to add new
     * variables without shifting down storage in the inheritance chain.
     * See https://docs.openzeppelin.com/contracts/4.x/upgradeable#storage_gaps
     */
    uint256[49] private __gap;
}
          

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (proxy/utils/Initializable.sol)

pragma solidity ^0.8.2;

import "../../utils/AddressUpgradeable.sol";

/**
 * @dev This is a base contract to aid in writing upgradeable contracts, or any kind of contract that will be deployed
 * behind a proxy. Since proxied contracts do not make use of a constructor, it's common to move constructor logic to an
 * external initializer function, usually called `initialize`. It then becomes necessary to protect this initializer
 * function so it can only be called once. The {initializer} modifier provided by this contract will have this effect.
 *
 * The initialization functions use a version number. Once a version number is used, it is consumed and cannot be
 * reused. This mechanism prevents re-execution of each "step" but allows the creation of new initialization steps in
 * case an upgrade adds a module that needs to be initialized.
 *
 * For example:
 *
 * [.hljs-theme-light.nopadding]
 * ```solidity
 * contract MyToken is ERC20Upgradeable {
 *     function initialize() initializer public {
 *         __ERC20_init("MyToken", "MTK");
 *     }
 * }
 *
 * contract MyTokenV2 is MyToken, ERC20PermitUpgradeable {
 *     function initializeV2() reinitializer(2) public {
 *         __ERC20Permit_init("MyToken");
 *     }
 * }
 * ```
 *
 * TIP: To avoid leaving the proxy in an uninitialized state, the initializer function should be called as early as
 * possible by providing the encoded function call as the `_data` argument to {ERC1967Proxy-constructor}.
 *
 * CAUTION: When used with inheritance, manual care must be taken to not invoke a parent initializer twice, or to ensure
 * that all initializers are idempotent. This is not verified automatically as constructors are by Solidity.
 *
 * [CAUTION]
 * ====
 * Avoid leaving a contract uninitialized.
 *
 * An uninitialized contract can be taken over by an attacker. This applies to both a proxy and its implementation
 * contract, which may impact the proxy. To prevent the implementation contract from being used, you should invoke
 * the {_disableInitializers} function in the constructor to automatically lock it when it is deployed:
 *
 * [.hljs-theme-light.nopadding]
 * ```
 * /// @custom:oz-upgrades-unsafe-allow constructor
 * constructor() {
 *     _disableInitializers();
 * }
 * ```
 * ====
 */
abstract contract Initializable {
    /**
     * @dev Indicates that the contract has been initialized.
     * @custom:oz-retyped-from bool
     */
    uint8 private _initialized;

    /**
     * @dev Indicates that the contract is in the process of being initialized.
     */
    bool private _initializing;

    /**
     * @dev Triggered when the contract has been initialized or reinitialized.
     */
    event Initialized(uint8 version);

    /**
     * @dev A modifier that defines a protected initializer function that can be invoked at most once. In its scope,
     * `onlyInitializing` functions can be used to initialize parent contracts.
     *
     * Similar to `reinitializer(1)`, except that functions marked with `initializer` can be nested in the context of a
     * constructor.
     *
     * Emits an {Initialized} event.
     */
    modifier initializer() {
        bool isTopLevelCall = !_initializing;
        require(
            (isTopLevelCall && _initialized < 1) || (!AddressUpgradeable.isContract(address(this)) && _initialized == 1),
            "Initializable: contract is already initialized"
        );
        _initialized = 1;
        if (isTopLevelCall) {
            _initializing = true;
        }
        _;
        if (isTopLevelCall) {
            _initializing = false;
            emit Initialized(1);
        }
    }

    /**
     * @dev A modifier that defines a protected reinitializer function that can be invoked at most once, and only if the
     * contract hasn't been initialized to a greater version before. In its scope, `onlyInitializing` functions can be
     * used to initialize parent contracts.
     *
     * A reinitializer may be used after the original initialization step. This is essential to configure modules that
     * are added through upgrades and that require initialization.
     *
     * When `version` is 1, this modifier is similar to `initializer`, except that functions marked with `reinitializer`
     * cannot be nested. If one is invoked in the context of another, execution will revert.
     *
     * Note that versions can jump in increments greater than 1; this implies that if multiple reinitializers coexist in
     * a contract, executing them in the right order is up to the developer or operator.
     *
     * WARNING: setting the version to 255 will prevent any future reinitialization.
     *
     * Emits an {Initialized} event.
     */
    modifier reinitializer(uint8 version) {
        require(!_initializing && _initialized < version, "Initializable: contract is already initialized");
        _initialized = version;
        _initializing = true;
        _;
        _initializing = false;
        emit Initialized(version);
    }

    /**
     * @dev Modifier to protect an initialization function so that it can only be invoked by functions with the
     * {initializer} and {reinitializer} modifiers, directly or indirectly.
     */
    modifier onlyInitializing() {
        require(_initializing, "Initializable: contract is not initializing");
        _;
    }

    /**
     * @dev Locks the contract, preventing any future reinitialization. This cannot be part of an initializer call.
     * Calling this in the constructor of a contract will prevent that contract from being initialized or reinitialized
     * to any version. It is recommended to use this to lock implementation contracts that are designed to be called
     * through proxies.
     *
     * Emits an {Initialized} event the first time it is successfully executed.
     */
    function _disableInitializers() internal virtual {
        require(!_initializing, "Initializable: contract is initializing");
        if (_initialized != type(uint8).max) {
            _initialized = type(uint8).max;
            emit Initialized(type(uint8).max);
        }
    }

    /**
     * @dev Returns the highest version that has been initialized. See {reinitializer}.
     */
    function _getInitializedVersion() internal view returns (uint8) {
        return _initialized;
    }

    /**
     * @dev Returns `true` if the contract is currently initializing. See {onlyInitializing}.
     */
    function _isInitializing() internal view returns (bool) {
        return _initializing;
    }
}
          

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (utils/Address.sol)

pragma solidity ^0.8.1;

/**
 * @dev Collection of functions related to the address type
 */
library AddressUpgradeable {
    /**
     * @dev Returns true if `account` is a contract.
     *
     * [IMPORTANT]
     * ====
     * It is unsafe to assume that an address for which this function returns
     * false is an externally-owned account (EOA) and not a contract.
     *
     * Among others, `isContract` will return false for the following
     * types of addresses:
     *
     *  - an externally-owned account
     *  - a contract in construction
     *  - an address where a contract will be created
     *  - an address where a contract lived, but was destroyed
     *
     * Furthermore, `isContract` will also return true if the target contract within
     * the same transaction is already scheduled for destruction by `SELFDESTRUCT`,
     * which only has an effect at the end of a transaction.
     * ====
     *
     * [IMPORTANT]
     * ====
     * You shouldn't rely on `isContract` to protect against flash loan attacks!
     *
     * Preventing calls from contracts is highly discouraged. It breaks composability, breaks support for smart wallets
     * like Gnosis Safe, and does not provide security since it can be circumvented by calling from a contract
     * constructor.
     * ====
     */
    function isContract(address account) internal view returns (bool) {
        // This method relies on extcodesize/address.code.length, which returns 0
        // for contracts in construction, since the code is only stored at the end
        // of the constructor execution.

        return account.code.length > 0;
    }

    /**
     * @dev Replacement for Solidity's `transfer`: sends `amount` wei to
     * `recipient`, forwarding all available gas and reverting on errors.
     *
     * https://eips.ethereum.org/EIPS/eip-1884[EIP1884] increases the gas cost
     * of certain opcodes, possibly making contracts go over the 2300 gas limit
     * imposed by `transfer`, making them unable to receive funds via
     * `transfer`. {sendValue} removes this limitation.
     *
     * https://consensys.net/diligence/blog/2019/09/stop-using-soliditys-transfer-now/[Learn more].
     *
     * IMPORTANT: because control is transferred to `recipient`, care must be
     * taken to not create reentrancy vulnerabilities. Consider using
     * {ReentrancyGuard} or the
     * https://solidity.readthedocs.io/en/v0.8.0/security-considerations.html#use-the-checks-effects-interactions-pattern[checks-effects-interactions pattern].
     */
    function sendValue(address payable recipient, uint256 amount) internal {
        require(address(this).balance >= amount, "Address: insufficient balance");

        (bool success, ) = recipient.call{value: amount}("");
        require(success, "Address: unable to send value, recipient may have reverted");
    }

    /**
     * @dev Performs a Solidity function call using a low level `call`. A
     * plain `call` is an unsafe replacement for a function call: use this
     * function instead.
     *
     * If `target` reverts with a revert reason, it is bubbled up by this
     * function (like regular Solidity function calls).
     *
     * Returns the raw returned data. To convert to the expected return value,
     * use https://solidity.readthedocs.io/en/latest/units-and-global-variables.html?highlight=abi.decode#abi-encoding-and-decoding-functions[`abi.decode`].
     *
     * Requirements:
     *
     * - `target` must be a contract.
     * - calling `target` with `data` must not revert.
     *
     * _Available since v3.1._
     */
    function functionCall(address target, bytes memory data) internal returns (bytes memory) {
        return functionCallWithValue(target, data, 0, "Address: low-level call failed");
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`], but with
     * `errorMessage` as a fallback revert reason when `target` reverts.
     *
     * _Available since v3.1._
     */
    function functionCall(
        address target,
        bytes memory data,
        string memory errorMessage
    ) internal returns (bytes memory) {
        return functionCallWithValue(target, data, 0, errorMessage);
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but also transferring `value` wei to `target`.
     *
     * Requirements:
     *
     * - the calling contract must have an ETH balance of at least `value`.
     * - the called Solidity function must be `payable`.
     *
     * _Available since v3.1._
     */
    function functionCallWithValue(address target, bytes memory data, uint256 value) internal returns (bytes memory) {
        return functionCallWithValue(target, data, value, "Address: low-level call with value failed");
    }

    /**
     * @dev Same as {xref-Address-functionCallWithValue-address-bytes-uint256-}[`functionCallWithValue`], but
     * with `errorMessage` as a fallback revert reason when `target` reverts.
     *
     * _Available since v3.1._
     */
    function functionCallWithValue(
        address target,
        bytes memory data,
        uint256 value,
        string memory errorMessage
    ) internal returns (bytes memory) {
        require(address(this).balance >= value, "Address: insufficient balance for call");
        (bool success, bytes memory returndata) = target.call{value: value}(data);
        return verifyCallResultFromTarget(target, success, returndata, errorMessage);
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but performing a static call.
     *
     * _Available since v3.3._
     */
    function functionStaticCall(address target, bytes memory data) internal view returns (bytes memory) {
        return functionStaticCall(target, data, "Address: low-level static call failed");
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-string-}[`functionCall`],
     * but performing a static call.
     *
     * _Available since v3.3._
     */
    function functionStaticCall(
        address target,
        bytes memory data,
        string memory errorMessage
    ) internal view returns (bytes memory) {
        (bool success, bytes memory returndata) = target.staticcall(data);
        return verifyCallResultFromTarget(target, success, returndata, errorMessage);
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-}[`functionCall`],
     * but performing a delegate call.
     *
     * _Available since v3.4._
     */
    function functionDelegateCall(address target, bytes memory data) internal returns (bytes memory) {
        return functionDelegateCall(target, data, "Address: low-level delegate call failed");
    }

    /**
     * @dev Same as {xref-Address-functionCall-address-bytes-string-}[`functionCall`],
     * but performing a delegate call.
     *
     * _Available since v3.4._
     */
    function functionDelegateCall(
        address target,
        bytes memory data,
        string memory errorMessage
    ) internal returns (bytes memory) {
        (bool success, bytes memory returndata) = target.delegatecall(data);
        return verifyCallResultFromTarget(target, success, returndata, errorMessage);
    }

    /**
     * @dev Tool to verify that a low level call to smart-contract was successful, and revert (either by bubbling
     * the revert reason or using the provided one) in case of unsuccessful call or if target was not a contract.
     *
     * _Available since v4.8._
     */
    function verifyCallResultFromTarget(
        address target,
        bool success,
        bytes memory returndata,
        string memory errorMessage
    ) internal view returns (bytes memory) {
        if (success) {
            if (returndata.length == 0) {
                // only check isContract if the call was successful and the return data is empty
                // otherwise we already know that it was a contract
                require(isContract(target), "Address: call to non-contract");
            }
            return returndata;
        } else {
            _revert(returndata, errorMessage);
        }
    }

    /**
     * @dev Tool to verify that a low level call was successful, and revert if it wasn't, either by bubbling the
     * revert reason or using the provided one.
     *
     * _Available since v4.3._
     */
    function verifyCallResult(
        bool success,
        bytes memory returndata,
        string memory errorMessage
    ) internal pure returns (bytes memory) {
        if (success) {
            return returndata;
        } else {
            _revert(returndata, errorMessage);
        }
    }

    function _revert(bytes memory returndata, string memory errorMessage) private pure {
        // Look for revert reason and bubble it up if present
        if (returndata.length > 0) {
            // The easiest way to bubble the revert reason is using memory via assembly
            /// @solidity memory-safe-assembly
            assembly {
                let returndata_size := mload(returndata)
                revert(add(32, returndata), returndata_size)
            }
        } else {
            revert(errorMessage);
        }
    }
}
          

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.4) (utils/Context.sol)

pragma solidity ^0.8.0;
import {Initializable} from "../proxy/utils/Initializable.sol";

/**
 * @dev Provides information about the current execution context, including the
 * sender of the transaction and its data. While these are generally available
 * via msg.sender and msg.data, they should not be accessed in such a direct
 * manner, since when dealing with meta-transactions the account sending and
 * paying for execution may not be the actual sender (as far as an application
 * is concerned).
 *
 * This contract is only required for intermediate, library-like contracts.
 */
abstract contract ContextUpgradeable is Initializable {
    function __Context_init() internal onlyInitializing {
    }

    function __Context_init_unchained() internal onlyInitializing {
    }
    function _msgSender() internal view virtual returns (address) {
        return msg.sender;
    }

    function _msgData() internal view virtual returns (bytes calldata) {
        return msg.data;
    }

    function _contextSuffixLength() internal view virtual returns (uint256) {
        return 0;
    }

    /**
     * @dev This empty reserved space is put in place to allow future versions to add new
     * variables without shifting down storage in the inheritance chain.
     * See https://docs.openzeppelin.com/contracts/4.x/upgradeable#storage_gaps
     */
    uint256[50] private __gap;
}
          

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (interfaces/IERC1967.sol)

pragma solidity ^0.8.0;

/**
 * @dev ERC-1967: Proxy Storage Slots. This interface contains the events defined in the ERC.
 *
 * _Available since v4.8.3._
 */
interface IERC1967 {
    /**
     * @dev Emitted when the implementation is upgraded.
     */
    event Upgraded(address indexed implementation);

    /**
     * @dev Emitted when the admin account has changed.
     */
    event AdminChanged(address previousAdmin, address newAdmin);

    /**
     * @dev Emitted when the beacon is changed.
     */
    event BeaconUpgraded(address indexed beacon);
}
          

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.5.0) (interfaces/draft-IERC1822.sol)

pragma solidity ^0.8.0;

/**
 * @dev ERC1822: Universal Upgradeable Proxy Standard (UUPS) documents a method for upgradeability through a simplified
 * proxy whose upgrades are fully controlled by the current implementation.
 */
interface IERC1822Proxiable {
    /**
     * @dev Returns the storage slot that the proxiable contract assumes is being used to store the implementation
     * address.
     *
     * IMPORTANT: A proxy pointing at a proxiable contract should not be considered proxiable itself, because this risks
     * bricking a proxy that upgrades to it, by delegating to itself until out of gas. Thus it is critical that this
     * function revert if invoked through a proxy.
     */
    function proxiableUUID() external view returns (bytes32);
}
          

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (proxy/ERC1967/ERC1967Upgrade.sol)

pragma solidity ^0.8.2;

import "../beacon/IBeacon.sol";
import "../../interfaces/IERC1967.sol";
import "../../interfaces/draft-IERC1822.sol";
import "../../utils/Address.sol";
import "../../utils/StorageSlot.sol";

/**
 * @dev This abstract contract provides getters and event emitting update functions for
 * https://eips.ethereum.org/EIPS/eip-1967[EIP1967] slots.
 *
 * _Available since v4.1._
 */
abstract contract ERC1967Upgrade is IERC1967 {
    // This is the keccak-256 hash of "eip1967.proxy.rollback" subtracted by 1
    bytes32 private constant _ROLLBACK_SLOT = 0x4910fdfa16fed3260ed0e7147f7cc6da11a60208b5b9406d12a635614ffd9143;

    /**
     * @dev Storage slot with the address of the current implementation.
     * This is the keccak-256 hash of "eip1967.proxy.implementation" subtracted by 1, and is
     * validated in the constructor.
     */
    bytes32 internal constant _IMPLEMENTATION_SLOT = 0x360894a13ba1a3210667c828492db98dca3e2076cc3735a920a3ca505d382bbc;

    /**
     * @dev Returns the current implementation address.
     */
    function _getImplementation() internal view returns (address) {
        return StorageSlot.getAddressSlot(_IMPLEMENTATION_SLOT).value;
    }

    /**
     * @dev Stores a new address in the EIP1967 implementation slot.
     */
    function _setImplementation(address newImplementation) private {
        require(Address.isContract(newImplementation), "ERC1967: new implementation is not a contract");
        StorageSlot.getAddressSlot(_IMPLEMENTATION_SLOT).value = newImplementation;
    }

    /**
     * @dev Perform implementation upgrade
     *
     * Emits an {Upgraded} event.
     */
    function _upgradeTo(address newImplementation) internal {
        _setImplementation(newImplementation);
        emit Upgraded(newImplementation);
    }

    /**
     * @dev Perform implementation upgrade with additional setup call.
     *
     * Emits an {Upgraded} event.
     */
    function _upgradeToAndCall(address newImplementation, bytes memory data, bool forceCall) internal {
        _upgradeTo(newImplementation);
        if (data.length > 0 || forceCall) {
            Address.functionDelegateCall(newImplementation, data);
        }
    }

    /**
     * @dev Perform implementation upgrade with security checks for UUPS proxies, and additional setup call.
     *
     * Emits an {Upgraded} event.
     */
    function _upgradeToAndCallUUPS(address newImplementation, bytes memory data, bool forceCall) internal {
        // Upgrades from old implementations will perform a rollback test. This test requires the new
        // implementation to upgrade back to the old, non-ERC1822 compliant, implementation. Removing
        // this special case will break upgrade paths from old UUPS implementation to new ones.
        if (StorageSlot.getBooleanSlot(_ROLLBACK_SLOT).value) {
            _setImplementation(newImplementation);
        } else {
            try IERC1822Proxiable(newImplementation).proxiableUUID() returns (bytes32 slot) {
                require(slot == _IMPLEMENTATION_SLOT, "ERC1967Upgrade: unsupported proxiableUUID");
            } catch {
                revert("ERC1967Upgrade: new implementation is not UUPS");
            }
            _upgradeToAndCall(newImplementation, data, forceCall);
        }
    }

    /**
     * @dev Storage slot with the admin of the contract.
     * This is the keccak-256 hash of "eip1967.proxy.admin" subtracted by 1, and is
     * validated in the constructor.
     */
    bytes32 internal constant _ADMIN_SLOT = 0xb53127684a568b3173ae13b9f8a6016e243e63b6e8ee1178d6a717850b5d6103;

    /**
     * @dev Returns the current admin.
     */
    function _getAdmin() internal view returns (address) {
        return StorageSlot.getAddressSlot(_ADMIN_SLOT).value;
    }

    /**
     * @dev Stores a new address in the EIP1967 admin slot.
     */
    function _setAdmin(address newAdmin) private {
        require(newAdmin != address(0), "ERC1967: new admin is the zero address");
        StorageSlot.getAddressSlot(_ADMIN_SLOT).value = newAdmin;
    }

    /**
     * @dev Changes the admin of the proxy.
     *
     * Emits an {AdminChanged} event.
     */
    function _changeAdmin(address newAdmin) internal {
        emit AdminChanged(_getAdmin(), newAdmin);
        _setAdmin(newAdmin);
    }

    /**
     * @dev The storage slot of the UpgradeableBeacon contract which defines the implementation for this proxy.
     * This is bytes32(uint256(keccak256('eip1967.proxy.beacon')) - 1)) and is validated in the constructor.
     */
    bytes32 internal constant _BEACON_SLOT = 0xa3f0ad74e5423aebfd80d3ef4346578335a9a72aeaee59ff6cb3582b35133d50;

    /**
     * @dev Returns the current beacon.
     */
    function _getBeacon() internal view returns (address) {
        return StorageSlot.getAddressSlot(_BEACON_SLOT).value;
    }

    /**
     * @dev Stores a new beacon in the EIP1967 beacon slot.
     */
    function _setBeacon(address newBeacon) private {
        require(Address.isContract(newBeacon), "ERC1967: new beacon is not a contract");
        require(
            Address.isContract(IBeacon(newBeacon).implementation()),
            "ERC1967: beacon implementation is not a contract"
        );
        StorageSlot.getAddressSlot(_BEACON_SLOT).value = newBeacon;
    }

    /**
     * @dev Perform beacon upgrade with additional setup call. Note: This upgrades the address of the beacon, it does
     * not upgrade the implementation contained in the beacon (see {UpgradeableBeacon-_setImplementation} for that).
     *
     * Emits a {BeaconUpgraded} event.
     */
    function _upgradeBeaconToAndCall(address newBeacon, bytes memory data, bool forceCall) internal {
        _setBeacon(newBeacon);
        emit BeaconUpgraded(newBeacon);
        if (data.length > 0 || forceCall) {
            Address.functionDelegateCall(IBeacon(newBeacon).implementation(), data);
        }
    }
}
          

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (utils/StorageSlot.sol)
// This file was procedurally generated from scripts/generate/templates/StorageSlot.js.

pragma solidity ^0.8.0;

/**
 * @dev Library for reading and writing primitive types to specific storage slots.
 *
 * Storage slots are often used to avoid storage conflict when dealing with upgradeable contracts.
 * This library helps with reading and writing to such slots without the need for inline assembly.
 *
 * The functions in this library return Slot structs that contain a `value` member that can be used to read or write.
 *
 * Example usage to set ERC1967 implementation slot:
 * ```solidity
 * contract ERC1967 {
 *     bytes32 internal constant _IMPLEMENTATION_SLOT = 0x360894a13ba1a3210667c828492db98dca3e2076cc3735a920a3ca505d382bbc;
 *
 *     function _getImplementation() internal view returns (address) {
 *         return StorageSlot.getAddressSlot(_IMPLEMENTATION_SLOT).value;
 *     }
 *
 *     function _setImplementation(address newImplementation) internal {
 *         require(Address.isContract(newImplementation), "ERC1967: new implementation is not a contract");
 *         StorageSlot.getAddressSlot(_IMPLEMENTATION_SLOT).value = newImplementation;
 *     }
 * }
 * ```
 *
 * _Available since v4.1 for `address`, `bool`, `bytes32`, `uint256`._
 * _Available since v4.9 for `string`, `bytes`._
 */
library StorageSlot {
    struct AddressSlot {
        address value;
    }

    struct BooleanSlot {
        bool value;
    }

    struct Bytes32Slot {
        bytes32 value;
    }

    struct Uint256Slot {
        uint256 value;
    }

    struct StringSlot {
        string value;
    }

    struct BytesSlot {
        bytes value;
    }

    /**
     * @dev Returns an `AddressSlot` with member `value` located at `slot`.
     */
    function getAddressSlot(bytes32 slot) internal pure returns (AddressSlot storage r) {
        /// @solidity memory-safe-assembly
        assembly {
            r.slot := slot
        }
    }

    /**
     * @dev Returns an `BooleanSlot` with member `value` located at `slot`.
     */
    function getBooleanSlot(bytes32 slot) internal pure returns (BooleanSlot storage r) {
        /// @solidity memory-safe-assembly
        assembly {
            r.slot := slot
        }
    }

    /**
     * @dev Returns an `Bytes32Slot` with member `value` located at `slot`.
     */
    function getBytes32Slot(bytes32 slot) internal pure returns (Bytes32Slot storage r) {
        /// @solidity memory-safe-assembly
        assembly {
            r.slot := slot
        }
    }

    /**
     * @dev Returns an `Uint256Slot` with member `value` located at `slot`.
     */
    function getUint256Slot(bytes32 slot) internal pure returns (Uint256Slot storage r) {
        /// @solidity memory-safe-assembly
        assembly {
            r.slot := slot
        }
    }

    /**
     * @dev Returns an `StringSlot` with member `value` located at `slot`.
     */
    function getStringSlot(bytes32 slot) internal pure returns (StringSlot storage r) {
        /// @solidity memory-safe-assembly
        assembly {
            r.slot := slot
        }
    }

    /**
     * @dev Returns an `StringSlot` representation of the string storage pointer `store`.
     */
    function getStringSlot(string storage store) internal pure returns (StringSlot storage r) {
        /// @solidity memory-safe-assembly
        assembly {
            r.slot := store.slot
        }
    }

    /**
     * @dev Returns an `BytesSlot` with member `value` located at `slot`.
     */
    function getBytesSlot(bytes32 slot) internal pure returns (BytesSlot storage r) {
        /// @solidity memory-safe-assembly
        assembly {
            r.slot := slot
        }
    }

    /**
     * @dev Returns an `BytesSlot` representation of the bytes storage pointer `store`.
     */
    function getBytesSlot(bytes storage store) internal pure returns (BytesSlot storage r) {
        /// @solidity memory-safe-assembly
        assembly {
            r.slot := store.slot
        }
    }
}
          

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (utils/Strings.sol)

pragma solidity ^0.8.0;

import "./math/Math.sol";
import "./math/SignedMath.sol";

/**
 * @dev String operations.
 */
library Strings {
    bytes16 private constant _SYMBOLS = "0123456789abcdef";
    uint8 private constant _ADDRESS_LENGTH = 20;

    /**
     * @dev Converts a `uint256` to its ASCII `string` decimal representation.
     */
    function toString(uint256 value) internal pure returns (string memory) {
        unchecked {
            uint256 length = Math.log10(value) + 1;
            string memory buffer = new string(length);
            uint256 ptr;
            /// @solidity memory-safe-assembly
            assembly {
                ptr := add(buffer, add(32, length))
            }
            while (true) {
                ptr--;
                /// @solidity memory-safe-assembly
                assembly {
                    mstore8(ptr, byte(mod(value, 10), _SYMBOLS))
                }
                value /= 10;
                if (value == 0) break;
            }
            return buffer;
        }
    }

    /**
     * @dev Converts a `int256` to its ASCII `string` decimal representation.
     */
    function toString(int256 value) internal pure returns (string memory) {
        return string(abi.encodePacked(value < 0 ? "-" : "", toString(SignedMath.abs(value))));
    }

    /**
     * @dev Converts a `uint256` to its ASCII `string` hexadecimal representation.
     */
    function toHexString(uint256 value) internal pure returns (string memory) {
        unchecked {
            return toHexString(value, Math.log256(value) + 1);
        }
    }

    /**
     * @dev Converts a `uint256` to its ASCII `string` hexadecimal representation with fixed length.
     */
    function toHexString(uint256 value, uint256 length) internal pure returns (string memory) {
        bytes memory buffer = new bytes(2 * length + 2);
        buffer[0] = "0";
        buffer[1] = "x";
        for (uint256 i = 2 * length + 1; i > 1; --i) {
            buffer[i] = _SYMBOLS[value & 0xf];
            value >>= 4;
        }
        require(value == 0, "Strings: hex length insufficient");
        return string(buffer);
    }

    /**
     * @dev Converts an `address` with fixed length of 20 bytes to its not checksummed ASCII `string` hexadecimal representation.
     */
    function toHexString(address addr) internal pure returns (string memory) {
        return toHexString(uint256(uint160(addr)), _ADDRESS_LENGTH);
    }

    /**
     * @dev Returns true if the two strings are equal.
     */
    function equal(string memory a, string memory b) internal pure returns (bool) {
        return keccak256(bytes(a)) == keccak256(bytes(b));
    }
}
          

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (utils/cryptography/ECDSA.sol)

pragma solidity ^0.8.0;

import "../Strings.sol";

/**
 * @dev Elliptic Curve Digital Signature Algorithm (ECDSA) operations.
 *
 * These functions can be used to verify that a message was signed by the holder
 * of the private keys of a given address.
 */
library ECDSA {
    enum RecoverError {
        NoError,
        InvalidSignature,
        InvalidSignatureLength,
        InvalidSignatureS,
        InvalidSignatureV // Deprecated in v4.8
    }

    function _throwError(RecoverError error) private pure {
        if (error == RecoverError.NoError) {
            return; // no error: do nothing
        } else if (error == RecoverError.InvalidSignature) {
            revert("ECDSA: invalid signature");
        } else if (error == RecoverError.InvalidSignatureLength) {
            revert("ECDSA: invalid signature length");
        } else if (error == RecoverError.InvalidSignatureS) {
            revert("ECDSA: invalid signature 's' value");
        }
    }

    /**
     * @dev Returns the address that signed a hashed message (`hash`) with
     * `signature` or error string. This address can then be used for verification purposes.
     *
     * The `ecrecover` EVM opcode allows for malleable (non-unique) signatures:
     * this function rejects them by requiring the `s` value to be in the lower
     * half order, and the `v` value to be either 27 or 28.
     *
     * IMPORTANT: `hash` _must_ be the result of a hash operation for the
     * verification to be secure: it is possible to craft signatures that
     * recover to arbitrary addresses for non-hashed data. A safe way to ensure
     * this is by receiving a hash of the original message (which may otherwise
     * be too long), and then calling {toEthSignedMessageHash} on it.
     *
     * Documentation for signature generation:
     * - with https://web3js.readthedocs.io/en/v1.3.4/web3-eth-accounts.html#sign[Web3.js]
     * - with https://docs.ethers.io/v5/api/signer/#Signer-signMessage[ethers]
     *
     * _Available since v4.3._
     */
    function tryRecover(bytes32 hash, bytes memory signature) internal pure returns (address, RecoverError) {
        if (signature.length == 65) {
            bytes32 r;
            bytes32 s;
            uint8 v;
            // ecrecover takes the signature parameters, and the only way to get them
            // currently is to use assembly.
            /// @solidity memory-safe-assembly
            assembly {
                r := mload(add(signature, 0x20))
                s := mload(add(signature, 0x40))
                v := byte(0, mload(add(signature, 0x60)))
            }
            return tryRecover(hash, v, r, s);
        } else {
            return (address(0), RecoverError.InvalidSignatureLength);
        }
    }

    /**
     * @dev Returns the address that signed a hashed message (`hash`) with
     * `signature`. This address can then be used for verification purposes.
     *
     * The `ecrecover` EVM opcode allows for malleable (non-unique) signatures:
     * this function rejects them by requiring the `s` value to be in the lower
     * half order, and the `v` value to be either 27 or 28.
     *
     * IMPORTANT: `hash` _must_ be the result of a hash operation for the
     * verification to be secure: it is possible to craft signatures that
     * recover to arbitrary addresses for non-hashed data. A safe way to ensure
     * this is by receiving a hash of the original message (which may otherwise
     * be too long), and then calling {toEthSignedMessageHash} on it.
     */
    function recover(bytes32 hash, bytes memory signature) internal pure returns (address) {
        (address recovered, RecoverError error) = tryRecover(hash, signature);
        _throwError(error);
        return recovered;
    }

    /**
     * @dev Overload of {ECDSA-tryRecover} that receives the `r` and `vs` short-signature fields separately.
     *
     * See https://eips.ethereum.org/EIPS/eip-2098[EIP-2098 short signatures]
     *
     * _Available since v4.3._
     */
    function tryRecover(bytes32 hash, bytes32 r, bytes32 vs) internal pure returns (address, RecoverError) {
        bytes32 s = vs & bytes32(0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff);
        uint8 v = uint8((uint256(vs) >> 255) + 27);
        return tryRecover(hash, v, r, s);
    }

    /**
     * @dev Overload of {ECDSA-recover} that receives the `r and `vs` short-signature fields separately.
     *
     * _Available since v4.2._
     */
    function recover(bytes32 hash, bytes32 r, bytes32 vs) internal pure returns (address) {
        (address recovered, RecoverError error) = tryRecover(hash, r, vs);
        _throwError(error);
        return recovered;
    }

    /**
     * @dev Overload of {ECDSA-tryRecover} that receives the `v`,
     * `r` and `s` signature fields separately.
     *
     * _Available since v4.3._
     */
    function tryRecover(bytes32 hash, uint8 v, bytes32 r, bytes32 s) internal pure returns (address, RecoverError) {
        // EIP-2 still allows signature malleability for ecrecover(). Remove this possibility and make the signature
        // unique. Appendix F in the Ethereum Yellow paper (https://ethereum.github.io/yellowpaper/paper.pdf), defines
        // the valid range for s in (301): 0 < s < secp256k1n ÷ 2 + 1, and for v in (302): v ∈ {27, 28}. Most
        // signatures from current libraries generate a unique signature with an s-value in the lower half order.
        //
        // If your library generates malleable signatures, such as s-values in the upper range, calculate a new s-value
        // with 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141 - s1 and flip v from 27 to 28 or
        // vice versa. If your library also generates signatures with 0/1 for v instead 27/28, add 27 to v to accept
        // these malleable signatures as well.
        if (uint256(s) > 0x7FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF5D576E7357A4501DDFE92F46681B20A0) {
            return (address(0), RecoverError.InvalidSignatureS);
        }

        // If the signature is valid (and not malleable), return the signer address
        address signer = ecrecover(hash, v, r, s);
        if (signer == address(0)) {
            return (address(0), RecoverError.InvalidSignature);
        }

        return (signer, RecoverError.NoError);
    }

    /**
     * @dev Overload of {ECDSA-recover} that receives the `v`,
     * `r` and `s` signature fields separately.
     */
    function recover(bytes32 hash, uint8 v, bytes32 r, bytes32 s) internal pure returns (address) {
        (address recovered, RecoverError error) = tryRecover(hash, v, r, s);
        _throwError(error);
        return recovered;
    }

    /**
     * @dev Returns an Ethereum Signed Message, created from a `hash`. This
     * produces hash corresponding to the one signed with the
     * https://eth.wiki/json-rpc/API#eth_sign[`eth_sign`]
     * JSON-RPC method as part of EIP-191.
     *
     * See {recover}.
     */
    function toEthSignedMessageHash(bytes32 hash) internal pure returns (bytes32 message) {
        // 32 is the length in bytes of hash,
        // enforced by the type signature above
        /// @solidity memory-safe-assembly
        assembly {
            mstore(0x00, "\x19Ethereum Signed Message:\n32")
            mstore(0x1c, hash)
            message := keccak256(0x00, 0x3c)
        }
    }

    /**
     * @dev Returns an Ethereum Signed Message, created from `s`. This
     * produces hash corresponding to the one signed with the
     * https://eth.wiki/json-rpc/API#eth_sign[`eth_sign`]
     * JSON-RPC method as part of EIP-191.
     *
     * See {recover}.
     */
    function toEthSignedMessageHash(bytes memory s) internal pure returns (bytes32) {
        return keccak256(abi.encodePacked("\x19Ethereum Signed Message:\n", Strings.toString(s.length), s));
    }

    /**
     * @dev Returns an Ethereum Signed Typed Data, created from a
     * `domainSeparator` and a `structHash`. This produces hash corresponding
     * to the one signed with the
     * https://eips.ethereum.org/EIPS/eip-712[`eth_signTypedData`]
     * JSON-RPC method as part of EIP-712.
     *
     * See {recover}.
     */
    function toTypedDataHash(bytes32 domainSeparator, bytes32 structHash) internal pure returns (bytes32 data) {
        /// @solidity memory-safe-assembly
        assembly {
            let ptr := mload(0x40)
            mstore(ptr, "\x19\x01")
            mstore(add(ptr, 0x02), domainSeparator)
            mstore(add(ptr, 0x22), structHash)
            data := keccak256(ptr, 0x42)
        }
    }

    /**
     * @dev Returns an Ethereum Signed Data with intended validator, created from a
     * `validator` and `data` according to the version 0 of EIP-191.
     *
     * See {recover}.
     */
    function toDataWithIntendedValidatorHash(address validator, bytes memory data) internal pure returns (bytes32) {
        return keccak256(abi.encodePacked("\x19\x00", validator, data));
    }
}
          

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.9.0) (utils/math/Math.sol)

pragma solidity ^0.8.0;

/**
 * @dev Standard math utilities missing in the Solidity language.
 */
library Math {
    enum Rounding {
        Down, // Toward negative infinity
        Up, // Toward infinity
        Zero // Toward zero
    }

    /**
     * @dev Returns the largest of two numbers.
     */
    function max(uint256 a, uint256 b) internal pure returns (uint256) {
        return a > b ? a : b;
    }

    /**
     * @dev Returns the smallest of two numbers.
     */
    function min(uint256 a, uint256 b) internal pure returns (uint256) {
        return a < b ? a : b;
    }

    /**
     * @dev Returns the average of two numbers. The result is rounded towards
     * zero.
     */
    function average(uint256 a, uint256 b) internal pure returns (uint256) {
        // (a + b) / 2 can overflow.
        return (a & b) + (a ^ b) / 2;
    }

    /**
     * @dev Returns the ceiling of the division of two numbers.
     *
     * This differs from standard division with `/` in that it rounds up instead
     * of rounding down.
     */
    function ceilDiv(uint256 a, uint256 b) internal pure returns (uint256) {
        // (a + b - 1) / b can overflow on addition, so we distribute.
        return a == 0 ? 0 : (a - 1) / b + 1;
    }

    /**
     * @notice Calculates floor(x * y / denominator) with full precision. Throws if result overflows a uint256 or denominator == 0
     * @dev Original credit to Remco Bloemen under MIT license (https://xn--2-umb.com/21/muldiv)
     * with further edits by Uniswap Labs also under MIT license.
     */
    function mulDiv(uint256 x, uint256 y, uint256 denominator) internal pure returns (uint256 result) {
        unchecked {
            // 512-bit multiply [prod1 prod0] = x * y. Compute the product mod 2^256 and mod 2^256 - 1, then use
            // use the Chinese Remainder Theorem to reconstruct the 512 bit result. The result is stored in two 256
            // variables such that product = prod1 * 2^256 + prod0.
            uint256 prod0; // Least significant 256 bits of the product
            uint256 prod1; // Most significant 256 bits of the product
            assembly {
                let mm := mulmod(x, y, not(0))
                prod0 := mul(x, y)
                prod1 := sub(sub(mm, prod0), lt(mm, prod0))
            }

            // Handle non-overflow cases, 256 by 256 division.
            if (prod1 == 0) {
                // Solidity will revert if denominator == 0, unlike the div opcode on its own.
                // The surrounding unchecked block does not change this fact.
                // See https://docs.soliditylang.org/en/latest/control-structures.html#checked-or-unchecked-arithmetic.
                return prod0 / denominator;
            }

            // Make sure the result is less than 2^256. Also prevents denominator == 0.
            require(denominator > prod1, "Math: mulDiv overflow");

            ///////////////////////////////////////////////
            // 512 by 256 division.
            ///////////////////////////////////////////////

            // Make division exact by subtracting the remainder from [prod1 prod0].
            uint256 remainder;
            assembly {
                // Compute remainder using mulmod.
                remainder := mulmod(x, y, denominator)

                // Subtract 256 bit number from 512 bit number.
                prod1 := sub(prod1, gt(remainder, prod0))
                prod0 := sub(prod0, remainder)
            }

            // Factor powers of two out of denominator and compute largest power of two divisor of denominator. Always >= 1.
            // See https://cs.stackexchange.com/q/138556/92363.

            // Does not overflow because the denominator cannot be zero at this stage in the function.
            uint256 twos = denominator & (~denominator + 1);
            assembly {
                // Divide denominator by twos.
                denominator := div(denominator, twos)

                // Divide [prod1 prod0] by twos.
                prod0 := div(prod0, twos)

                // Flip twos such that it is 2^256 / twos. If twos is zero, then it becomes one.
                twos := add(div(sub(0, twos), twos), 1)
            }

            // Shift in bits from prod1 into prod0.
            prod0 |= prod1 * twos;

            // Invert denominator mod 2^256. Now that denominator is an odd number, it has an inverse modulo 2^256 such
            // that denominator * inv = 1 mod 2^256. Compute the inverse by starting with a seed that is correct for
            // four bits. That is, denominator * inv = 1 mod 2^4.
            uint256 inverse = (3 * denominator) ^ 2;

            // Use the Newton-Raphson iteration to improve the precision. Thanks to Hensel's lifting lemma, this also works
            // in modular arithmetic, doubling the correct bits in each step.
            inverse *= 2 - denominator * inverse; // inverse mod 2^8
            inverse *= 2 - denominator * inverse; // inverse mod 2^16
            inverse *= 2 - denominator * inverse; // inverse mod 2^32
            inverse *= 2 - denominator * inverse; // inverse mod 2^64
            inverse *= 2 - denominator * inverse; // inverse mod 2^128
            inverse *= 2 - denominator * inverse; // inverse mod 2^256

            // Because the division is now exact we can divide by multiplying with the modular inverse of denominator.
            // This will give us the correct result modulo 2^256. Since the preconditions guarantee that the outcome is
            // less than 2^256, this is the final result. We don't need to compute the high bits of the result and prod1
            // is no longer required.
            result = prod0 * inverse;
            return result;
        }
    }

    /**
     * @notice Calculates x * y / denominator with full precision, following the selected rounding direction.
     */
    function mulDiv(uint256 x, uint256 y, uint256 denominator, Rounding rounding) internal pure returns (uint256) {
        uint256 result = mulDiv(x, y, denominator);
        if (rounding == Rounding.Up && mulmod(x, y, denominator) > 0) {
            result += 1;
        }
        return result;
    }

    /**
     * @dev Returns the square root of a number. If the number is not a perfect square, the value is rounded down.
     *
     * Inspired by Henry S. Warren, Jr.'s "Hacker's Delight" (Chapter 11).
     */
    function sqrt(uint256 a) internal pure returns (uint256) {
        if (a == 0) {
            return 0;
        }

        // For our first guess, we get the biggest power of 2 which is smaller than the square root of the target.
        //
        // We know that the "msb" (most significant bit) of our target number `a` is a power of 2 such that we have
        // `msb(a) <= a < 2*msb(a)`. This value can be written `msb(a)=2**k` with `k=log2(a)`.
        //
        // This can be rewritten `2**log2(a) <= a < 2**(log2(a) + 1)`
        // → `sqrt(2**k) <= sqrt(a) < sqrt(2**(k+1))`
        // → `2**(k/2) <= sqrt(a) < 2**((k+1)/2) <= 2**(k/2 + 1)`
        //
        // Consequently, `2**(log2(a) / 2)` is a good first approximation of `sqrt(a)` with at least 1 correct bit.
        uint256 result = 1 << (log2(a) >> 1);

        // At this point `result` is an estimation with one bit of precision. We know the true value is a uint128,
        // since it is the square root of a uint256. Newton's method converges quadratically (precision doubles at
        // every iteration). We thus need at most 7 iteration to turn our partial result with one bit of precision
        // into the expected uint128 result.
        unchecked {
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            result = (result + a / result) >> 1;
            return min(result, a / result);
        }
    }

    /**
     * @notice Calculates sqrt(a), following the selected rounding direction.
     */
    function sqrt(uint256 a, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = sqrt(a);
            return result + (rounding == Rounding.Up && result * result < a ? 1 : 0);
        }
    }

    /**
     * @dev Return the log in base 2, rounded down, of a positive value.
     * Returns 0 if given 0.
     */
    function log2(uint256 value) internal pure returns (uint256) {
        uint256 result = 0;
        unchecked {
            if (value >> 128 > 0) {
                value >>= 128;
                result += 128;
            }
            if (value >> 64 > 0) {
                value >>= 64;
                result += 64;
            }
            if (value >> 32 > 0) {
                value >>= 32;
                result += 32;
            }
            if (value >> 16 > 0) {
                value >>= 16;
                result += 16;
            }
            if (value >> 8 > 0) {
                value >>= 8;
                result += 8;
            }
            if (value >> 4 > 0) {
                value >>= 4;
                result += 4;
            }
            if (value >> 2 > 0) {
                value >>= 2;
                result += 2;
            }
            if (value >> 1 > 0) {
                result += 1;
            }
        }
        return result;
    }

    /**
     * @dev Return the log in base 2, following the selected rounding direction, of a positive value.
     * Returns 0 if given 0.
     */
    function log2(uint256 value, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = log2(value);
            return result + (rounding == Rounding.Up && 1 << result < value ? 1 : 0);
        }
    }

    /**
     * @dev Return the log in base 10, rounded down, of a positive value.
     * Returns 0 if given 0.
     */
    function log10(uint256 value) internal pure returns (uint256) {
        uint256 result = 0;
        unchecked {
            if (value >= 10 ** 64) {
                value /= 10 ** 64;
                result += 64;
            }
            if (value >= 10 ** 32) {
                value /= 10 ** 32;
                result += 32;
            }
            if (value >= 10 ** 16) {
                value /= 10 ** 16;
                result += 16;
            }
            if (value >= 10 ** 8) {
                value /= 10 ** 8;
                result += 8;
            }
            if (value >= 10 ** 4) {
                value /= 10 ** 4;
                result += 4;
            }
            if (value >= 10 ** 2) {
                value /= 10 ** 2;
                result += 2;
            }
            if (value >= 10 ** 1) {
                result += 1;
            }
        }
        return result;
    }

    /**
     * @dev Return the log in base 10, following the selected rounding direction, of a positive value.
     * Returns 0 if given 0.
     */
    function log10(uint256 value, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = log10(value);
            return result + (rounding == Rounding.Up && 10 ** result < value ? 1 : 0);
        }
    }

    /**
     * @dev Return the log in base 256, rounded down, of a positive value.
     * Returns 0 if given 0.
     *
     * Adding one to the result gives the number of pairs of hex symbols needed to represent `value` as a hex string.
     */
    function log256(uint256 value) internal pure returns (uint256) {
        uint256 result = 0;
        unchecked {
            if (value >> 128 > 0) {
                value >>= 128;
                result += 16;
            }
            if (value >> 64 > 0) {
                value >>= 64;
                result += 8;
            }
            if (value >> 32 > 0) {
                value >>= 32;
                result += 4;
            }
            if (value >> 16 > 0) {
                value >>= 16;
                result += 2;
            }
            if (value >> 8 > 0) {
                result += 1;
            }
        }
        return result;
    }

    /**
     * @dev Return the log in base 256, following the selected rounding direction, of a positive value.
     * Returns 0 if given 0.
     */
    function log256(uint256 value, Rounding rounding) internal pure returns (uint256) {
        unchecked {
            uint256 result = log256(value);
            return result + (rounding == Rounding.Up && 1 << (result << 3) < value ? 1 : 0);
        }
    }
}
          

// SPDX-License-Identifier: MIT
// OpenZeppelin Contracts (last updated v4.8.0) (utils/math/SignedMath.sol)

pragma solidity ^0.8.0;

/**
 * @dev Standard signed math utilities missing in the Solidity language.
 */
library SignedMath {
    /**
     * @dev Returns the largest of two signed numbers.
     */
    function max(int256 a, int256 b) internal pure returns (int256) {
        return a > b ? a : b;
    }

    /**
     * @dev Returns the smallest of two signed numbers.
     */
    function min(int256 a, int256 b) internal pure returns (int256) {
        return a < b ? a : b;
    }

    /**
     * @dev Returns the average of two signed numbers without overflow.
     * The result is rounded towards zero.
     */
    function average(int256 a, int256 b) internal pure returns (int256) {
        // Formula from the book "Hacker's Delight"
        int256 x = (a & b) + ((a ^ b) >> 1);
        return x + (int256(uint256(x) >> 255) & (a ^ b));
    }

    /**
     * @dev Returns the absolute unsigned value of a signed value.
     */
    function abs(int256 n) internal pure returns (uint256) {
        unchecked {
            // must be unchecked in order to support `n = type(int256).min`
            return uint256(n >= 0 ? n : -n);
        }
    }
}