github.com/dominant-strategies/go-quai@v0.28.2/trie/proof.go (about)

     1  // Copyright 2015 The go-ethereum Authors
     2  // This file is part of the go-ethereum library.
     3  //
     4  // The go-ethereum library is free software: you can redistribute it and/or modify
     5  // it under the terms of the GNU Lesser General Public License as published by
     6  // the Free Software Foundation, either version 3 of the License, or
     7  // (at your option) any later version.
     8  //
     9  // The go-ethereum library is distributed in the hope that it will be useful,
    10  // but WITHOUT ANY WARRANTY; without even the implied warranty of
    11  // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
    12  // GNU Lesser General Public License for more details.
    13  //
    14  // You should have received a copy of the GNU Lesser General Public License
    15  // along with the go-ethereum library. If not, see <http://www.gnu.org/licenses/>.
    16  
    17  package trie
    18  
    19  import (
    20  	"bytes"
    21  	"errors"
    22  	"fmt"
    23  
    24  	"github.com/dominant-strategies/go-quai/common"
    25  	"github.com/dominant-strategies/go-quai/ethdb"
    26  	"github.com/dominant-strategies/go-quai/ethdb/memorydb"
    27  	"github.com/dominant-strategies/go-quai/log"
    28  	"github.com/dominant-strategies/go-quai/rlp"
    29  )
    30  
    31  // Prove constructs a merkle proof for key. The result contains all encoded nodes
    32  // on the path to the value at key. The value itself is also included in the last
    33  // node and can be retrieved by verifying the proof.
    34  //
    35  // If the trie does not contain a value for key, the returned proof contains all
    36  // nodes of the longest existing prefix of the key (at least the root node), ending
    37  // with the node that proves the absence of the key.
    38  func (t *Trie) Prove(key []byte, fromLevel uint, proofDb ethdb.KeyValueWriter) error {
    39  	// Collect all nodes on the path to key.
    40  	key = keybytesToHex(key)
    41  	var nodes []node
    42  	tn := t.root
    43  	for len(key) > 0 && tn != nil {
    44  		switch n := tn.(type) {
    45  		case *shortNode:
    46  			if len(key) < len(n.Key) || !bytes.Equal(n.Key, key[:len(n.Key)]) {
    47  				// The trie doesn't contain the key.
    48  				tn = nil
    49  			} else {
    50  				tn = n.Val
    51  				key = key[len(n.Key):]
    52  			}
    53  			nodes = append(nodes, n)
    54  		case *fullNode:
    55  			tn = n.Children[key[0]]
    56  			key = key[1:]
    57  			nodes = append(nodes, n)
    58  		case hashNode:
    59  			var err error
    60  			tn, err = t.resolveHash(n, nil)
    61  			if err != nil {
    62  				log.Error(fmt.Sprintf("Unhandled trie error: %v", err))
    63  				return err
    64  			}
    65  		default:
    66  			panic(fmt.Sprintf("%T: invalid node: %v", tn, tn))
    67  		}
    68  	}
    69  	hasher := newHasher(false)
    70  	defer returnHasherToPool(hasher)
    71  
    72  	for i, n := range nodes {
    73  		if fromLevel > 0 {
    74  			fromLevel--
    75  			continue
    76  		}
    77  		var hn node
    78  		n, hn = hasher.proofHash(n)
    79  		if hash, ok := hn.(hashNode); ok || i == 0 {
    80  			// If the node's database encoding is a hash (or is the
    81  			// root node), it becomes a proof element.
    82  			enc, _ := rlp.EncodeToBytes(n)
    83  			if !ok {
    84  				hash = hasher.hashData(enc)
    85  			}
    86  			proofDb.Put(hash, enc)
    87  		}
    88  	}
    89  	return nil
    90  }
    91  
    92  // Prove constructs a merkle proof for key. The result contains all encoded nodes
    93  // on the path to the value at key. The value itself is also included in the last
    94  // node and can be retrieved by verifying the proof.
    95  //
    96  // If the trie does not contain a value for key, the returned proof contains all
    97  // nodes of the longest existing prefix of the key (at least the root node), ending
    98  // with the node that proves the absence of the key.
    99  func (t *SecureTrie) Prove(key []byte, fromLevel uint, proofDb ethdb.KeyValueWriter) error {
   100  	return t.trie.Prove(key, fromLevel, proofDb)
   101  }
   102  
   103  // VerifyProof checks merkle proofs. The given proof must contain the value for
   104  // key in a trie with the given root hash. VerifyProof returns an error if the
   105  // proof contains invalid trie nodes or the wrong value.
   106  func VerifyProof(rootHash common.Hash, key []byte, proofDb ethdb.KeyValueReader) (value []byte, err error) {
   107  	key = keybytesToHex(key)
   108  	wantHash := rootHash
   109  	for i := 0; ; i++ {
   110  		buf, _ := proofDb.Get(wantHash[:])
   111  		if buf == nil {
   112  			return nil, fmt.Errorf("proof node %d (hash %064x) missing", i, wantHash)
   113  		}
   114  		n, err := decodeNode(wantHash[:], buf)
   115  		if err != nil {
   116  			return nil, fmt.Errorf("bad proof node %d: %v", i, err)
   117  		}
   118  		keyrest, cld := get(n, key, true)
   119  		switch cld := cld.(type) {
   120  		case nil:
   121  			// The trie doesn't contain the key.
   122  			return nil, nil
   123  		case hashNode:
   124  			key = keyrest
   125  			copy(wantHash[:], cld)
   126  		case valueNode:
   127  			return cld, nil
   128  		}
   129  	}
   130  }
   131  
   132  // proofToPath converts a merkle proof to trie node path. The main purpose of
   133  // this function is recovering a node path from the merkle proof stream. All
   134  // necessary nodes will be resolved and leave the remaining as hashnode.
   135  //
   136  // The given edge proof is allowed to be an existent or non-existent proof.
   137  func proofToPath(rootHash common.Hash, root node, key []byte, proofDb ethdb.KeyValueReader, allowNonExistent bool) (node, []byte, error) {
   138  	// resolveNode retrieves and resolves trie node from merkle proof stream
   139  	resolveNode := func(hash common.Hash) (node, error) {
   140  		buf, _ := proofDb.Get(hash[:])
   141  		if buf == nil {
   142  			return nil, fmt.Errorf("proof node (hash %064x) missing", hash)
   143  		}
   144  		n, err := decodeNode(hash[:], buf)
   145  		if err != nil {
   146  			return nil, fmt.Errorf("bad proof node %v", err)
   147  		}
   148  		return n, err
   149  	}
   150  	// If the root node is empty, resolve it first.
   151  	// Root node must be included in the proof.
   152  	if root == nil {
   153  		n, err := resolveNode(rootHash)
   154  		if err != nil {
   155  			return nil, nil, err
   156  		}
   157  		root = n
   158  	}
   159  	var (
   160  		err           error
   161  		child, parent node
   162  		keyrest       []byte
   163  		valnode       []byte
   164  	)
   165  	key, parent = keybytesToHex(key), root
   166  	for {
   167  		keyrest, child = get(parent, key, false)
   168  		switch cld := child.(type) {
   169  		case nil:
   170  			// The trie doesn't contain the key. It's possible
   171  			// the proof is a non-existing proof, but at least
   172  			// we can prove all resolved nodes are correct, it's
   173  			// enough for us to prove range.
   174  			if allowNonExistent {
   175  				return root, nil, nil
   176  			}
   177  			return nil, nil, errors.New("the node is not contained in trie")
   178  		case *shortNode:
   179  			key, parent = keyrest, child // Already resolved
   180  			continue
   181  		case *fullNode:
   182  			key, parent = keyrest, child // Already resolved
   183  			continue
   184  		case hashNode:
   185  			child, err = resolveNode(common.BytesToHash(cld))
   186  			if err != nil {
   187  				return nil, nil, err
   188  			}
   189  		case valueNode:
   190  			valnode = cld
   191  		}
   192  		// Link the parent and child.
   193  		switch pnode := parent.(type) {
   194  		case *shortNode:
   195  			pnode.Val = child
   196  		case *fullNode:
   197  			pnode.Children[key[0]] = child
   198  		default:
   199  			panic(fmt.Sprintf("%T: invalid node: %v", pnode, pnode))
   200  		}
   201  		if len(valnode) > 0 {
   202  			return root, valnode, nil // The whole path is resolved
   203  		}
   204  		key, parent = keyrest, child
   205  	}
   206  }
   207  
   208  // unsetInternal removes all internal node references(hashnode, embedded node).
   209  // It should be called after a trie is constructed with two edge paths. Also
   210  // the given boundary keys must be the one used to construct the edge paths.
   211  //
   212  // It's the key step for range proof. All visited nodes should be marked dirty
   213  // since the node content might be modified. Besides it can happen that some
   214  // fullnodes only have one child which is disallowed. But if the proof is valid,
   215  // the missing children will be filled, otherwise it will be thrown anyway.
   216  //
   217  // Note we have the assumption here the given boundary keys are different
   218  // and right is larger than left.
   219  func unsetInternal(n node, left []byte, right []byte) (bool, error) {
   220  	left, right = keybytesToHex(left), keybytesToHex(right)
   221  
   222  	// Step down to the fork point. There are two scenarios can happen:
   223  	// - the fork point is a shortnode: either the key of left proof or
   224  	//   right proof doesn't match with shortnode's key.
   225  	// - the fork point is a fullnode: both two edge proofs are allowed
   226  	//   to point to a non-existent key.
   227  	var (
   228  		pos    = 0
   229  		parent node
   230  
   231  		// fork indicator, 0 means no fork, -1 means proof is less, 1 means proof is greater
   232  		shortForkLeft, shortForkRight int
   233  	)
   234  findFork:
   235  	for {
   236  		switch rn := (n).(type) {
   237  		case *shortNode:
   238  			rn.flags = nodeFlag{dirty: true}
   239  
   240  			// If either the key of left proof or right proof doesn't match with
   241  			// shortnode, stop here and the forkpoint is the shortnode.
   242  			if len(left)-pos < len(rn.Key) {
   243  				shortForkLeft = bytes.Compare(left[pos:], rn.Key)
   244  			} else {
   245  				shortForkLeft = bytes.Compare(left[pos:pos+len(rn.Key)], rn.Key)
   246  			}
   247  			if len(right)-pos < len(rn.Key) {
   248  				shortForkRight = bytes.Compare(right[pos:], rn.Key)
   249  			} else {
   250  				shortForkRight = bytes.Compare(right[pos:pos+len(rn.Key)], rn.Key)
   251  			}
   252  			if shortForkLeft != 0 || shortForkRight != 0 {
   253  				break findFork
   254  			}
   255  			parent = n
   256  			n, pos = rn.Val, pos+len(rn.Key)
   257  		case *fullNode:
   258  			rn.flags = nodeFlag{dirty: true}
   259  
   260  			// If either the node pointed by left proof or right proof is nil,
   261  			// stop here and the forkpoint is the fullnode.
   262  			leftnode, rightnode := rn.Children[left[pos]], rn.Children[right[pos]]
   263  			if leftnode == nil || rightnode == nil || leftnode != rightnode {
   264  				break findFork
   265  			}
   266  			parent = n
   267  			n, pos = rn.Children[left[pos]], pos+1
   268  		default:
   269  			panic(fmt.Sprintf("%T: invalid node: %v", n, n))
   270  		}
   271  	}
   272  	switch rn := n.(type) {
   273  	case *shortNode:
   274  		// There can have these five scenarios:
   275  		// - both proofs are less than the trie path => no valid range
   276  		// - both proofs are greater than the trie path => no valid range
   277  		// - left proof is less and right proof is greater => valid range, unset the shortnode entirely
   278  		// - left proof points to the shortnode, but right proof is greater
   279  		// - right proof points to the shortnode, but left proof is less
   280  		if shortForkLeft == -1 && shortForkRight == -1 {
   281  			return false, errors.New("empty range")
   282  		}
   283  		if shortForkLeft == 1 && shortForkRight == 1 {
   284  			return false, errors.New("empty range")
   285  		}
   286  		if shortForkLeft != 0 && shortForkRight != 0 {
   287  			// The fork point is root node, unset the entire trie
   288  			if parent == nil {
   289  				return true, nil
   290  			}
   291  			parent.(*fullNode).Children[left[pos-1]] = nil
   292  			return false, nil
   293  		}
   294  		// Only one proof points to non-existent key.
   295  		if shortForkRight != 0 {
   296  			if _, ok := rn.Val.(valueNode); ok {
   297  				// The fork point is root node, unset the entire trie
   298  				if parent == nil {
   299  					return true, nil
   300  				}
   301  				parent.(*fullNode).Children[left[pos-1]] = nil
   302  				return false, nil
   303  			}
   304  			return false, unset(rn, rn.Val, left[pos:], len(rn.Key), false)
   305  		}
   306  		if shortForkLeft != 0 {
   307  			if _, ok := rn.Val.(valueNode); ok {
   308  				// The fork point is root node, unset the entire trie
   309  				if parent == nil {
   310  					return true, nil
   311  				}
   312  				parent.(*fullNode).Children[right[pos-1]] = nil
   313  				return false, nil
   314  			}
   315  			return false, unset(rn, rn.Val, right[pos:], len(rn.Key), true)
   316  		}
   317  		return false, nil
   318  	case *fullNode:
   319  		// unset all internal nodes in the forkpoint
   320  		for i := left[pos] + 1; i < right[pos]; i++ {
   321  			rn.Children[i] = nil
   322  		}
   323  		if err := unset(rn, rn.Children[left[pos]], left[pos:], 1, false); err != nil {
   324  			return false, err
   325  		}
   326  		if err := unset(rn, rn.Children[right[pos]], right[pos:], 1, true); err != nil {
   327  			return false, err
   328  		}
   329  		return false, nil
   330  	default:
   331  		panic(fmt.Sprintf("%T: invalid node: %v", n, n))
   332  	}
   333  }
   334  
   335  // unset removes all internal node references either the left most or right most.
   336  // It can meet these scenarios:
   337  //
   338  //   - The given path is existent in the trie, unset the associated nodes with the
   339  //     specific direction
   340  //   - The given path is non-existent in the trie
   341  //   - the fork point is a fullnode, the corresponding child pointed by path
   342  //     is nil, return
   343  //   - the fork point is a shortnode, the shortnode is included in the range,
   344  //     keep the entire branch and return.
   345  //   - the fork point is a shortnode, the shortnode is excluded in the range,
   346  //     unset the entire branch.
   347  func unset(parent node, child node, key []byte, pos int, removeLeft bool) error {
   348  	switch cld := child.(type) {
   349  	case *fullNode:
   350  		if removeLeft {
   351  			for i := 0; i < int(key[pos]); i++ {
   352  				cld.Children[i] = nil
   353  			}
   354  			cld.flags = nodeFlag{dirty: true}
   355  		} else {
   356  			for i := key[pos] + 1; i < 16; i++ {
   357  				cld.Children[i] = nil
   358  			}
   359  			cld.flags = nodeFlag{dirty: true}
   360  		}
   361  		return unset(cld, cld.Children[key[pos]], key, pos+1, removeLeft)
   362  	case *shortNode:
   363  		if len(key[pos:]) < len(cld.Key) || !bytes.Equal(cld.Key, key[pos:pos+len(cld.Key)]) {
   364  			// Find the fork point, it's an non-existent branch.
   365  			if removeLeft {
   366  				if bytes.Compare(cld.Key, key[pos:]) < 0 {
   367  					// The key of fork shortnode is less than the path
   368  					// (it belongs to the range), unset the entrie
   369  					// branch. The parent must be a fullnode.
   370  					fn := parent.(*fullNode)
   371  					fn.Children[key[pos-1]] = nil
   372  				}
   373  			} else {
   374  				if bytes.Compare(cld.Key, key[pos:]) > 0 {
   375  					// The key of fork shortnode is greater than the
   376  					// path(it belongs to the range), unset the entrie
   377  					// branch. The parent must be a fullnode.
   378  					fn := parent.(*fullNode)
   379  					fn.Children[key[pos-1]] = nil
   380  				}
   381  			}
   382  			return nil
   383  		}
   384  		if _, ok := cld.Val.(valueNode); ok {
   385  			fn := parent.(*fullNode)
   386  			fn.Children[key[pos-1]] = nil
   387  			return nil
   388  		}
   389  		cld.flags = nodeFlag{dirty: true}
   390  		return unset(cld, cld.Val, key, pos+len(cld.Key), removeLeft)
   391  	case nil:
   392  		// If the node is nil, then it's a child of the fork point
   393  		// fullnode(it's a non-existent branch).
   394  		return nil
   395  	default:
   396  		panic("it shouldn't happen") // hashNode, valueNode
   397  	}
   398  }
   399  
   400  // hasRightElement returns the indicator whether there exists more elements
   401  // in the right side of the given path. The given path can point to an existent
   402  // key or a non-existent one. This function has the assumption that the whole
   403  // path should already be resolved.
   404  func hasRightElement(node node, key []byte) bool {
   405  	pos, key := 0, keybytesToHex(key)
   406  	for node != nil {
   407  		switch rn := node.(type) {
   408  		case *fullNode:
   409  			for i := key[pos] + 1; i < 16; i++ {
   410  				if rn.Children[i] != nil {
   411  					return true
   412  				}
   413  			}
   414  			node, pos = rn.Children[key[pos]], pos+1
   415  		case *shortNode:
   416  			if len(key)-pos < len(rn.Key) || !bytes.Equal(rn.Key, key[pos:pos+len(rn.Key)]) {
   417  				return bytes.Compare(rn.Key, key[pos:]) > 0
   418  			}
   419  			node, pos = rn.Val, pos+len(rn.Key)
   420  		case valueNode:
   421  			return false // We have resolved the whole path
   422  		default:
   423  			panic(fmt.Sprintf("%T: invalid node: %v", node, node)) // hashnode
   424  		}
   425  	}
   426  	return false
   427  }
   428  
   429  // VerifyRangeProof checks whether the given leaf nodes and edge proof
   430  // can prove the given trie leaves range is matched with the specific root.
   431  // Besides, the range should be consecutive (no gap inside) and monotonic
   432  // increasing.
   433  //
   434  // Note the given proof actually contains two edge proofs. Both of them can
   435  // be non-existent proofs. For example the first proof is for a non-existent
   436  // key 0x03, the last proof is for a non-existent key 0x10. The given batch
   437  // leaves are [0x04, 0x05, .. 0x09]. It's still feasible to prove the given
   438  // batch is valid.
   439  //
   440  // The firstKey is paired with firstProof, not necessarily the same as keys[0]
   441  // (unless firstProof is an existent proof). Similarly, lastKey and lastProof
   442  // are paired.
   443  //
   444  // Expect the normal case, this function can also be used to verify the following
   445  // range proofs:
   446  //
   447  //   - All elements proof. In this case the proof can be nil, but the range should
   448  //     be all the leaves in the trie.
   449  //
   450  //   - One element proof. In this case no matter the edge proof is a non-existent
   451  //     proof or not, we can always verify the correctness of the proof.
   452  //
   453  //   - Zero element proof. In this case a single non-existent proof is enough to prove.
   454  //     Besides, if there are still some other leaves available on the right side, then
   455  //     an error will be returned.
   456  //
   457  // Except returning the error to indicate the proof is valid or not, the function will
   458  // also return a flag to indicate whether there exists more accounts/slots in the trie.
   459  //
   460  // Note: This method does not verify that the proof is of minimal form. If the input
   461  // proofs are 'bloated' with neighbour leaves or random data, aside from the 'useful'
   462  // data, then the proof will still be accepted.
   463  func VerifyRangeProof(rootHash common.Hash, firstKey []byte, lastKey []byte, keys [][]byte, values [][]byte, proof ethdb.KeyValueReader) (bool, error) {
   464  	if len(keys) != len(values) {
   465  		return false, fmt.Errorf("inconsistent proof data, keys: %d, values: %d", len(keys), len(values))
   466  	}
   467  	// Ensure the received batch is monotonic increasing.
   468  	for i := 0; i < len(keys)-1; i++ {
   469  		if bytes.Compare(keys[i], keys[i+1]) >= 0 {
   470  			return false, errors.New("range is not monotonically increasing")
   471  		}
   472  	}
   473  	// Special case, there is no edge proof at all. The given range is expected
   474  	// to be the whole leaf-set in the trie.
   475  	if proof == nil {
   476  		tr := NewStackTrie(nil)
   477  		for index, key := range keys {
   478  			tr.TryUpdate(key, values[index])
   479  		}
   480  		if have, want := tr.Hash(), rootHash; have != want {
   481  			return false, fmt.Errorf("invalid proof, want hash %x, got %x", want, have)
   482  		}
   483  		return false, nil // No more elements
   484  	}
   485  	// Special case, there is a provided edge proof but zero key/value
   486  	// pairs, ensure there are no more accounts / slots in the trie.
   487  	if len(keys) == 0 {
   488  		root, val, err := proofToPath(rootHash, nil, firstKey, proof, true)
   489  		if err != nil {
   490  			return false, err
   491  		}
   492  		if val != nil || hasRightElement(root, firstKey) {
   493  			return false, errors.New("more entries available")
   494  		}
   495  		return hasRightElement(root, firstKey), nil
   496  	}
   497  	// Special case, there is only one element and two edge keys are same.
   498  	// In this case, we can't construct two edge paths. So handle it here.
   499  	if len(keys) == 1 && bytes.Equal(firstKey, lastKey) {
   500  		root, val, err := proofToPath(rootHash, nil, firstKey, proof, false)
   501  		if err != nil {
   502  			return false, err
   503  		}
   504  		if !bytes.Equal(firstKey, keys[0]) {
   505  			return false, errors.New("correct proof but invalid key")
   506  		}
   507  		if !bytes.Equal(val, values[0]) {
   508  			return false, errors.New("correct proof but invalid data")
   509  		}
   510  		return hasRightElement(root, firstKey), nil
   511  	}
   512  	// Ok, in all other cases, we require two edge paths available.
   513  	// First check the validity of edge keys.
   514  	if bytes.Compare(firstKey, lastKey) >= 0 {
   515  		return false, errors.New("invalid edge keys")
   516  	}
   517  	// todo(rjl493456442) different length edge keys should be supported
   518  	if len(firstKey) != len(lastKey) {
   519  		return false, errors.New("inconsistent edge keys")
   520  	}
   521  	// Convert the edge proofs to edge trie paths. Then we can
   522  	// have the same tree architecture with the original one.
   523  	// For the first edge proof, non-existent proof is allowed.
   524  	root, _, err := proofToPath(rootHash, nil, firstKey, proof, true)
   525  	if err != nil {
   526  		return false, err
   527  	}
   528  	// Pass the root node here, the second path will be merged
   529  	// with the first one. For the last edge proof, non-existent
   530  	// proof is also allowed.
   531  	root, _, err = proofToPath(rootHash, root, lastKey, proof, true)
   532  	if err != nil {
   533  		return false, err
   534  	}
   535  	// Remove all internal references. All the removed parts should
   536  	// be re-filled(or re-constructed) by the given leaves range.
   537  	empty, err := unsetInternal(root, firstKey, lastKey)
   538  	if err != nil {
   539  		return false, err
   540  	}
   541  	// Rebuild the trie with the leaf stream, the shape of trie
   542  	// should be same with the original one.
   543  	tr := &Trie{root: root, db: NewDatabase(memorydb.New())}
   544  	if empty {
   545  		tr.root = nil
   546  	}
   547  	for index, key := range keys {
   548  		tr.TryUpdate(key, values[index])
   549  	}
   550  	if tr.Hash() != rootHash {
   551  		return false, fmt.Errorf("invalid proof, want hash %x, got %x", rootHash, tr.Hash())
   552  	}
   553  	return hasRightElement(root, keys[len(keys)-1]), nil
   554  }
   555  
   556  // get returns the child of the given node. Return nil if the
   557  // node with specified key doesn't exist at all.
   558  //
   559  // There is an additional flag `skipResolved`. If it's set then
   560  // all resolved nodes won't be returned.
   561  func get(tn node, key []byte, skipResolved bool) ([]byte, node) {
   562  	for {
   563  		switch n := tn.(type) {
   564  		case *shortNode:
   565  			if len(key) < len(n.Key) || !bytes.Equal(n.Key, key[:len(n.Key)]) {
   566  				return nil, nil
   567  			}
   568  			tn = n.Val
   569  			key = key[len(n.Key):]
   570  			if !skipResolved {
   571  				return key, tn
   572  			}
   573  		case *fullNode:
   574  			tn = n.Children[key[0]]
   575  			key = key[1:]
   576  			if !skipResolved {
   577  				return key, tn
   578  			}
   579  		case hashNode:
   580  			return key, n
   581  		case nil:
   582  			return key, nil
   583  		case valueNode:
   584  			return nil, n
   585  		default:
   586  			panic(fmt.Sprintf("%T: invalid node: %v", tn, tn))
   587  		}
   588  	}
   589  }