// File: @openzeppelin/contracts/access/Ownable.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

import "../utils/Context.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 Ownable is Context {
    address private _owner;

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

    /**
     * @dev Initializes the contract setting the deployer as the initial owner.
     */
    constructor() {
        _setOwner(_msgSender());
    }

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

    /**
     * @dev Throws if called by any account other than the owner.
     */
    modifier onlyOwner() {
        require(owner() == _msgSender(), "Ownable: caller is not the owner");
        _;
    }

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

    function _setOwner(address newOwner) private {
        address oldOwner = _owner;
        _owner = newOwner;
        emit OwnershipTransferred(oldOwner, newOwner);
    }
}

// File: @openzeppelin/contracts/utils/Context.sol



// SPDX-License-Identifier: MIT

pragma solidity ^0.8.0;

/**
 * @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 Context {
    function _msgSender() internal view virtual returns (address) {
        return msg.sender;
    }

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

// File: contracts/L1/rollup/ICanonicalTransactionChain.sol



// SPDX-License-Identifier: MIT
pragma solidity >0.5.0 <0.9.0;

/* Library Imports */
import { Lib_OVMCodec } from "../../libraries/codec/Lib_OVMCodec.sol";

/* Interface Imports */
import { IChainStorageContainer } from "./IChainStorageContainer.sol";

/**
 * @title ICanonicalTransactionChain
 */
interface ICanonicalTransactionChain {
    /**********
     * Events *
     **********/

    event L2GasParamsUpdated(
        uint256 l2GasDiscountDivisor,
        uint256 enqueueGasCost,
        uint256 enqueueL2GasPrepaid
    );

    event TransactionEnqueued(
        address indexed _l1TxOrigin,
        address indexed _target,
        uint256 _gasLimit,
        bytes _data,
        uint256 indexed _queueIndex,
        uint256 _timestamp
    );

    event QueueBatchAppended(
        uint256 _startingQueueIndex,
        uint256 _numQueueElements,
        uint256 _totalElements
    );

    event SequencerBatchAppended(
        uint256 _startingQueueIndex,
        uint256 _numQueueElements,
        uint256 _totalElements
    );

    event TransactionBatchAppended(
        uint256 indexed _batchIndex,
        bytes32 _batchRoot,
        uint256 _batchSize,
        uint256 _prevTotalElements,
        bytes _extraData
    );

    /***********
     * Structs *
     ***********/

    struct BatchContext {
        uint256 numSequencedTransactions;
        uint256 numSubsequentQueueTransactions;
        uint256 timestamp;
        uint256 blockNumber;
    }

    /*******************************
     * Authorized Setter Functions *
     *******************************/

    /**
     * Allows the Burn Admin to update the parameters which determine the amount of gas to burn.
     * The value of enqueueL2GasPrepaid is immediately updated as well.
     */
    function setGasParams(uint256 _l2GasDiscountDivisor, uint256 _enqueueGasCost) external;

    /********************
     * Public Functions *
     ********************/

    /**
     * Accesses the batch storage container.
     * @return Reference to the batch storage container.
     */
    function batches() external view returns (IChainStorageContainer);

    /**
     * Retrieves the total number of elements submitted.
     * @return _totalElements Total submitted elements.
     */
    function getTotalElements() external view returns (uint256 _totalElements);

    /**
     * Retrieves the total number of batches submitted.
     * @return _totalBatches Total submitted batches.
     */
    function getTotalBatches() external view returns (uint256 _totalBatches);

    /**
     * Returns the index of the next element to be enqueued.
     * @return Index for the next queue element.
     */
    function getNextQueueIndex() external view returns (uint40);

    /**
     * Gets the queue element at a particular index.
     * @param _index Index of the queue element to access.
     * @return _element Queue element at the given index.
     */
    function getQueueElement(uint256 _index)
        external
        view
        returns (Lib_OVMCodec.QueueElement memory _element);

    /**
     * Returns the timestamp of the last transaction.
     * @return Timestamp for the last transaction.
     */
    function getLastTimestamp() external view returns (uint40);

    /**
     * Returns the blocknumber of the last transaction.
     * @return Blocknumber for the last transaction.
     */
    function getLastBlockNumber() external view returns (uint40);

    /**
     * Get the number of queue elements which have not yet been included.
     * @return Number of pending queue elements.
     */
    function getNumPendingQueueElements() external view returns (uint40);

    /**
     * Retrieves the length of the queue, including
     * both pending and canonical transactions.
     * @return Length of the queue.
     */
    function getQueueLength() external view returns (uint40);

    /**
     * Adds a transaction to the queue.
     * @param _target Target contract to send the transaction to.
     * @param _gasLimit Gas limit for the given transaction.
     * @param _data Transaction data.
     */
    function enqueue(
        address _target,
        uint256 _gasLimit,
        bytes memory _data
    ) external;

    /**
     * Allows the sequencer to append a batch of transactions.
     * @dev This function uses a custom encoding scheme for efficiency reasons.
     * .param _shouldStartAtElement Specific batch we expect to start appending to.
     * .param _totalElementsToAppend Total number of batch elements we expect to append.
     * .param _contexts Array of batch contexts.
     * .param _transactionDataFields Array of raw transaction data.
     */
    function appendSequencerBatch(
        // uint40 _shouldStartAtElement,
        // uint24 _totalElementsToAppend,
        // BatchContext[] _contexts,
        // bytes[] _transactionDataFields
    ) external;
}

// File: contracts/L1/rollup/IChainStorageContainer.sol



// SPDX-License-Identifier: MIT
pragma solidity >0.5.0 <0.9.0;

/**
 * @title IChainStorageContainer
 */
interface IChainStorageContainer {
    /********************
     * Public Functions *
     ********************/

    /**
     * Sets the container's global metadata field. We're using `bytes27` here because we use five
     * bytes to maintain the length of the underlying data structure, meaning we have an extra
     * 27 bytes to store arbitrary data.
     * @param _globalMetadata New global metadata to set.
     */
    function setGlobalMetadata(bytes27 _globalMetadata) external;

    /**
     * Retrieves the container's global metadata field.
     * @return Container global metadata field.
     */
    function getGlobalMetadata() external view returns (bytes27);

    /**
     * Retrieves the number of objects stored in the container.
     * @return Number of objects in the container.
     */
    function length() external view returns (uint256);

    /**
     * Pushes an object into the container.
     * @param _object A 32 byte value to insert into the container.
     */
    function push(bytes32 _object) external;

    /**
     * Pushes an object into the container. Function allows setting the global metadata since
     * we'll need to touch the "length" storage slot anyway, which also contains the global
     * metadata (it's an optimization).
     * @param _object A 32 byte value to insert into the container.
     * @param _globalMetadata New global metadata for the container.
     */
    function push(bytes32 _object, bytes27 _globalMetadata) external;

    /**
     * Retrieves an object from the container.
     * @param _index Index of the particular object to access.
     * @return 32 byte object value.
     */
    function get(uint256 _index) external view returns (bytes32);

    /**
     * Removes all objects after and including a given index.
     * @param _index Object index to delete from.
     */
    function deleteElementsAfterInclusive(uint256 _index) external;

    /**
     * Removes all objects after and including a given index. Also allows setting the global
     * metadata field.
     * @param _index Object index to delete from.
     * @param _globalMetadata New global metadata for the container.
     */
    function deleteElementsAfterInclusive(uint256 _index, bytes27 _globalMetadata) external;
}

// File: contracts/L1/rollup/IStateCommitmentChain.sol



// SPDX-License-Identifier: MIT
pragma solidity >0.5.0 <0.9.0;

/* Library Imports */
import { Lib_OVMCodec } from "../../libraries/codec/Lib_OVMCodec.sol";

/**
 * @title IStateCommitmentChain
 */
interface IStateCommitmentChain {
    /**********
     * Events *
     **********/

    event StateBatchAppended(
        uint256 indexed _batchIndex,
        bytes32 _batchRoot,
        uint256 _batchSize,
        uint256 _prevTotalElements,
        bytes _extraData
    );

    event StateBatchDeleted(uint256 indexed _batchIndex, bytes32 _batchRoot);

    /********************
     * Public Functions *
     ********************/

    /**
     * Retrieves the total number of elements submitted.
     * @return _totalElements Total submitted elements.
     */
    function getTotalElements() external view returns (uint256 _totalElements);

    /**
     * Retrieves the total number of batches submitted.
     * @return _totalBatches Total submitted batches.
     */
    function getTotalBatches() external view returns (uint256 _totalBatches);

    /**
     * Retrieves the timestamp of the last batch submitted by the sequencer.
     * @return _lastSequencerTimestamp Last sequencer batch timestamp.
     */
    function getLastSequencerTimestamp() external view returns (uint256 _lastSequencerTimestamp);

    /**
     * Appends a batch of state roots to the chain.
     * @param _batch Batch of state roots.
     * @param _shouldStartAtElement Index of the element at which this batch should start.
     */
    function appendStateBatch(bytes32[] calldata _batch, uint256 _shouldStartAtElement) external;

    /**
     * Deletes all state roots after (and including) a given batch.
     * @param _batchHeader Header of the batch to start deleting from.
     */
    function deleteStateBatch(Lib_OVMCodec.ChainBatchHeader memory _batchHeader) external;

    /**
     * Verifies a batch inclusion proof.
     * @param _element Hash of the element to verify a proof for.
     * @param _batchHeader Header of the batch in which the element was included.
     * @param _proof Merkle inclusion proof for the element.
     */
    function verifyStateCommitment(
        bytes32 _element,
        Lib_OVMCodec.ChainBatchHeader memory _batchHeader,
        Lib_OVMCodec.ChainInclusionProof memory _proof
    ) external view returns (bool _verified);

    /**
     * Checks whether a given batch is still inside its fraud proof window.
     * @param _batchHeader Header of the batch to check.
     * @return _inside Whether or not the batch is inside the fraud proof window.
     */
    function insideFraudProofWindow(Lib_OVMCodec.ChainBatchHeader memory _batchHeader)
        external
        view
        returns (bool _inside);
}

// File: contracts/L1/rollup/StateCommitmentChain.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.9;

/* Library Imports */
import { Lib_OVMCodec } from "../../libraries/codec/Lib_OVMCodec.sol";
import { Lib_AddressResolver } from "../../libraries/resolver/Lib_AddressResolver.sol";
import { Lib_MerkleTree } from "../../libraries/utils/Lib_MerkleTree.sol";

/* Interface Imports */
import { IStateCommitmentChain } from "./IStateCommitmentChain.sol";
import { ICanonicalTransactionChain } from "./ICanonicalTransactionChain.sol";
import { IBondManager } from "../verification/IBondManager.sol";
import { IChainStorageContainer } from "./IChainStorageContainer.sol";

/**
 * @title StateCommitmentChain
 * @dev The State Commitment Chain (SCC) contract contains a list of proposed state roots which
 * Proposers assert to be a result of each transaction in the Canonical Transaction Chain (CTC).
 * Elements here have a 1:1 correspondence with transactions in the CTC, and should be the unique
 * state root calculated off-chain by applying the canonical transactions one by one.
 *
 */
contract StateCommitmentChain is IStateCommitmentChain, Lib_AddressResolver {
    /*************
     * Constants *
     *************/

    uint256 public FRAUD_PROOF_WINDOW;
    uint256 public SEQUENCER_PUBLISH_WINDOW;

    /***************
     * Constructor *
     ***************/

    /**
     * @param _libAddressManager Address of the Address Manager.
     */
    constructor(
        address _libAddressManager,
        uint256 _fraudProofWindow,
        uint256 _sequencerPublishWindow
    ) Lib_AddressResolver(_libAddressManager) {
        FRAUD_PROOF_WINDOW = _fraudProofWindow;
        SEQUENCER_PUBLISH_WINDOW = _sequencerPublishWindow;
    }

    /********************
     * Public Functions *
     ********************/

    /**
     * Accesses the batch storage container.
     * @return Reference to the batch storage container.
     */
    function batches() public view returns (IChainStorageContainer) {
        return IChainStorageContainer(resolve("ChainStorageContainer-SCC-batches"));
    }

    /**
     * @inheritdoc IStateCommitmentChain
     */
    function getTotalElements() public view returns (uint256 _totalElements) {
        (uint40 totalElements, ) = _getBatchExtraData();
        return uint256(totalElements);
    }

    /**
     * @inheritdoc IStateCommitmentChain
     */
    function getTotalBatches() public view returns (uint256 _totalBatches) {
        return batches().length();
    }

    /**
     * @inheritdoc IStateCommitmentChain
     */
    // slither-disable-next-line external-function
    function getLastSequencerTimestamp() public view returns (uint256 _lastSequencerTimestamp) {
        (, uint40 lastSequencerTimestamp) = _getBatchExtraData();
        return uint256(lastSequencerTimestamp);
    }

    /**
     * @inheritdoc IStateCommitmentChain
     */
    // slither-disable-next-line external-function
    function appendStateBatch(bytes32[] memory _batch, uint256 _shouldStartAtElement) public {
        // Fail fast in to make sure our batch roots aren't accidentally made fraudulent by the
        // publication of batches by some other user.
        require(
            _shouldStartAtElement == getTotalElements(),
            "Actual batch start index does not match expected start index."
        );

        // Proposers must have previously staked at the BondManager
        require(
            IBondManager(resolve("BondManager")).isCollateralized(msg.sender),
            "Proposer does not have enough collateral posted"
        );

        require(_batch.length > 0, "Cannot submit an empty state batch.");

        require(
            getTotalElements() + _batch.length <=
                ICanonicalTransactionChain(resolve("CanonicalTransactionChain")).getTotalElements(),
            "Number of state roots cannot exceed the number of canonical transactions."
        );

        // Pass the block's timestamp and the publisher of the data
        // to be used in the fraud proofs
        _appendBatch(_batch, abi.encode(block.timestamp, msg.sender));
    }

    /**
     * @inheritdoc IStateCommitmentChain
     */
    // slither-disable-next-line external-function
    function deleteStateBatch(Lib_OVMCodec.ChainBatchHeader memory _batchHeader) public {
        require(
            msg.sender == resolve("OVM_FraudVerifier"),
            "State batches can only be deleted by the OVM_FraudVerifier."
        );

        require(_isValidBatchHeader(_batchHeader), "Invalid batch header.");

        require(
            insideFraudProofWindow(_batchHeader),
            "State batches can only be deleted within the fraud proof window."
        );

        _deleteBatch(_batchHeader);
    }

    /**
     * @inheritdoc IStateCommitmentChain
     */
    // slither-disable-next-line external-function
    function verifyStateCommitment(
        bytes32 _element,
        Lib_OVMCodec.ChainBatchHeader memory _batchHeader,
        Lib_OVMCodec.ChainInclusionProof memory _proof
    ) public view returns (bool) {
        require(_isValidBatchHeader(_batchHeader), "Invalid batch header.");

        require(
            Lib_MerkleTree.verify(
                _batchHeader.batchRoot,
                _element,
                _proof.index,
                _proof.siblings,
                _batchHeader.batchSize
            ),
            "Invalid inclusion proof."
        );

        return true;
    }

    /**
     * @inheritdoc IStateCommitmentChain
     */
    function insideFraudProofWindow(Lib_OVMCodec.ChainBatchHeader memory _batchHeader)
        public
        view
        returns (bool _inside)
    {
        (uint256 timestamp, ) = abi.decode(_batchHeader.extraData, (uint256, address));

        require(timestamp != 0, "Batch header timestamp cannot be zero");
        return (timestamp + FRAUD_PROOF_WINDOW) > block.timestamp;
    }

    /**********************
     * Internal Functions *
     **********************/

    /**
     * Parses the batch context from the extra data.
     * @return Total number of elements submitted.
     * @return Timestamp of the last batch submitted by the sequencer.
     */
    function _getBatchExtraData() internal view returns (uint40, uint40) {
        bytes27 extraData = batches().getGlobalMetadata();

        // solhint-disable max-line-length
        uint40 totalElements;
        uint40 lastSequencerTimestamp;
        assembly {
            extraData := shr(40, extraData)
            totalElements := and(
                extraData,
                0x000000000000000000000000000000000000000000000000000000FFFFFFFFFF
            )
            lastSequencerTimestamp := shr(
                40,
                and(extraData, 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF0000000000)
            )
        }
        // solhint-enable max-line-length

        return (totalElements, lastSequencerTimestamp);
    }

    /**
     * Encodes the batch context for the extra data.
     * @param _totalElements Total number of elements submitted.
     * @param _lastSequencerTimestamp Timestamp of the last batch submitted by the sequencer.
     * @return Encoded batch context.
     */
    function _makeBatchExtraData(uint40 _totalElements, uint40 _lastSequencerTimestamp)
        internal
        pure
        returns (bytes27)
    {
        bytes27 extraData;
        assembly {
            extraData := _totalElements
            extraData := or(extraData, shl(40, _lastSequencerTimestamp))
            extraData := shl(40, extraData)
        }

        return extraData;
    }

    /**
     * Appends a batch to the chain.
     * @param _batch Elements within the batch.
     * @param _extraData Any extra data to append to the batch.
     */
    function _appendBatch(bytes32[] memory _batch, bytes memory _extraData) internal {
        address sequencer = resolve("OVM_Proposer");
        (uint40 totalElements, uint40 lastSequencerTimestamp) = _getBatchExtraData();

        if (msg.sender == sequencer) {
            lastSequencerTimestamp = uint40(block.timestamp);
        } else {
            // We keep track of the last batch submitted by the sequencer so there's a window in
            // which only the sequencer can publish state roots. A window like this just reduces
            // the chance of "system breaking" state roots being published while we're still in
            // testing mode. This window should be removed or significantly reduced in the future.
            require(
                lastSequencerTimestamp + SEQUENCER_PUBLISH_WINDOW < block.timestamp,
                "Cannot publish state roots within the sequencer publication window."
            );
        }

        // For efficiency reasons getMerkleRoot modifies the `_batch` argument in place
        // while calculating the root hash therefore any arguments passed to it must not
        // be used again afterwards
        Lib_OVMCodec.ChainBatchHeader memory batchHeader = Lib_OVMCodec.ChainBatchHeader({
            batchIndex: getTotalBatches(),
            batchRoot: Lib_MerkleTree.getMerkleRoot(_batch),
            batchSize: _batch.length,
            prevTotalElements: totalElements,
            extraData: _extraData
        });

        emit StateBatchAppended(
            batchHeader.batchIndex,
            batchHeader.batchRoot,
            batchHeader.batchSize,
            batchHeader.prevTotalElements,
            batchHeader.extraData
        );

        batches().push(
            Lib_OVMCodec.hashBatchHeader(batchHeader),
            _makeBatchExtraData(
                uint40(batchHeader.prevTotalElements + batchHeader.batchSize),
                lastSequencerTimestamp
            )
        );
    }

    /**
     * Removes a batch and all subsequent batches from the chain.
     * @param _batchHeader Header of the batch to remove.
     */
    function _deleteBatch(Lib_OVMCodec.ChainBatchHeader memory _batchHeader) internal {
        require(_batchHeader.batchIndex < batches().length(), "Invalid batch index.");

        require(_isValidBatchHeader(_batchHeader), "Invalid batch header.");

        // slither-disable-next-line reentrancy-events
        batches().deleteElementsAfterInclusive(
            _batchHeader.batchIndex,
            _makeBatchExtraData(uint40(_batchHeader.prevTotalElements), 0)
        );

        // slither-disable-next-line reentrancy-events
        emit StateBatchDeleted(_batchHeader.batchIndex, _batchHeader.batchRoot);
    }

    /**
     * Checks that a batch header matches the stored hash for the given index.
     * @param _batchHeader Batch header to validate.
     * @return Whether or not the header matches the stored one.
     */
    function _isValidBatchHeader(Lib_OVMCodec.ChainBatchHeader memory _batchHeader)
        internal
        view
        returns (bool)
    {
        return Lib_OVMCodec.hashBatchHeader(_batchHeader) == batches().get(_batchHeader.batchIndex);
    }
}

// File: contracts/L1/verification/IBondManager.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.9;

/**
 * @title IBondManager
 */
interface IBondManager {
    /********************
     * Public Functions *
     ********************/

    function isCollateralized(address _who) external view returns (bool);
}

// File: contracts/libraries/codec/Lib_OVMCodec.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.9;

/* Library Imports */
import { Lib_RLPReader } from "../rlp/Lib_RLPReader.sol";
import { Lib_RLPWriter } from "../rlp/Lib_RLPWriter.sol";
import { Lib_BytesUtils } from "../utils/Lib_BytesUtils.sol";
import { Lib_Bytes32Utils } from "../utils/Lib_Bytes32Utils.sol";

/**
 * @title Lib_OVMCodec
 */
library Lib_OVMCodec {
    /*********
     * Enums *
     *********/

    enum QueueOrigin {
        SEQUENCER_QUEUE,
        L1TOL2_QUEUE
    }

    /***********
     * Structs *
     ***********/

    struct EVMAccount {
        uint256 nonce;
        uint256 balance;
        bytes32 storageRoot;
        bytes32 codeHash;
    }

    struct ChainBatchHeader {
        uint256 batchIndex;
        bytes32 batchRoot;
        uint256 batchSize;
        uint256 prevTotalElements;
        bytes extraData;
    }

    struct ChainInclusionProof {
        uint256 index;
        bytes32[] siblings;
    }

    struct Transaction {
        uint256 timestamp;
        uint256 blockNumber;
        QueueOrigin l1QueueOrigin;
        address l1TxOrigin;
        address entrypoint;
        uint256 gasLimit;
        bytes data;
    }

    struct TransactionChainElement {
        bool isSequenced;
        uint256 queueIndex; // QUEUED TX ONLY
        uint256 timestamp; // SEQUENCER TX ONLY
        uint256 blockNumber; // SEQUENCER TX ONLY
        bytes txData; // SEQUENCER TX ONLY
    }

    struct QueueElement {
        bytes32 transactionHash;
        uint40 timestamp;
        uint40 blockNumber;
    }

    /**********************
     * Internal Functions *
     **********************/

    /**
     * Encodes a standard OVM transaction.
     * @param _transaction OVM transaction to encode.
     * @return Encoded transaction bytes.
     */
    function encodeTransaction(Transaction memory _transaction)
        internal
        pure
        returns (bytes memory)
    {
        return
            abi.encodePacked(
                _transaction.timestamp,
                _transaction.blockNumber,
                _transaction.l1QueueOrigin,
                _transaction.l1TxOrigin,
                _transaction.entrypoint,
                _transaction.gasLimit,
                _transaction.data
            );
    }

    /**
     * Hashes a standard OVM transaction.
     * @param _transaction OVM transaction to encode.
     * @return Hashed transaction
     */
    function hashTransaction(Transaction memory _transaction) internal pure returns (bytes32) {
        return keccak256(encodeTransaction(_transaction));
    }

    /**
     * @notice Decodes an RLP-encoded account state into a useful struct.
     * @param _encoded RLP-encoded account state.
     * @return Account state struct.
     */
    function decodeEVMAccount(bytes memory _encoded) internal pure returns (EVMAccount memory) {
        Lib_RLPReader.RLPItem[] memory accountState = Lib_RLPReader.readList(_encoded);

        return
            EVMAccount({
                nonce: Lib_RLPReader.readUint256(accountState[0]),
                balance: Lib_RLPReader.readUint256(accountState[1]),
                storageRoot: Lib_RLPReader.readBytes32(accountState[2]),
                codeHash: Lib_RLPReader.readBytes32(accountState[3])
            });
    }

    /**
     * Calculates a hash for a given batch header.
     * @param _batchHeader Header to hash.
     * @return Hash of the header.
     */
    function hashBatchHeader(Lib_OVMCodec.ChainBatchHeader memory _batchHeader)
        internal
        pure
        returns (bytes32)
    {
        return
            keccak256(
                abi.encode(
                    _batchHeader.batchRoot,
                    _batchHeader.batchSize,
                    _batchHeader.prevTotalElements,
                    _batchHeader.extraData
                )
            );
    }
}

// File: contracts/libraries/resolver/Lib_AddressManager.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.9;

/* External Imports */
import { Ownable } from "@openzeppelin/contracts/access/Ownable.sol";

/**
 * @title Lib_AddressManager
 */
contract Lib_AddressManager is Ownable {
    /**********
     * Events *
     **********/

    event AddressSet(string indexed _name, address _newAddress, address _oldAddress);

    /*************
     * Variables *
     *************/

    mapping(bytes32 => address) private addresses;

    /********************
     * Public Functions *
     ********************/

    /**
     * Changes the address associated with a particular name.
     * @param _name String name to associate an address with.
     * @param _address Address to associate with the name.
     */
    function setAddress(string memory _name, address _address) external onlyOwner {
        bytes32 nameHash = _getNameHash(_name);
        address oldAddress = addresses[nameHash];
        addresses[nameHash] = _address;

        emit AddressSet(_name, _address, oldAddress);
    }

    /**
     * Retrieves the address associated with a given name.
     * @param _name Name to retrieve an address for.
     * @return Address associated with the given name.
     */
    function getAddress(string memory _name) external view returns (address) {
        return addresses[_getNameHash(_name)];
    }

    /**********************
     * Internal Functions *
     **********************/

    /**
     * Computes the hash of a name.
     * @param _name Name to compute a hash for.
     * @return Hash of the given name.
     */
    function _getNameHash(string memory _name) internal pure returns (bytes32) {
        return keccak256(abi.encodePacked(_name));
    }
}

// File: contracts/libraries/resolver/Lib_AddressResolver.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.9;

/* Library Imports */
import { Lib_AddressManager } from "./Lib_AddressManager.sol";

/**
 * @title Lib_AddressResolver
 */
abstract contract Lib_AddressResolver {
    /*************
     * Variables *
     *************/

    Lib_AddressManager public libAddressManager;

    /***************
     * Constructor *
     ***************/

    /**
     * @param _libAddressManager Address of the Lib_AddressManager.
     */
    constructor(address _libAddressManager) {
        libAddressManager = Lib_AddressManager(_libAddressManager);
    }

    /********************
     * Public Functions *
     ********************/

    /**
     * Resolves the address associated with a given name.
     * @param _name Name to resolve an address for.
     * @return Address associated with the given name.
     */
    function resolve(string memory _name) public view returns (address) {
        return libAddressManager.getAddress(_name);
    }
}

// File: contracts/libraries/rlp/Lib_RLPReader.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.9;

/**
 * @title Lib_RLPReader
 * @dev Adapted from "RLPReader" by Hamdi Allam (hamdi.allam97@gmail.com).
 */
library Lib_RLPReader {
    /*************
     * Constants *
     *************/

    uint256 internal constant MAX_LIST_LENGTH = 32;

    /*********
     * Enums *
     *********/

    enum RLPItemType {
        DATA_ITEM,
        LIST_ITEM
    }

    /***********
     * Structs *
     ***********/

    struct RLPItem {
        uint256 length;
        uint256 ptr;
    }

    /**********************
     * Internal Functions *
     **********************/

    /**
     * Converts bytes to a reference to memory position and length.
     * @param _in Input bytes to convert.
     * @return Output memory reference.
     */
    function toRLPItem(bytes memory _in) internal pure returns (RLPItem memory) {
        uint256 ptr;
        assembly {
            ptr := add(_in, 32)
        }

        return RLPItem({ length: _in.length, ptr: ptr });
    }

    /**
     * Reads an RLP list value into a list of RLP items.
     * @param _in RLP list value.
     * @return Decoded RLP list items.
     */
    function readList(RLPItem memory _in) internal pure returns (RLPItem[] memory) {
        (uint256 listOffset, , RLPItemType itemType) = _decodeLength(_in);

        require(itemType == RLPItemType.LIST_ITEM, "Invalid RLP list value.");

        // Solidity in-memory arrays can't be increased in size, but *can* be decreased in size by
        // writing to the length. Since we can't know the number of RLP items without looping over
        // the entire input, we'd have to loop twice to accurately size this array. It's easier to
        // simply set a reasonable maximum list length and decrease the size before we finish.
        RLPItem[] memory out = new RLPItem[](MAX_LIST_LENGTH);

        uint256 itemCount = 0;
        uint256 offset = listOffset;
        while (offset < _in.length) {
            require(itemCount < MAX_LIST_LENGTH, "Provided RLP list exceeds max list length.");

            (uint256 itemOffset, uint256 itemLength, ) = _decodeLength(
                RLPItem({ length: _in.length - offset, ptr: _in.ptr + offset })
            );

            out[itemCount] = RLPItem({ length: itemLength + itemOffset, ptr: _in.ptr + offset });

            itemCount += 1;
            offset += itemOffset + itemLength;
        }

        // Decrease the array size to match the actual item count.
        assembly {
            mstore(out, itemCount)
        }

        return out;
    }

    /**
     * Reads an RLP list value into a list of RLP items.
     * @param _in RLP list value.
     * @return Decoded RLP list items.
     */
    function readList(bytes memory _in) internal pure returns (RLPItem[] memory) {
        return readList(toRLPItem(_in));
    }

    /**
     * Reads an RLP bytes value into bytes.
     * @param _in RLP bytes value.
     * @return Decoded bytes.
     */
    function readBytes(RLPItem memory _in) internal pure returns (bytes memory) {
        (uint256 itemOffset, uint256 itemLength, RLPItemType itemType) = _decodeLength(_in);

        require(itemType == RLPItemType.DATA_ITEM, "Invalid RLP bytes value.");

        return _copy(_in.ptr, itemOffset, itemLength);
    }

    /**
     * Reads an RLP bytes value into bytes.
     * @param _in RLP bytes value.
     * @return Decoded bytes.
     */
    function readBytes(bytes memory _in) internal pure returns (bytes memory) {
        return readBytes(toRLPItem(_in));
    }

    /**
     * Reads an RLP string value into a string.
     * @param _in RLP string value.
     * @return Decoded string.
     */
    function readString(RLPItem memory _in) internal pure returns (string memory) {
        return string(readBytes(_in));
    }

    /**
     * Reads an RLP string value into a string.
     * @param _in RLP string value.
     * @return Decoded string.
     */
    function readString(bytes memory _in) internal pure returns (string memory) {
        return readString(toRLPItem(_in));
    }

    /**
     * Reads an RLP bytes32 value into a bytes32.
     * @param _in RLP bytes32 value.
     * @return Decoded bytes32.
     */
    function readBytes32(RLPItem memory _in) internal pure returns (bytes32) {
        require(_in.length <= 33, "Invalid RLP bytes32 value.");

        (uint256 itemOffset, uint256 itemLength, RLPItemType itemType) = _decodeLength(_in);

        require(itemType == RLPItemType.DATA_ITEM, "Invalid RLP bytes32 value.");

        uint256 ptr = _in.ptr + itemOffset;
        bytes32 out;
        assembly {
            out := mload(ptr)

            // Shift the bytes over to match the item size.
            if lt(itemLength, 32) {
                out := div(out, exp(256, sub(32, itemLength)))
            }
        }

        return out;
    }

    /**
     * Reads an RLP bytes32 value into a bytes32.
     * @param _in RLP bytes32 value.
     * @return Decoded bytes32.
     */
    function readBytes32(bytes memory _in) internal pure returns (bytes32) {
        return readBytes32(toRLPItem(_in));
    }

    /**
     * Reads an RLP uint256 value into a uint256.
     * @param _in RLP uint256 value.
     * @return Decoded uint256.
     */
    function readUint256(RLPItem memory _in) internal pure returns (uint256) {
        return uint256(readBytes32(_in));
    }

    /**
     * Reads an RLP uint256 value into a uint256.
     * @param _in RLP uint256 value.
     * @return Decoded uint256.
     */
    function readUint256(bytes memory _in) internal pure returns (uint256) {
        return readUint256(toRLPItem(_in));
    }

    /**
     * Reads an RLP bool value into a bool.
     * @param _in RLP bool value.
     * @return Decoded bool.
     */
    function readBool(RLPItem memory _in) internal pure returns (bool) {
        require(_in.length == 1, "Invalid RLP boolean value.");

        uint256 ptr = _in.ptr;
        uint256 out;
        assembly {
            out := byte(0, mload(ptr))
        }

        require(out == 0 || out == 1, "Lib_RLPReader: Invalid RLP boolean value, must be 0 or 1");

        return out != 0;
    }

    /**
     * Reads an RLP bool value into a bool.
     * @param _in RLP bool value.
     * @return Decoded bool.
     */
    function readBool(bytes memory _in) internal pure returns (bool) {
        return readBool(toRLPItem(_in));
    }

    /**
     * Reads an RLP address value into a address.
     * @param _in RLP address value.
     * @return Decoded address.
     */
    function readAddress(RLPItem memory _in) internal pure returns (address) {
        if (_in.length == 1) {
            return address(0);
        }

        require(_in.length == 21, "Invalid RLP address value.");

        return address(uint160(readUint256(_in)));
    }

    /**
     * Reads an RLP address value into a address.
     * @param _in RLP address value.
     * @return Decoded address.
     */
    function readAddress(bytes memory _in) internal pure returns (address) {
        return readAddress(toRLPItem(_in));
    }

    /**
     * Reads the raw bytes of an RLP item.
     * @param _in RLP item to read.
     * @return Raw RLP bytes.
     */
    function readRawBytes(RLPItem memory _in) internal pure returns (bytes memory) {
        return _copy(_in);
    }

    /*********************
     * Private Functions *
     *********************/

    /**
     * Decodes the length of an RLP item.
     * @param _in RLP item to decode.
     * @return Offset of the encoded data.
     * @return Length of the encoded data.
     * @return RLP item type (LIST_ITEM or DATA_ITEM).
     */
    function _decodeLength(RLPItem memory _in)
        private
        pure
        returns (
            uint256,
            uint256,
            RLPItemType
        )
    {
        require(_in.length > 0, "RLP item cannot be null.");

        uint256 ptr = _in.ptr;
        uint256 prefix;
        assembly {
            prefix := byte(0, mload(ptr))
        }

        if (prefix <= 0x7f) {
            // Single byte.

            return (0, 1, RLPItemType.DATA_ITEM);
        } else if (prefix <= 0xb7) {
            // Short string.

            // slither-disable-next-line variable-scope
            uint256 strLen = prefix - 0x80;

            require(_in.length > strLen, "Invalid RLP short string.");

            return (1, strLen, RLPItemType.DATA_ITEM);
        } else if (prefix <= 0xbf) {
            // Long string.
            uint256 lenOfStrLen = prefix - 0xb7;

            require(_in.length > lenOfStrLen, "Invalid RLP long string length.");

            uint256 strLen;
            assembly {
                // Pick out the string length.
                strLen := div(mload(add(ptr, 1)), exp(256, sub(32, lenOfStrLen)))
            }

            require(_in.length > lenOfStrLen + strLen, "Invalid RLP long string.");

            return (1 + lenOfStrLen, strLen, RLPItemType.DATA_ITEM);
        } else if (prefix <= 0xf7) {
            // Short list.
            // slither-disable-next-line variable-scope
            uint256 listLen = prefix - 0xc0;

            require(_in.length > listLen, "Invalid RLP short list.");

            return (1, listLen, RLPItemType.LIST_ITEM);
        } else {
            // Long list.
            uint256 lenOfListLen = prefix - 0xf7;

            require(_in.length > lenOfListLen, "Invalid RLP long list length.");

            uint256 listLen;
            assembly {
                // Pick out the list length.
                listLen := div(mload(add(ptr, 1)), exp(256, sub(32, lenOfListLen)))
            }

            require(_in.length > lenOfListLen + listLen, "Invalid RLP long list.");

            return (1 + lenOfListLen, listLen, RLPItemType.LIST_ITEM);
        }
    }

    /**
     * Copies the bytes from a memory location.
     * @param _src Pointer to the location to read from.
     * @param _offset Offset to start reading from.
     * @param _length Number of bytes to read.
     * @return Copied bytes.
     */
    function _copy(
        uint256 _src,
        uint256 _offset,
        uint256 _length
    ) private pure returns (bytes memory) {
        bytes memory out = new bytes(_length);
        if (out.length == 0) {
            return out;
        }

        uint256 src = _src + _offset;
        uint256 dest;
        assembly {
            dest := add(out, 32)
        }

        // Copy over as many complete words as we can.
        for (uint256 i = 0; i < _length / 32; i++) {
            assembly {
                mstore(dest, mload(src))
            }

            src += 32;
            dest += 32;
        }

        // Pick out the remaining bytes.
        uint256 mask;
        unchecked {
            mask = 256**(32 - (_length % 32)) - 1;
        }

        assembly {
            mstore(dest, or(and(mload(src), not(mask)), and(mload(dest), mask)))
        }
        return out;
    }

    /**
     * Copies an RLP item into bytes.
     * @param _in RLP item to copy.
     * @return Copied bytes.
     */
    function _copy(RLPItem memory _in) private pure returns (bytes memory) {
        return _copy(_in.ptr, 0, _in.length);
    }
}

// File: contracts/libraries/rlp/Lib_RLPWriter.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.9;

/**
 * @title Lib_RLPWriter
 * @author Bakaoh (with modifications)
 */
library Lib_RLPWriter {
    /**********************
     * Internal Functions *
     **********************/

    /**
     * RLP encodes a byte string.
     * @param _in The byte string to encode.
     * @return The RLP encoded string in bytes.
     */
    function writeBytes(bytes memory _in) internal pure returns (bytes memory) {
        bytes memory encoded;

        if (_in.length == 1 && uint8(_in[0]) < 128) {
            encoded = _in;
        } else {
            encoded = abi.encodePacked(_writeLength(_in.length, 128), _in);
        }

        return encoded;
    }

    /**
     * RLP encodes a list of RLP encoded byte byte strings.
     * @param _in The list of RLP encoded byte strings.
     * @return The RLP encoded list of items in bytes.
     */
    function writeList(bytes[] memory _in) internal pure returns (bytes memory) {
        bytes memory list = _flatten(_in);
        return abi.encodePacked(_writeLength(list.length, 192), list);
    }

    /**
     * RLP encodes a string.
     * @param _in The string to encode.
     * @return The RLP encoded string in bytes.
     */
    function writeString(string memory _in) internal pure returns (bytes memory) {
        return writeBytes(bytes(_in));
    }

    /**
     * RLP encodes an address.
     * @param _in The address to encode.
     * @return The RLP encoded address in bytes.
     */
    function writeAddress(address _in) internal pure returns (bytes memory) {
        return writeBytes(abi.encodePacked(_in));
    }

    /**
     * RLP encodes a uint.
     * @param _in The uint256 to encode.
     * @return The RLP encoded uint256 in bytes.
     */
    function writeUint(uint256 _in) internal pure returns (bytes memory) {
        return writeBytes(_toBinary(_in));
    }

    /**
     * RLP encodes a bool.
     * @param _in The bool to encode.
     * @return The RLP encoded bool in bytes.
     */
    function writeBool(bool _in) internal pure returns (bytes memory) {
        bytes memory encoded = new bytes(1);
        encoded[0] = (_in ? bytes1(0x01) : bytes1(0x80));
        return encoded;
    }

    /*********************
     * Private Functions *
     *********************/

    /**
     * Encode the first byte, followed by the `len` in binary form if `length` is more than 55.
     * @param _len The length of the string or the payload.
     * @param _offset 128 if item is string, 192 if item is list.
     * @return RLP encoded bytes.
     */
    function _writeLength(uint256 _len, uint256 _offset) private pure returns (bytes memory) {
        bytes memory encoded;

        if (_len < 56) {
            encoded = new bytes(1);
            encoded[0] = bytes1(uint8(_len) + uint8(_offset));
        } else {
            uint256 lenLen;
            uint256 i = 1;
            while (_len / i != 0) {
                lenLen++;
                i *= 256;
            }

            encoded = new bytes(lenLen + 1);
            encoded[0] = bytes1(uint8(lenLen) + uint8(_offset) + 55);
            for (i = 1; i <= lenLen; i++) {
                encoded[i] = bytes1(uint8((_len / (256**(lenLen - i))) % 256));
            }
        }

        return encoded;
    }

    /**
     * Encode integer in big endian binary form with no leading zeroes.
     * @notice TODO: This should be optimized with assembly to save gas costs.
     * @param _x The integer to encode.
     * @return RLP encoded bytes.
     */
    function _toBinary(uint256 _x) private pure returns (bytes memory) {
        bytes memory b = abi.encodePacked(_x);

        uint256 i = 0;
        for (; i < 32; i++) {
            if (b[i] != 0) {
                break;
            }
        }

        bytes memory res = new bytes(32 - i);
        for (uint256 j = 0; j < res.length; j++) {
            res[j] = b[i++];
        }

        return res;
    }

    /**
     * Copies a piece of memory to another location.
     * @notice From: https://github.com/Arachnid/solidity-stringutils/blob/master/src/strings.sol.
     * @param _dest Destination location.
     * @param _src Source location.
     * @param _len Length of memory to copy.
     */
    function _memcpy(
        uint256 _dest,
        uint256 _src,
        uint256 _len
    ) private pure {
        uint256 dest = _dest;
        uint256 src = _src;
        uint256 len = _len;

        for (; len >= 32; len -= 32) {
            assembly {
                mstore(dest, mload(src))
            }
            dest += 32;
            src += 32;
        }

        uint256 mask;
        unchecked {
            mask = 256**(32 - len) - 1;
        }
        assembly {
            let srcpart := and(mload(src), not(mask))
            let destpart := and(mload(dest), mask)
            mstore(dest, or(destpart, srcpart))
        }
    }

    /**
     * Flattens a list of byte strings into one byte string.
     * @notice From: https://github.com/sammayo/solidity-rlp-encoder/blob/master/RLPEncode.sol.
     * @param _list List of byte strings to flatten.
     * @return The flattened byte string.
     */
    function _flatten(bytes[] memory _list) private pure returns (bytes memory) {
        if (_list.length == 0) {
            return new bytes(0);
        }

        uint256 len;
        uint256 i = 0;
        for (; i < _list.length; i++) {
            len += _list[i].length;
        }

        bytes memory flattened = new bytes(len);
        uint256 flattenedPtr;
        assembly {
            flattenedPtr := add(flattened, 0x20)
        }

        for (i = 0; i < _list.length; i++) {
            bytes memory item = _list[i];

            uint256 listPtr;
            assembly {
                listPtr := add(item, 0x20)
            }

            _memcpy(flattenedPtr, listPtr, item.length);
            flattenedPtr += _list[i].length;
        }

        return flattened;
    }
}

// File: contracts/libraries/utils/Lib_Bytes32Utils.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.9;

/**
 * @title Lib_Byte32Utils
 */
library Lib_Bytes32Utils {
    /**********************
     * Internal Functions *
     **********************/

    /**
     * Converts a bytes32 value to a boolean. Anything non-zero will be converted to "true."
     * @param _in Input bytes32 value.
     * @return Bytes32 as a boolean.
     */
    function toBool(bytes32 _in) internal pure returns (bool) {
        return _in != 0;
    }

    /**
     * Converts a boolean to a bytes32 value.
     * @param _in Input boolean value.
     * @return Boolean as a bytes32.
     */
    function fromBool(bool _in) internal pure returns (bytes32) {
        return bytes32(uint256(_in ? 1 : 0));
    }

    /**
     * Converts a bytes32 value to an address. Takes the *last* 20 bytes.
     * @param _in Input bytes32 value.
     * @return Bytes32 as an address.
     */
    function toAddress(bytes32 _in) internal pure returns (address) {
        return address(uint160(uint256(_in)));
    }

    /**
     * Converts an address to a bytes32.
     * @param _in Input address value.
     * @return Address as a bytes32.
     */
    function fromAddress(address _in) internal pure returns (bytes32) {
        return bytes32(uint256(uint160(_in)));
    }
}

// File: contracts/libraries/utils/Lib_BytesUtils.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.9;

/**
 * @title Lib_BytesUtils
 */
library Lib_BytesUtils {
    /**********************
     * Internal Functions *
     **********************/

    function slice(
        bytes memory _bytes,
        uint256 _start,
        uint256 _length
    ) internal pure returns (bytes memory) {
        require(_length + 31 >= _length, "slice_overflow");
        require(_start + _length >= _start, "slice_overflow");
        require(_bytes.length >= _start + _length, "slice_outOfBounds");

        bytes memory tempBytes;

        assembly {
            switch iszero(_length)
            case 0 {
                // Get a location of some free memory and store it in tempBytes as
                // Solidity does for memory variables.
                tempBytes := mload(0x40)

                // The first word of the slice result is potentially a partial
                // word read from the original array. To read it, we calculate
                // the length of that partial word and start copying that many
                // bytes into the array. The first word we copy will start with
                // data we don't care about, but the last `lengthmod` bytes will
                // land at the beginning of the contents of the new array. When
                // we're done copying, we overwrite the full first word with
                // the actual length of the slice.
                let lengthmod := and(_length, 31)

                // The multiplication in the next line is necessary
                // because when slicing multiples of 32 bytes (lengthmod == 0)
                // the following copy loop was copying the origin's length
                // and then ending prematurely not copying everything it should.
                let mc := add(add(tempBytes, lengthmod), mul(0x20, iszero(lengthmod)))
                let end := add(mc, _length)

                for {
                    // The multiplication in the next line has the same exact purpose
                    // as the one above.
                    let cc := add(add(add(_bytes, lengthmod), mul(0x20, iszero(lengthmod))), _start)
                } lt(mc, end) {
                    mc := add(mc, 0x20)
                    cc := add(cc, 0x20)
                } {
                    mstore(mc, mload(cc))
                }

                mstore(tempBytes, _length)

                //update free-memory pointer
                //allocating the array padded to 32 bytes like the compiler does now
                mstore(0x40, and(add(mc, 31), not(31)))
            }
            //if we want a zero-length slice let's just return a zero-length array
            default {
                tempBytes := mload(0x40)

                //zero out the 32 bytes slice we are about to return
                //we need to do it because Solidity does not garbage collect
                mstore(tempBytes, 0)

                mstore(0x40, add(tempBytes, 0x20))
            }
        }

        return tempBytes;
    }

    function slice(bytes memory _bytes, uint256 _start) internal pure returns (bytes memory) {
        if (_start >= _bytes.length) {
            return bytes("");
        }

        return slice(_bytes, _start, _bytes.length - _start);
    }

    function toBytes32(bytes memory _bytes) internal pure returns (bytes32) {
        if (_bytes.length < 32) {
            bytes32 ret;
            assembly {
                ret := mload(add(_bytes, 32))
            }
            return ret;
        }

        return abi.decode(_bytes, (bytes32)); // will truncate if input length > 32 bytes
    }

    function toUint256(bytes memory _bytes) internal pure returns (uint256) {
        return uint256(toBytes32(_bytes));
    }

    function toNibbles(bytes memory _bytes) internal pure returns (bytes memory) {
        bytes memory nibbles = new bytes(_bytes.length * 2);

        for (uint256 i = 0; i < _bytes.length; i++) {
            nibbles[i * 2] = _bytes[i] >> 4;
            nibbles[i * 2 + 1] = bytes1(uint8(_bytes[i]) % 16);
        }

        return nibbles;
    }

    function fromNibbles(bytes memory _bytes) internal pure returns (bytes memory) {
        bytes memory ret = new bytes(_bytes.length / 2);

        for (uint256 i = 0; i < ret.length; i++) {
            ret[i] = (_bytes[i * 2] << 4) | (_bytes[i * 2 + 1]);
        }

        return ret;
    }

    function equal(bytes memory _bytes, bytes memory _other) internal pure returns (bool) {
        return keccak256(_bytes) == keccak256(_other);
    }
}

// File: contracts/libraries/utils/Lib_MerkleTree.sol



// SPDX-License-Identifier: MIT
pragma solidity ^0.8.9;

/**
 * @title Lib_MerkleTree
 * @author River Keefer
 */
library Lib_MerkleTree {
    /**********************
     * Internal Functions *
     **********************/

    /**
     * Calculates a merkle root for a list of 32-byte leaf hashes.  WARNING: If the number
     * of leaves passed in is not a power of two, it pads out the tree with zero hashes.
     * If you do not know the original length of elements for the tree you are verifying, then
     * this may allow empty leaves past _elements.length to pass a verification check down the line.
     * Note that the _elements argument is modified, therefore it must not be used again afterwards
     * @param _elements Array of hashes from which to generate a merkle root.
     * @return Merkle root of the leaves, with zero hashes for non-powers-of-two (see above).
     */
    function getMerkleRoot(bytes32[] memory _elements) internal pure returns (bytes32) {
        require(_elements.length > 0, "Lib_MerkleTree: Must provide at least one leaf hash.");

        if (_elements.length == 1) {
            return _elements[0];
        }

        uint256[16] memory defaults = [
            0x290decd9548b62a8d60345a988386fc84ba6bc95484008f6362f93160ef3e563,
            0x633dc4d7da7256660a892f8f1604a44b5432649cc8ec5cb3ced4c4e6ac94dd1d,
            0x890740a8eb06ce9be422cb8da5cdafc2b58c0a5e24036c578de2a433c828ff7d,
            0x3b8ec09e026fdc305365dfc94e189a81b38c7597b3d941c279f042e8206e0bd8,
            0xecd50eee38e386bd62be9bedb990706951b65fe053bd9d8a521af753d139e2da,
            0xdefff6d330bb5403f63b14f33b578274160de3a50df4efecf0e0db73bcdd3da5,
            0x617bdd11f7c0a11f49db22f629387a12da7596f9d1704d7465177c63d88ec7d7,
            0x292c23a9aa1d8bea7e2435e555a4a60e379a5a35f3f452bae60121073fb6eead,
            0xe1cea92ed99acdcb045a6726b2f87107e8a61620a232cf4d7d5b5766b3952e10,
            0x7ad66c0a68c72cb89e4fb4303841966e4062a76ab97451e3b9fb526a5ceb7f82,
            0xe026cc5a4aed3c22a58cbd3d2ac754c9352c5436f638042dca99034e83636516,
            0x3d04cffd8b46a874edf5cfae63077de85f849a660426697b06a829c70dd1409c,
            0xad676aa337a485e4728a0b240d92b3ef7b3c372d06d189322bfd5f61f1e7203e,
            0xa2fca4a49658f9fab7aa63289c91b7c7b6c832a6d0e69334ff5b0a3483d09dab,
            0x4ebfd9cd7bca2505f7bef59cc1c12ecc708fff26ae4af19abe852afe9e20c862,
            0x2def10d13dd169f550f578bda343d9717a138562e0093b380a1120789d53cf10
        ];

        // Reserve memory space for our hashes.
        bytes memory buf = new bytes(64);

        // We'll need to keep track of left and right siblings.
        bytes32 leftSibling;
        bytes32 rightSibling;

        // Number of non-empty nodes at the current depth.
        uint256 rowSize = _elements.length;

        // Current depth, counting from 0 at the leaves
        uint256 depth = 0;

        // Common sub-expressions
        uint256 halfRowSize; // rowSize / 2
        bool rowSizeIsOdd; // rowSize % 2 == 1

        while (rowSize > 1) {
            halfRowSize = rowSize / 2;
            rowSizeIsOdd = rowSize % 2 == 1;

            for (uint256 i = 0; i < halfRowSize; i++) {
                leftSibling = _elements[(2 * i)];
                rightSibling = _elements[(2 * i) + 1];
                assembly {
                    mstore(add(buf, 32), leftSibling)
                    mstore(add(buf, 64), rightSibling)
                }

                _elements[i] = keccak256(buf);
            }

            if (rowSizeIsOdd) {
                leftSibling = _elements[rowSize - 1];
                rightSibling = bytes32(defaults[depth]);
                assembly {
                    mstore(add(buf, 32), leftSibling)
                    mstore(add(buf, 64), rightSibling)
                }

                _elements[halfRowSize] = keccak256(buf);
            }

            rowSize = halfRowSize + (rowSizeIsOdd ? 1 : 0);
            depth++;
        }

        return _elements[0];
    }

    /**
     * Verifies a merkle branch for the given leaf hash.  Assumes the original length
     * of leaves generated is a known, correct input, and does not return true for indices
     * extending past that index (even if _siblings would be otherwise valid.)
     * @param _root The Merkle root to verify against.
     * @param _leaf The leaf hash to verify inclusion of.
     * @param _index The index in the tree of this leaf.
     * @param _siblings Array of sibline nodes in the inclusion proof, starting from depth 0
     * (bottom of the tree).
     * @param _totalLeaves The total number of leaves originally passed into.
     * @return Whether or not the merkle branch and leaf passes verification.
     */
    function verify(
        bytes32 _root,
        bytes32 _leaf,
        uint256 _index,
        bytes32[] memory _siblings,
        uint256 _totalLeaves
    ) internal pure returns (bool) {
        require(_totalLeaves > 0, "Lib_MerkleTree: Total leaves must be greater than zero.");

        require(_index < _totalLeaves, "Lib_MerkleTree: Index out of bounds.");

        require(
            _siblings.length == _ceilLog2(_totalLeaves),
            "Lib_MerkleTree: Total siblings does not correctly correspond to total leaves."
        );

        bytes32 computedRoot = _leaf;

        for (uint256 i = 0; i < _siblings.length; i++) {
            if ((_index & 1) == 1) {
                computedRoot = keccak256(abi.encodePacked(_siblings[i], computedRoot));
            } else {
                computedRoot = keccak256(abi.encodePacked(computedRoot, _siblings[i]));
            }

            _index >>= 1;
        }

        return _root == computedRoot;
    }

    /*********************
     * Private Functions *
     *********************/

    /**
     * Calculates the integer ceiling of the log base 2 of an input.
     * @param _in Unsigned input to calculate the log.
     * @return ceil(log_base_2(_in))
     */
    function _ceilLog2(uint256 _in) private pure returns (uint256) {
        require(_in > 0, "Lib_MerkleTree: Cannot compute ceil(log_2) of 0.");

        if (_in == 1) {
            return 0;
        }

        // Find the highest set bit (will be floor(log_2)).
        // Borrowed with <3 from https://github.com/ethereum/solidity-examples
        uint256 val = _in;
        uint256 highest = 0;
        for (uint256 i = 128; i >= 1; i >>= 1) {
            if (val & (((uint256(1) << i) - 1) << i) != 0) {
                highest += i;
                val >>= i;
            }
        }

        // Increment by one if this is not a perfect logarithm.
        if ((uint256(1) << highest) != _in) {
            highest += 1;
        }

        return highest;
    }
}