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optimistic roll up\n *\n * @dev Append only purpose Sparse Merkle Tree solidity library for optimistic roll up\n */\nlibrary SMT256 {\n // in Solidity: keccak256('exist')\n // in Web3JS: soliditySha3('exist')\n bytes32 constant public EXIST = 0xb0b4e07bb5592f3d3821b2c1331b436763d7be555cf452d6c6836f74d5201e85;\n // in Solidity: keccak256(abi.encodePacked(bytes32(0)))\n // in Web3JS: soliditySha3(0)\n bytes32 constant public NON_EXIST = 0x290decd9548b62a8d60345a988386fc84ba6bc95484008f6362f93160ef3e563;\n\n struct RollUp {\n bytes32 root;\n bytes32[] leaves;\n bytes32[256][] siblings;\n }\n\n struct OPRU {\n bytes32 prev;\n bytes32 next;\n bytes32 mergedLeaves;\n }\n\n function inclusionProof(\n bytes32 root,\n bytes32 leaf,\n bytes32[256] memory siblings\n ) internal pure returns(bool) {\n return merkleProof(root, leaf, EXIST, siblings);\n }\n\n function nonInclusionProof(\n bytes32 root,\n bytes32 leaf,\n bytes32[256] memory siblings\n ) internal pure returns(bool) {\n return merkleProof(root, leaf, NON_EXIST, siblings);\n }\n\n function merkleProof(\n bytes32 root,\n bytes32 leaf,\n bytes32 value,\n bytes32[256] memory siblings\n ) internal pure returns(bool) {\n require(calculateRoot(leaf, value, siblings) == root, \"Invalid merkle proof\");\n return true;\n }\n\n function calculateRoot(\n bytes32 leaf,\n bytes32 value,\n bytes32[256] memory siblings\n ) internal pure returns (bytes32) {\n bytes32 cursor = value;\n uint path = uint(leaf);\n for (uint16 i = 0; i < siblings.length; i++) {\n if (path % 2 == 0) {\n // Right sibling\n cursor = keccak256(abi.encodePacked(cursor, siblings[i]));\n } else {\n // Left sibling\n cursor = keccak256(abi.encodePacked(siblings[i], cursor));\n }\n path = path >> 1;\n }\n return cursor;\n }\n\n function append(\n bytes32 root,\n bytes32 leaf,\n bytes32[256] memory siblings\n ) internal pure returns (bytes32 nextRoot) {\n // Prove that the array of sibling is valid and also the leaf does not exist in the tree\n require(nonInclusionProof(root, leaf, siblings), \"Failed to build the previous root using jthe leaf and its sibling\");\n // Calculate the new root when the leaf exists using its proven siblings\n nextRoot = calculateRoot(leaf, EXIST, siblings);\n // Make sure it has been updated\n require(root != nextRoot, \"Already exisiting leaf\");\n }\n\n function rollUp(RollUp memory proof) internal pure returns (bytes32) {\n // Inspect the RollUp structure\n require(proof.leaves.length == proof.siblings.length, \"Both array should have same length\");\n // Start from the root\n bytes32 root = proof.root;\n // Update the root using append function\n for (uint i = 0; i < proof.leaves.length; i ++) {\n root = append(root, proof.leaves[i], proof.siblings[i]);\n }\n return root;\n }\n\n function rollUp(\n bytes32 root,\n bytes32[] memory leaves,\n bytes32[256][] memory siblings\n ) internal pure returns (bytes32 nextRoot) {\n nextRoot = rollUp(RollUp(root, leaves, siblings));\n }\n\n function 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