library MerkleProof {
    /**
     * @dev Verifies a Merkle proof proving the existence of a leaf in a Merkle tree. Assumes that each pair of leaves
     * and each pair of pre-images are sorted.
     * @param proof Merkle proof containing sibling hashes on the branch from the leaf to the root of the Merkle tree
     * @param root Merkle root
     * @param leaf Leaf of Merkle tree
     */
    function verify(bytes32[] memory proof, bytes32 root, bytes32 leaf) internal pure returns (bool) {
        bytes32 computedHash = leaf;

        for (uint256 i = 0; i < proof.length; i++) {
            bytes32 proofElement = proof[i];

            if (computedHash < proofElement) {
                // Hash(current computed hash + current element of the proof)
                computedHash = keccak256(abi.encodePacked(computedHash, proofElement));
            } else {
                // Hash(current element of the proof + current computed hash)
                computedHash = keccak256(abi.encodePacked(proofElement, computedHash));
            }
        }

        // Check if the computed hash (root) is equal to the provided root
        return computedHash == root;
    }
}
/**
 * @title MerkleProof
 * @dev Merkle proof verification based on
 * https://github.com/ameensol/merkle-tree-solidity/blob/master/src/MerkleProof.sol
 */
function verify(bytes32[] memory proof, bytes32 root, bytes32 leaf) internal pure returns (bool) {
    bytes32 computedHash = leaf;

    for (uint256 i = 0; i < proof.length; i++) {
        bytes32 proofElement = proof[i];

        if (computedHash < proofElement) {
            // Hash(current computed hash + current element of the proof)
            computedHash = keccak256(abi.encodePacked(computedHash, proofElement));
        } else {
            // Hash(current element of the proof + current computed hash)
            computedHash = keccak256(abi.encodePacked(proofElement, computedHash));
        }
    }

    // Check if the computed hash (root) is equal to the provided root
    return computedHash == root;
}

/**
 * @dev Verifies a Merkle proof proving the existence of a leaf in a Merkle tree. Assumes that each pair of leaves
 * and each pair of pre-images are sorted.
 * @param proof Merkle proof containing sibling hashes on the branch from the leaf to the root of the Merkle tree
 * @param root Merkle root
 * @param leaf Leaf of Merkle tree
 */