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postgresql/src/common/pg_lzcompress.c

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/* ----------
* pg_lzcompress.c -
*
* This is an implementation of LZ compression for PostgreSQL.
* It uses a simple history table and generates 2-3 byte tags
* capable of backward copy information for 3-273 bytes with
* a max offset of 4095.
*
* Entry routines:
*
* int32
* pglz_compress(const char *source, int32 slen, char *dest,
* const PGLZ_Strategy *strategy);
*
* source is the input data to be compressed.
*
* slen is the length of the input data.
*
* dest is the output area for the compressed result.
* It must be at least as big as PGLZ_MAX_OUTPUT(slen).
*
* strategy is a pointer to some information controlling
* the compression algorithm. If NULL, the compiled
* in default strategy is used.
*
* The return value is the number of bytes written in the
* buffer dest, or -1 if compression fails; in the latter
* case the contents of dest are undefined.
*
* int32
* pglz_decompress(const char *source, int32 slen, char *dest,
* int32 rawsize, bool check_complete)
*
* source is the compressed input.
*
* slen is the length of the compressed input.
*
* dest is the area where the uncompressed data will be
* written to. It is the callers responsibility to
* provide enough space.
*
* The data is written to buff exactly as it was handed
* to pglz_compress(). No terminating zero byte is added.
*
* rawsize is the length of the uncompressed data.
*
* check_complete is a flag to let us know if -1 should be
* returned in cases where we don't reach the end of the
* source or dest buffers, or not. This should be false
* if the caller is asking for only a partial result and
* true otherwise.
*
* The return value is the number of bytes written in the
* buffer dest, or -1 if decompression fails.
*
* The decompression algorithm and internal data format:
*
* It is made with the compressed data itself.
*
* The data representation is easiest explained by describing
* the process of decompression.
*
* If compressed_size == rawsize, then the data
* is stored uncompressed as plain bytes. Thus, the decompressor
* simply copies rawsize bytes to the destination.
*
* Otherwise the first byte tells what to do the next 8 times.
* We call this the control byte.
*
* An unset bit in the control byte means, that one uncompressed
* byte follows, which is copied from input to output.
*
* A set bit in the control byte means, that a tag of 2-3 bytes
* follows. A tag contains information to copy some bytes, that
* are already in the output buffer, to the current location in
* the output. Let's call the three tag bytes T1, T2 and T3. The
* position of the data to copy is coded as an offset from the
* actual output position.
*
* The offset is in the upper nibble of T1 and in T2.
* The length is in the lower nibble of T1.
*
* So the 16 bits of a 2 byte tag are coded as
*
* 7---T1--0 7---T2--0
* OOOO LLLL OOOO OOOO
*
* This limits the offset to 1-4095 (12 bits) and the length
* to 3-18 (4 bits) because 3 is always added to it. To emit
* a tag of 2 bytes with a length of 2 only saves one control
* bit. But we lose one byte in the possible length of a tag.
*
* In the actual implementation, the 2 byte tag's length is
* limited to 3-17, because the value 0xF in the length nibble
* has special meaning. It means, that the next following
* byte (T3) has to be added to the length value of 18. That
* makes total limits of 1-4095 for offset and 3-273 for length.
*
* Now that we have successfully decoded a tag. We simply copy
* the output that occurred <offset> bytes back to the current
* output location in the specified <length>. Thus, a
* sequence of 200 spaces (think about bpchar fields) could be
* coded in 4 bytes. One literal space and a three byte tag to
* copy 199 bytes with a -1 offset. Whow - that's a compression
* rate of 98%! Well, the implementation needs to save the
* original data size too, so we need another 4 bytes for it
* and end up with a total compression rate of 96%, what's still
* worth a Whow.
*
* The compression algorithm
*
* The following uses numbers used in the default strategy.
*
* The compressor works best for attributes of a size between
* 1K and 1M. For smaller items there's not that much chance of
* redundancy in the character sequence (except for large areas
* of identical bytes like trailing spaces) and for bigger ones
* our 4K maximum look-back distance is too small.
*
* The compressor creates a table for lists of positions.
* For each input position (except the last 3), a hash key is
* built from the 4 next input bytes and the position remembered
* in the appropriate list. Thus, the table points to linked
* lists of likely to be at least in the first 4 characters
* matching strings. This is done on the fly while the input
* is compressed into the output area. Table entries are only
* kept for the last 4096 input positions, since we cannot use
* back-pointers larger than that anyway. The size of the hash
* table is chosen based on the size of the input - a larger table
* has a larger startup cost, as it needs to be initialized to
* zero, but reduces the number of hash collisions on long inputs.
*
* For each byte in the input, its hash key (built from this
* byte and the next 3) is used to find the appropriate list
* in the table. The lists remember the positions of all bytes
* that had the same hash key in the past in increasing backward
* offset order. Now for all entries in the used lists, the
* match length is computed by comparing the characters from the
* entries position with the characters from the actual input
* position.
*
* The compressor starts with a so called "good_match" of 128.
* It is a "prefer speed against compression ratio" optimizer.
* So if the first entry looked at already has 128 or more
* matching characters, the lookup stops and that position is
* used for the next tag in the output.
*
* For each subsequent entry in the history list, the "good_match"
* is lowered by 10%. So the compressor will be more happy with
* short matches the further it has to go back in the history.
* Another "speed against ratio" preference characteristic of
* the algorithm.
*
* Thus there are 3 stop conditions for the lookup of matches:
*
* - a match >= good_match is found
* - there are no more history entries to look at
* - the next history entry is already too far back
* to be coded into a tag.
*
* Finally the match algorithm checks that at least a match
* of 3 or more bytes has been found, because that is the smallest
* amount of copy information to code into a tag. If so, a tag
* is omitted and all the input bytes covered by that are just
* scanned for the history add's, otherwise a literal character
* is omitted and only his history entry added.
*
* Acknowledgments:
*
* Many thanks to Adisak Pochanayon, who's article about SLZ
* inspired me to write the PostgreSQL compression this way.
*
* Jan Wieck
*
* Copyright (c) 1999-2024, PostgreSQL Global Development Group
*
* src/common/pg_lzcompress.c
* ----------
*/
#ifndef FRONTEND
#include "postgres.h"
#else
#include "postgres_fe.h"
#endif
#include <limits.h>
#include "common/pg_lzcompress.h"
/* ----------
* Local definitions
* ----------
*/
#define PGLZ_MAX_HISTORY_LISTS 8192 /* must be power of 2 */
#define PGLZ_HISTORY_SIZE 4096
#define PGLZ_MAX_MATCH 273
/* ----------
* PGLZ_HistEntry -
*
* Linked list for the backward history lookup
*
* All the entries sharing a hash key are linked in a doubly linked list.
* This makes it easy to remove an entry when it's time to recycle it
* (because it's more than 4K positions old).
* ----------
*/
typedef struct PGLZ_HistEntry
{
struct PGLZ_HistEntry *next; /* links for my hash key's list */
struct PGLZ_HistEntry *prev;
int hindex; /* my current hash key */
const char *pos; /* my input position */
} PGLZ_HistEntry;
/* ----------
* The provided standard strategies
* ----------
*/
static const PGLZ_Strategy strategy_default_data = {
32, /* Data chunks less than 32 bytes are not
* compressed */
INT_MAX, /* No upper limit on what we'll try to
* compress */
25, /* Require 25% compression rate, or not worth
* it */
1024, /* Give up if no compression in the first 1KB */
128, /* Stop history lookup if a match of 128 bytes
* is found */
10 /* Lower good match size by 10% at every loop
* iteration */
};
const PGLZ_Strategy *const PGLZ_strategy_default = &strategy_default_data;
static const PGLZ_Strategy strategy_always_data = {
0, /* Chunks of any size are compressed */
INT_MAX,
0, /* It's enough to save one single byte */
INT_MAX, /* Never give up early */
128, /* Stop history lookup if a match of 128 bytes
* is found */
6 /* Look harder for a good match */
};
const PGLZ_Strategy *const PGLZ_strategy_always = &strategy_always_data;
/* ----------
* Statically allocated work arrays for history
* ----------
*/
static int16 hist_start[PGLZ_MAX_HISTORY_LISTS];
static PGLZ_HistEntry hist_entries[PGLZ_HISTORY_SIZE + 1];
/*
* Element 0 in hist_entries is unused, and means 'invalid'. Likewise,
* INVALID_ENTRY_PTR in next/prev pointers mean 'invalid'.
*/
#define INVALID_ENTRY 0
#define INVALID_ENTRY_PTR (&hist_entries[INVALID_ENTRY])
/* ----------
* pglz_hist_idx -
*
* Computes the history table slot for the lookup by the next 4
* characters in the input.
*
* NB: because we use the next 4 characters, we are not guaranteed to
* find 3-character matches; they very possibly will be in the wrong
* hash list. This seems an acceptable tradeoff for spreading out the
* hash keys more.
* ----------
*/
#define pglz_hist_idx(_s,_e, _mask) ( \
((((_e) - (_s)) < 4) ? (int) (_s)[0] : \
(((_s)[0] << 6) ^ ((_s)[1] << 4) ^ \
((_s)[2] << 2) ^ (_s)[3])) & (_mask) \
)
/* ----------
* pglz_hist_add -
*
* Adds a new entry to the history table.
*
* If _recycle is true, then we are recycling a previously used entry,
* and must first delink it from its old hashcode's linked list.
*
* NOTE: beware of multiple evaluations of macro's arguments, and note that
* _hn and _recycle are modified in the macro.
* ----------
*/
#define pglz_hist_add(_hs,_he,_hn,_recycle,_s,_e, _mask) \
do { \
int __hindex = pglz_hist_idx((_s),(_e), (_mask)); \
int16 *__myhsp = &(_hs)[__hindex]; \
PGLZ_HistEntry *__myhe = &(_he)[_hn]; \
if (_recycle) { \
if (__myhe->prev == NULL) \
(_hs)[__myhe->hindex] = __myhe->next - (_he); \
else \
__myhe->prev->next = __myhe->next; \
if (__myhe->next != NULL) \
__myhe->next->prev = __myhe->prev; \
} \
__myhe->next = &(_he)[*__myhsp]; \
__myhe->prev = NULL; \
__myhe->hindex = __hindex; \
__myhe->pos = (_s); \
/* If there was an existing entry in this hash slot, link */ \
/* this new entry to it. However, the 0th entry in the */ \
/* entries table is unused, so we can freely scribble on it. */ \
/* So don't bother checking if the slot was used - we'll */ \
/* scribble on the unused entry if it was not, but that's */ \
/* harmless. Avoiding the branch in this critical path */ \
/* speeds this up a little bit. */ \
/* if (*__myhsp != INVALID_ENTRY) */ \
(_he)[(*__myhsp)].prev = __myhe; \
*__myhsp = _hn; \
if (++(_hn) >= PGLZ_HISTORY_SIZE + 1) { \
(_hn) = 1; \
(_recycle) = true; \
} \
} while (0)
/* ----------
* pglz_out_ctrl -
*
* Outputs the last and allocates a new control byte if needed.
* ----------
*/
#define pglz_out_ctrl(__ctrlp,__ctrlb,__ctrl,__buf) \
do { \
if ((__ctrl & 0xff) == 0) \
{ \
*(__ctrlp) = __ctrlb; \
__ctrlp = (__buf)++; \
__ctrlb = 0; \
__ctrl = 1; \
} \
} while (0)
/* ----------
* pglz_out_literal -
*
* Outputs a literal byte to the destination buffer including the
* appropriate control bit.
* ----------
*/
#define pglz_out_literal(_ctrlp,_ctrlb,_ctrl,_buf,_byte) \
do { \
pglz_out_ctrl(_ctrlp,_ctrlb,_ctrl,_buf); \
*(_buf)++ = (unsigned char)(_byte); \
_ctrl <<= 1; \
} while (0)
/* ----------
* pglz_out_tag -
*
* Outputs a backward reference tag of 2-4 bytes (depending on
* offset and length) to the destination buffer including the
* appropriate control bit.
* ----------
*/
#define pglz_out_tag(_ctrlp,_ctrlb,_ctrl,_buf,_len,_off) \
do { \
pglz_out_ctrl(_ctrlp,_ctrlb,_ctrl,_buf); \
_ctrlb |= _ctrl; \
_ctrl <<= 1; \
if (_len > 17) \
{ \
(_buf)[0] = (unsigned char)((((_off) & 0xf00) >> 4) | 0x0f); \
(_buf)[1] = (unsigned char)(((_off) & 0xff)); \
(_buf)[2] = (unsigned char)((_len) - 18); \
(_buf) += 3; \
} else { \
(_buf)[0] = (unsigned char)((((_off) & 0xf00) >> 4) | ((_len) - 3)); \
(_buf)[1] = (unsigned char)((_off) & 0xff); \
(_buf) += 2; \
} \
} while (0)
/* ----------
* pglz_find_match -
*
* Lookup the history table if the actual input stream matches
* another sequence of characters, starting somewhere earlier
* in the input buffer.
* ----------
*/
static inline int
pglz_find_match(int16 *hstart, const char *input, const char *end,
int *lenp, int *offp, int good_match, int good_drop, int mask)
{
PGLZ_HistEntry *hent;
int16 hentno;
int32 len = 0;
int32 off = 0;
/*
* Traverse the linked history list until a good enough match is found.
*/
hentno = hstart[pglz_hist_idx(input, end, mask)];
hent = &hist_entries[hentno];
while (hent != INVALID_ENTRY_PTR)
{
const char *ip = input;
const char *hp = hent->pos;
int32 thisoff;
int32 thislen;
/*
* Stop if the offset does not fit into our tag anymore.
*/
thisoff = ip - hp;
if (thisoff >= 0x0fff)
break;
/*
* Determine length of match. A better match must be larger than the
* best so far. And if we already have a match of 16 or more bytes,
* it's worth the call overhead to use memcmp() to check if this match
* is equal for the same size. After that we must fallback to
* character by character comparison to know the exact position where
* the diff occurred.
*/
thislen = 0;
if (len >= 16)
{
if (memcmp(ip, hp, len) == 0)
{
thislen = len;
ip += len;
hp += len;
while (ip < end && *ip == *hp && thislen < PGLZ_MAX_MATCH)
{
thislen++;
ip++;
hp++;
}
}
}
else
{
while (ip < end && *ip == *hp && thislen < PGLZ_MAX_MATCH)
{
thislen++;
ip++;
hp++;
}
}
/*
* Remember this match as the best (if it is)
*/
if (thislen > len)
{
len = thislen;
off = thisoff;
}
/*
* Advance to the next history entry
*/
hent = hent->next;
/*
* Be happy with lesser good matches the more entries we visited. But
* no point in doing calculation if we're at end of list.
*/
if (hent != INVALID_ENTRY_PTR)
{
if (len >= good_match)
break;
good_match -= (good_match * good_drop) / 100;
}
}
/*
* Return match information only if it results at least in one byte
* reduction.
*/
if (len > 2)
{
*lenp = len;
*offp = off;
return 1;
}
return 0;
}
/* ----------
* pglz_compress -
*
* Compresses source into dest using strategy. Returns the number of
* bytes written in buffer dest, or -1 if compression fails.
* ----------
*/
int32
pglz_compress(const char *source, int32 slen, char *dest,
const PGLZ_Strategy *strategy)
{
unsigned char *bp = (unsigned char *) dest;
unsigned char *bstart = bp;
int hist_next = 1;
bool hist_recycle = false;
const char *dp = source;
const char *dend = source + slen;
unsigned char ctrl_dummy = 0;
unsigned char *ctrlp = &ctrl_dummy;
unsigned char ctrlb = 0;
unsigned char ctrl = 0;
bool found_match = false;
int32 match_len;
int32 match_off;
int32 good_match;
int32 good_drop;
int32 result_size;
int32 result_max;
int32 need_rate;
int hashsz;
int mask;
/*
* Our fallback strategy is the default.
*/
if (strategy == NULL)
strategy = PGLZ_strategy_default;
/*
* If the strategy forbids compression (at all or if source chunk size out
* of range), fail.
*/
if (strategy->match_size_good <= 0 ||
slen < strategy->min_input_size ||
slen > strategy->max_input_size)
return -1;
/*
* Limit the match parameters to the supported range.
*/
good_match = strategy->match_size_good;
if (good_match > PGLZ_MAX_MATCH)
good_match = PGLZ_MAX_MATCH;
else if (good_match < 17)
good_match = 17;
good_drop = strategy->match_size_drop;
if (good_drop < 0)
good_drop = 0;
else if (good_drop > 100)
good_drop = 100;
need_rate = strategy->min_comp_rate;
if (need_rate < 0)
need_rate = 0;
else if (need_rate > 99)
need_rate = 99;
/*
* Compute the maximum result size allowed by the strategy, namely the
* input size minus the minimum wanted compression rate. This had better
* be <= slen, else we might overrun the provided output buffer.
*/
if (slen > (INT_MAX / 100))
{
/* Approximate to avoid overflow */
result_max = (slen / 100) * (100 - need_rate);
}
else
result_max = (slen * (100 - need_rate)) / 100;
/*
* Experiments suggest that these hash sizes work pretty well. A large
* hash table minimizes collision, but has a higher startup cost. For a
* small input, the startup cost dominates. The table size must be a power
* of two.
*/
if (slen < 128)
hashsz = 512;
else if (slen < 256)
hashsz = 1024;
else if (slen < 512)
hashsz = 2048;
else if (slen < 1024)
hashsz = 4096;
else
hashsz = 8192;
mask = hashsz - 1;
/*
* Initialize the history lists to empty. We do not need to zero the
* hist_entries[] array; its entries are initialized as they are used.
*/
memset(hist_start, 0, hashsz * sizeof(int16));
/*
* Compress the source directly into the output buffer.
*/
while (dp < dend)
{
/*
* If we already exceeded the maximum result size, fail.
*
* We check once per loop; since the loop body could emit as many as 4
* bytes (a control byte and 3-byte tag), PGLZ_MAX_OUTPUT() had better
* allow 4 slop bytes.
*/
if (bp - bstart >= result_max)
return -1;
/*
* If we've emitted more than first_success_by bytes without finding
* anything compressible at all, fail. This lets us fall out
* reasonably quickly when looking at incompressible input (such as
* pre-compressed data).
*/
if (!found_match && bp - bstart >= strategy->first_success_by)
return -1;
/*
* Try to find a match in the history
*/
if (pglz_find_match(hist_start, dp, dend, &match_len,
&match_off, good_match, good_drop, mask))
{
/*
* Create the tag and add history entries for all matched
* characters.
*/
pglz_out_tag(ctrlp, ctrlb, ctrl, bp, match_len, match_off);
while (match_len--)
{
pglz_hist_add(hist_start, hist_entries,
hist_next, hist_recycle,
dp, dend, mask);
dp++; /* Do not do this ++ in the line above! */
/* The macro would do it four times - Jan. */
}
found_match = true;
}
else
{
/*
* No match found. Copy one literal byte.
*/
pglz_out_literal(ctrlp, ctrlb, ctrl, bp, *dp);
pglz_hist_add(hist_start, hist_entries,
hist_next, hist_recycle,
dp, dend, mask);
dp++; /* Do not do this ++ in the line above! */
/* The macro would do it four times - Jan. */
}
}
/*
* Write out the last control byte and check that we haven't overrun the
* output size allowed by the strategy.
*/
*ctrlp = ctrlb;
result_size = bp - bstart;
if (result_size >= result_max)
return -1;
/* success */
return result_size;
}
/* ----------
* pglz_decompress -
*
* Decompresses source into dest. Returns the number of bytes
* decompressed into the destination buffer, or -1 if the
* compressed data is corrupted.
*
* If check_complete is true, the data is considered corrupted
* if we don't exactly fill the destination buffer. Callers that
* are extracting a slice typically can't apply this check.
* ----------
*/
int32
pglz_decompress(const char *source, int32 slen, char *dest,
int32 rawsize, bool check_complete)
{
const unsigned char *sp;
const unsigned char *srcend;
unsigned char *dp;
unsigned char *destend;
sp = (const unsigned char *) source;
srcend = ((const unsigned char *) source) + slen;
dp = (unsigned char *) dest;
destend = dp + rawsize;
while (sp < srcend && dp < destend)
{
/*
* Read one control byte and process the next 8 items (or as many as
* remain in the compressed input).
*/
unsigned char ctrl = *sp++;
int ctrlc;
for (ctrlc = 0; ctrlc < 8 && sp < srcend && dp < destend; ctrlc++)
{
if (ctrl & 1)
{
/*
* Set control bit means we must read a match tag. The match
* is coded with two bytes. First byte uses lower nibble to
* code length - 3. Higher nibble contains upper 4 bits of the
* offset. The next following byte contains the lower 8 bits
* of the offset. If the length is coded as 18, another
* extension tag byte tells how much longer the match really
* was (0-255).
*/
int32 len;
int32 off;
len = (sp[0] & 0x0f) + 3;
off = ((sp[0] & 0xf0) << 4) | sp[1];
sp += 2;
if (len == 18)
len += *sp++;
/*
* Check for corrupt data: if we fell off the end of the
* source, or if we obtained off = 0, or if off is more than
* the distance back to the buffer start, we have problems.
* (We must check for off = 0, else we risk an infinite loop
* below in the face of corrupt data. Likewise, the upper
* limit on off prevents accessing outside the buffer
* boundaries.)
*/
if (unlikely(sp > srcend || off == 0 ||
off > (dp - (unsigned char *) dest)))
return -1;
/*
* Don't emit more data than requested.
*/
len = Min(len, destend - dp);
/*
* Now we copy the bytes specified by the tag from OUTPUT to
* OUTPUT (copy len bytes from dp - off to dp). The copied
* areas could overlap, so to avoid undefined behavior in
* memcpy(), be careful to copy only non-overlapping regions.
*
* Note that we cannot use memmove() instead, since while its
* behavior is well-defined, it's also not what we want.
*/
while (off < len)
{
/*
* We can safely copy "off" bytes since that clearly
* results in non-overlapping source and destination.
*/
memcpy(dp, dp - off, off);
len -= off;
dp += off;
/*----------
* This bit is less obvious: we can double "off" after
* each such step. Consider this raw input:
* 112341234123412341234
* This will be encoded as 5 literal bytes "11234" and
* then a match tag with length 16 and offset 4. After
* memcpy'ing the first 4 bytes, we will have emitted
* 112341234
* so we can double "off" to 8, then after the next step
* we have emitted
* 11234123412341234
* Then we can double "off" again, after which it is more
* than the remaining "len" so we fall out of this loop
* and finish with a non-overlapping copy of the
* remainder. In general, a match tag with off < len
* implies that the decoded data has a repeat length of
* "off". We can handle 1, 2, 4, etc repetitions of the
* repeated string per memcpy until we get to a situation
* where the final copy step is non-overlapping.
*
* (Another way to understand this is that we are keeping
* the copy source point dp - off the same throughout.)
*----------
*/
off += off;
}
memcpy(dp, dp - off, len);
dp += len;
}
else
{
/*
* An unset control bit means LITERAL BYTE. So we just copy
* one from INPUT to OUTPUT.
*/
*dp++ = *sp++;
}
/*
* Advance the control bit
*/
ctrl >>= 1;
}
}
/*
* If requested, check we decompressed the right amount.
*/
if (check_complete && (dp != destend || sp != srcend))
return -1;
/*
* That's it.
*/
return (char *) dp - dest;
}
/* ----------
* pglz_maximum_compressed_size -
*
* Calculate the maximum compressed size for a given amount of raw data.
* Return the maximum size, or total compressed size if maximum size is
* larger than total compressed size.
*
* We can't use PGLZ_MAX_OUTPUT for this purpose, because that's used to size
* the compression buffer (and abort the compression). It does not really say
* what's the maximum compressed size for an input of a given length, and it
* may happen that while the whole value is compressible (and thus fits into
* PGLZ_MAX_OUTPUT nicely), the prefix is not compressible at all.
* ----------
*/
int32
pglz_maximum_compressed_size(int32 rawsize, int32 total_compressed_size)
{
int64 compressed_size;
/*
* pglz uses one control bit per byte, so if the entire desired prefix is
* represented as literal bytes, we'll need (rawsize * 9) bits. We care
* about bytes though, so be sure to round up not down.
*
* Use int64 here to prevent overflow during calculation.
*/
compressed_size = ((int64) rawsize * 9 + 7) / 8;
/*
* The above fails to account for a corner case: we could have compressed
* data that starts with N-1 or N-2 literal bytes and then has a match tag
* of 2 or 3 bytes. It's therefore possible that we need to fetch 1 or 2
* more bytes in order to have the whole match tag. (Match tags earlier
* in the compressed data don't cause a problem, since they should
* represent more decompressed bytes than they occupy themselves.)
*/
compressed_size += 2;
/*
* Maximum compressed size can't be larger than total compressed size.
* (This also ensures that our result fits in int32.)
*/
compressed_size = Min(compressed_size, total_compressed_size);
return (int32) compressed_size;
}
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