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"content": "// SPDX-License-Identifier: MIT\n// OpenZeppelin Contracts (last updated v4.7.0) (utils/cryptography/MerkleProof.sol)\n\npragma solidity ^0.8.0;\n\n/**\n * @dev These functions deal with verification of Merkle Tree proofs.\n *\n * The proofs can be generated using the JavaScript library\n * https://github.com/miguelmota/merkletreejs[merkletreejs].\n * Note: the hashing algorithm should be keccak256 and pair sorting should be enabled.\n *\n * See `test/utils/cryptography/MerkleProof.test.js` for some examples.\n *\n * WARNING: You should avoid using leaf values that are 64 bytes long prior to\n * hashing, or use a hash function other than keccak256 for hashing leaves.\n * This is because the concatenation of a sorted pair of internal nodes in\n * the merkle tree could be reinterpreted as a leaf value.\n */\nlibrary MerkleProof {\n /**\n * @dev Returns true if a `leaf` can be proved to be a part of a Merkle tree\n * defined by `root`. For this, a `proof` must be provided, containing\n * sibling hashes on the branch from the leaf to the root of the tree. Each\n * pair of leaves and each pair of pre-images are assumed to be sorted.\n */\n function verify(\n bytes32[] memory proof,\n bytes32 root,\n bytes32 leaf\n ) internal pure returns (bool) {\n return processProof(proof, leaf) == root;\n }\n\n /**\n * @dev Calldata version of {verify}\n *\n * _Available since v4.7._\n */\n function verifyCalldata(\n bytes32[] calldata proof,\n bytes32 root,\n bytes32 leaf\n ) internal pure returns (bool) {\n return processProofCalldata(proof, leaf) == root;\n }\n\n /**\n * @dev Returns the rebuilt hash obtained by traversing a Merkle tree up\n * from `leaf` using `proof`. A `proof` is valid if and only if the rebuilt\n * hash matches the root of the tree. When processing the proof, the pairs\n * of leafs & pre-images are assumed to be sorted.\n *\n * _Available since v4.4._\n */\n function processProof(bytes32[] memory proof, bytes32 leaf) internal pure returns (bytes32) {\n bytes32 computedHash = leaf;\n for (uint256 i = 0; i < proof.length; i++) {\n computedHash = _hashPair(computedHash, proof[i]);\n }\n return computedHash;\n }\n\n /**\n * @dev Calldata version of {processProof}\n *\n * _Available since v4.7._\n */\n function processProofCalldata(bytes32[] calldata proof, bytes32 leaf) internal pure returns (bytes32) {\n bytes32 computedHash = leaf;\n for (uint256 i = 0; i < proof.length; i++) {\n computedHash = _hashPair(computedHash, proof[i]);\n }\n return computedHash;\n }\n\n /**\n * @dev Returns true if the `leaves` can be proved to be a part of a Merkle tree defined by\n * `root`, according to `proof` and `proofFlags` as described in {processMultiProof}.\n *\n * _Available since v4.7._\n */\n function multiProofVerify(\n bytes32[] memory proof,\n bool[] memory proofFlags,\n bytes32 root,\n bytes32[] memory leaves\n ) internal pure returns (bool) {\n return processMultiProof(proof, proofFlags, leaves) == root;\n }\n\n /**\n * @dev Calldata version of {multiProofVerify}\n *\n * _Available since v4.7._\n */\n function multiProofVerifyCalldata(\n bytes32[] calldata proof,\n bool[] calldata proofFlags,\n bytes32 root,\n bytes32[] memory leaves\n ) internal pure returns (bool) {\n return processMultiProofCalldata(proof, proofFlags, leaves) == root;\n }\n\n /**\n * @dev Returns the root of a tree reconstructed from `leaves` and the sibling nodes in `proof`,\n * consuming from one or the other at each step according to the instructions given by\n * `proofFlags`.\n *\n * _Available since v4.7._\n */\n function processMultiProof(\n bytes32[] memory proof,\n bool[] memory proofFlags,\n bytes32[] memory leaves\n ) internal pure returns (bytes32 merkleRoot) {\n // This function rebuild the root hash by traversing the tree up from the leaves. The root is rebuilt by\n // consuming and producing values on a queue. The queue starts with the `leaves` array, then goes onto the\n // `hashes` array. At the end of the process, the last hash in the `hashes` array should contain the root of\n // the merkle tree.\n uint256 leavesLen = leaves.length;\n uint256 totalHashes = proofFlags.length;\n\n // Check proof validity.\n require(leavesLen + proof.length - 1 == totalHashes, \"MerkleProof: invalid multiproof\");\n\n // The xxxPos values are \"pointers\" to the next value to consume in each array. All accesses are done using\n // `xxx[xxxPos++]`, which return the current value and increment the pointer, thus mimicking a queue's \"pop\".\n bytes32[] memory hashes = new bytes32[](totalHashes);\n uint256 leafPos = 0;\n uint256 hashPos = 0;\n uint256 proofPos = 0;\n // At each step, we compute the next hash using two values:\n // - a value from the \"main queue\". If not all leaves have been consumed, we get the next leaf, otherwise we\n // get the next hash.\n // - depending on the flag, either another value for the \"main queue\" (merging branches) or an element from the\n // `proof` array.\n for (uint256 i = 0; i < totalHashes; i++) {\n bytes32 a = leafPos < leavesLen ? leaves[leafPos++] : hashes[hashPos++];\n bytes32 b = proofFlags[i] ? leafPos < leavesLen ? leaves[leafPos++] : hashes[hashPos++] : proof[proofPos++];\n hashes[i] = _hashPair(a, b);\n }\n\n if (totalHashes > 0) {\n return hashes[totalHashes - 1];\n } else if (leavesLen > 0) {\n return leaves[0];\n } else {\n return proof[0];\n }\n }\n\n /**\n * @dev Calldata version of {processMultiProof}\n *\n * _Available since v4.7._\n */\n function processMultiProofCalldata(\n bytes32[] calldata proof,\n bool[] calldata proofFlags,\n bytes32[] memory leaves\n ) internal pure returns (bytes32 merkleRoot) {\n // This function rebuild the root hash by traversing the tree up from the leaves. The root is rebuilt by\n // consuming and producing values on a queue. The queue starts with the `leaves` array, then goes onto the\n // `hashes` array. At the end of the process, the last hash in the `hashes` array should contain the root of\n // the merkle tree.\n uint256 leavesLen = leaves.length;\n uint256 totalHashes = proofFlags.length;\n\n // Check proof validity.\n require(leavesLen + proof.length - 1 == totalHashes, \"MerkleProof: invalid multiproof\");\n\n // The xxxPos values are \"pointers\" to the next value to consume in each array. All accesses are done using\n // `xxx[xxxPos++]`, which return the current value and increment the pointer, thus mimicking a queue's \"pop\".\n bytes32[] memory hashes = new bytes32[](totalHashes);\n uint256 leafPos = 0;\n uint256 hashPos = 0;\n uint256 proofPos = 0;\n // At each step, we compute the next hash using two values:\n // - a value from the \"main queue\". If not all leaves have been consumed, we get the next leaf, otherwise we\n // get the next hash.\n // - depending on the flag, either another value for the \"main queue\" (merging branches) or an element from the\n // `proof` array.\n for (uint256 i = 0; i < totalHashes; i++) {\n bytes32 a = leafPos < leavesLen ? leaves[leafPos++] : hashes[hashPos++];\n bytes32 b = proofFlags[i] ? leafPos < leavesLen ? leaves[leafPos++] : hashes[hashPos++] : proof[proofPos++];\n hashes[i] = _hashPair(a, b);\n }\n\n if (totalHashes > 0) {\n return hashes[totalHashes - 1];\n } else if (leavesLen > 0) {\n return leaves[0];\n } else {\n return proof[0];\n }\n }\n\n function _hashPair(bytes32 a, bytes32 b) private pure returns (bytes32) {\n return a < b ? _efficientHash(a, b) : _efficientHash(b, a);\n }\n\n function _efficientHash(bytes32 a, bytes32 b) private pure returns (bytes32 value) {\n /// @solidity memory-safe-assembly\n assembly {\n mstore(0x00, a)\n mstore(0x20, b)\n value := keccak256(0x00, 0x40)\n }\n }\n}\n"
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