Postgres 10

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CREATE TABLE posts_lists AS
SELECT substring(md5(id::TEXT), 0, 21)::VARCHAR(20)                 AS id,
         id::VARCHAR(20)                                            AS user_id,
         ('["'|| trunc(random() * 1000) || '","b","c"]')::JSONB     AS tags,
         (trunc(random() * 1000) - trunc(random() * 1000))::INTEGER AS score,
         extract(epoch FROM current_timestamp(0))::INTEGER          AS created_at
FROM   generate_series(1, 100000) AS id;  -- just 100k

UPDATE posts_lists
SET tags = '["Qui"]'::jsonb
WHERE id IN (substring(md5('1'), 0, 21),
             substring(md5('100'), 0, 21),
             substring(md5('1000'), 0, 21),
             substring(md5('10000'), 0, 21));
             
ALTER TABLE posts_lists  ADD PRIMARY KEY (id);

create or replace function jsonb_array_lower(arr jsonb)
  returns jsonb as $$
SELECT jsonb_agg(lower(elem))
FROM jsonb_array_elements_text(arr) elem
$$
language sql
immutable;

create or replace function score_rank(score integer, id text)
  returns text as $$
select case when score < 0
  then '0' || lpad((100000000 + score) :: text, 8, '0') || id
       else '1' || lpad(score :: text, 8, '0') || id
       end
$$
language sql
immutable;

CREATE INDEX posts_lists_idx_tags_func  ON posts_lists USING gin (jsonb_array_lower(tags));
CREATE INDEX posts_lists_idx_tags_func2 ON posts_lists USING gin (jsonb_array_lower(tags) jsonb_path_ops);
CREATE INDEX posts_lists_idx_tags_fts   ON posts_lists USING gin (to_tsvector('simple', tags));
CREATE INDEX posts_lists_idx_score_id   ON posts_lists (score DESC, id DESC);
CREATE INDEX posts_lists_idx_score_func ON posts_lists (score_rank(score, id::text) DESC);

SELECT 100000

UPDATE 4

ALTER TABLE

CREATE FUNCTION

CREATE FUNCTION

CREATE INDEX

CREATE INDEX

CREATE INDEX

CREATE INDEX

CREATE INDEX

VACUUM ANALYZE posts_lists;

VACUUM

SELECT * FROM pg_stats
WHERE tablename IN ('posts_lists_idx_tags_fts', 'posts_lists_idx_tags_func');

schemaname
tablename
attname
inherited
null_frac
avg_width
n_distinct
most_common_vals
most_common_freqs
histogram_bounds
correlation
most_common_elems
most_common_elem_freqs
elem_count_histogram

public
posts_lists_idx_tags_func
jsonb_array_lower
f
0
21
1001
{"["205", "b", "c"]","["897", "b", "c"]","["934", "b", "c"]","["25", "b", "c"]","["557", "b", "c"]","["987", "b", "c"]","["92", "b", "c"]","["166", "b", "c"]","["425", "b", "c"]","["604", "b", "c"]","["274", "b", "c"]","["35", "b", "c"]","["560", "b", "c"]","["860", "b", "c"]","["944", "b", "c"]","["172", "b", "c"]","["247", "b", "c"]","["579", "b", "c"]","["61", "b", "c"]","["691", "b", "c"]","["862", "b", "c"]","["880", "b", "c"]","["142", "b", "c"]","["195", "b", "c"]","["209", "b", "c"]","["275", "b", "c"]","["352", "b", "c"]","["383", "b", "c"]","["409", "b", "c"]","["463", "b", "c"]","["472", "b", "c"]","["617", "b", "c"]","["646", "b", "c"]","["651", "b", "c"]","["736", "b", "c"]","["936", "b", "c"]","["989", "b", "c"]","["105", "b", "c"]","["135", "b", "c"]","["149", "b", "c"]","["299", "b", "c"]","["441", "b", "c"]","["51", "b", "c"]","["540", "b", "c"]","["664", "b", "c"]","["702", "b", "c"]","["841", "b", "c"]","["145", "b", "c"]","["181", "b", "c"]","["289", "b", "c"]","["292", "b", "c"]","["322", "b", "c"]","["378", "b", "c"]","["386", "b", "c"]","["455", "b", "c"]","["456", "b", "c"]","["590", "b", "c"]","["607", "b", "c"]","["625", "b", "c"]","["638", "b", "c"]","["90", "b", "c"]","["910", "b", "c"]","["929", "b", "c"]","["931", "b", "c"]","["952", "b", "c"]","["965", "b", "c"]","["127", "b", "c"]","["17", "b", "c"]","["203", "b", "c"]","["26", "b", "c"]","["291", "b", "c"]","["319", "b", "c"]","["350", "b", "c"]","["356", "b", "c"]","["411", "b", "c"]","["429", "b", "c"]","["543", "b", "c"]","["614", "b", "c"]","["656", "b", "c"]","["665", "b", "c"]","["681", "b", "c"]","["708", "b", "c"]","["761", "b", "c"]","["868", "b", "c"]","["937", "b", "c"]"}
{0.00156667,0.00156667,0.00156667,0.00153333,0.00153333,0.00153333,0.0015,0.00146667,0.00146667,0.00146667,0.00143333,0.00143333,0.00143333,0.00143333,0.00143333,0.0014,0.0014,0.0014,0.0014,0.0014,0.0014,0.0014,0.00136667,0.00136667,0.00136667,0.00136667,0.00136667,0.00136667,0.00136667,0.00136667,0.00136667,0.00136667,0.00136667,0.00136667,0.00136667,0.00136667,0.00136667,0.00133333,0.00133333,0.00133333,0.00133333,0.00133333,0.00133333,0.00133333,0.00133333,0.00133333,0.00133333,0.0013,0.0013,0.0013,0.0013,0.0013,0.0013,0.0013,0.0013,0.0013,0.0013,0.0013,0.0013,0.0013,0.0013,0.0013,0.0013,0.0013,0.0013,0.0013,0.00126667,0.00126667,0.00126667,0.00126667,0.00126667,0.00126667,0.00126667,0.00126667,0.00126667,0.00126667,0.00126667,0.00126667,0.00126667,0.00126667,0.00126667,0.00126667,0.00126667,0.00126667,0.00126667}
{"["qui"]","["107", "b", "c"]","["116", "b", "c"]","["123", "b", "c"]","["133", "b", "c"]","["141", "b", "c"]","["152", "b", "c"]","["160", "b", "c"]","["170", "b", "c"]","["18", "b", "c"]","["189", "b", "c"]","["197", "b", "c"]","["207", "b", "c"]","["216", "b", "c"]","["224", "b", "c"]","["232", "b", "c"]","["240", "b", "c"]","["250", "b", "c"]","["258", "b", "c"]","["267", "b", "c"]","["278", "b", "c"]","["286", "b", "c"]","["297", "b", "c"]","["305", "b", "c"]","["313", "b", "c"]","["324", "b", "c"]","["331", "b", "c"]","["340", "b", "c"]","["349", "b", "c"]","["360", "b", "c"]","["369", "b", "c"]","["377", "b", "c"]","["388", "b", "c"]","["397", "b", "c"]","["405", "b", "c"]","["415", "b", "c"]","["423", "b", "c"]","["432", "b", "c"]","["442", "b", "c"]","["45", "b", "c"]","["460", "b", "c"]","["47", "b", "c"]","["48", "b", "c"]","["488", "b", "c"]","["497", "b", "c"]","["504", "b", "c"]","["513", "b", "c"]","["521", "b", "c"]","["530", "b", "c"]","["54", "b", "c"]","["55", "b", "c"]","["559", "b", "c"]","["567", "b", "c"]","["576", "b", "c"]","["585", "b", "c"]","["594", "b", "c"]","["602", "b", "c"]","["613", "b", "c"]","["622", "b", "c"]","["632", "b", "c"]","["641", "b", "c"]","["650", "b", "c"]","["661", "b", "c"]","["671", "b", "c"]","["680", "b", "c"]","["69", "b", "c"]","["699", "b", "c"]","["707", "b", "c"]","["717", "b", "c"]","["725", "b", "c"]","["733", "b", "c"]","["742", "b", "c"]","["751", "b", "c"]","["76", "b", "c"]","["769", "b", "c"]","["777", "b", "c"]","["785", "b", "c"]","["793", "b", "c"]","["800", "b", "c"]","["808", "b", "c"]","["817", "b", "c"]","["825", "b", "c"]","["834", "b", "c"]","["843", "b", "c"]","["851", "b", "c"]","["86", "b", "c"]","["870", "b", "c"]","["88", "b", "c"]","["888", "b", "c"]","["896", "b", "c"]","["906", "b", "c"]","["915", "b", "c"]","["924", "b", "c"]","["935", "b", "c"]","["946", "b", "c"]","["955", "b", "c"]","["963", "b", "c"]","["972", "b", "c"]","["980", "b", "c"]","["991", "b", "c"]","["999", "b", "c"]"}
0.00608567
null
null
null

public
posts_lists_idx_tags_fts
to_tsvector
f
0
39
-1
null
null
null
null
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null

SELECT 2

EXPLAIN ANALYZE
SELECT * FROM posts_lists
WHERE  jsonb_array_lower(tags) ? lower('Qui') -- change
ORDER  BY score DESC, id DESC
LIMIT  2;

QUERY PLAN

Limit  (cost=339.48..339.49 rows=2 width=55) (actual time=0.233..0.234 rows=2 loops=1)

  ->  Sort  (cost=339.48..339.73 rows=100 width=55) (actual time=0.223..0.224 rows=2 loops=1)

        Sort Key: score DESC, id DESC

        Sort Method: quicksort  Memory: 25kB

        ->  Bitmap Heap Scan on posts_lists  (cost=12.78..338.48 rows=100 width=55) (actual time=0.145..0.211 rows=4 loops=1)

              Recheck Cond: (jsonb_array_lower(tags) ? 'qui'::text)

              Heap Blocks: exact=1

              ->  Bitmap Index Scan on posts_lists_idx_tags_func  (cost=0.00..12.75 rows=100 width=0) (actual time=0.014..0.014 rows=4 loops=1)

                    Index Cond: (jsonb_array_lower(tags) ? 'qui'::text)

Planning time: 1.150 ms

Execution time: 0.288 ms

EXPLAIN

EXPLAIN ANALYZE
SELECT * FROM posts_lists
WHERE  to_tsvector('simple', tags) @@ to_tsquery('simple', 'qui') -- case insensitive anyway
ORDER  BY score DESC, id DESC
LIMIT  2;

QUERY PLAN

Limit  (cost=114.95..114.96 rows=2 width=55) (actual time=0.018..0.019 rows=2 loops=1)

  ->  Sort  (cost=114.95..115.02 rows=27 width=55) (actual time=0.017..0.018 rows=2 loops=1)

        Sort Key: score DESC, id DESC

        Sort Method: quicksort  Memory: 25kB

        ->  Bitmap Heap Scan on posts_lists  (cost=12.21..114.68 rows=27 width=55) (actual time=0.012..0.013 rows=4 loops=1)

              Recheck Cond: (to_tsvector('simple'::regconfig, tags) @@ '''qui'''::tsquery)

              Heap Blocks: exact=1

              ->  Bitmap Index Scan on posts_lists_idx_tags_fts  (cost=0.00..12.20 rows=27 width=0) (actual time=0.009..0.009 rows=4 loops=1)

                    Index Cond: (to_tsvector('simple'::regconfig, tags) @@ '''qui'''::tsquery)

Planning time: 0.512 ms

Execution time: 0.046 ms

EXPLAIN

EXPLAIN ANALYZE  -- org query
SELECT * FROM posts_lists
WHERE  jsonb_array_lower(tags) ? lower('Qui')
ORDER  BY score_rank(score, id::text) DESC
LIMIT  2;

QUERY PLAN

Limit  (cost=342.48..342.49 rows=2 width=87) (actual time=0.145..0.146 rows=2 loops=1)

  ->  Sort  (cost=342.48..342.73 rows=100 width=87) (actual time=0.145..0.145 rows=2 loops=1)

        Sort Key: (CASE WHEN (score < 0) THEN (('0'::text || lpad(((100000000 + score))::text, 8, '0'::text)) || (id)::text) ELSE (('1'::text || lpad((score)::text, 8, '0'::text)) || (id)::text) END) DESC

        Sort Method: quicksort  Memory: 25kB

        ->  Bitmap Heap Scan on posts_lists  (cost=12.78..341.48 rows=100 width=87) (actual time=0.087..0.136 rows=4 loops=1)

              Recheck Cond: (jsonb_array_lower(tags) ? 'qui'::text)

              Heap Blocks: exact=1

              ->  Bitmap Index Scan on posts_lists_idx_tags_func  (cost=0.00..12.75 rows=100 width=0) (actual time=0.006..0.006 rows=4 loops=1)

                    Index Cond: (jsonb_array_lower(tags) ? 'qui'::text)

Planning time: 0.237 ms

Execution time: 0.179 ms

EXPLAIN

EXPLAIN ANALYZE  -- Variant with json_path_ops
SELECT * FROM posts_lists
WHERE  jsonb_array_lower(tags) @> '["qui"]'  -- !
ORDER  BY score DESC, id DESC
LIMIT  2;

QUERY PLAN

Limit  (cost=339.48..339.49 rows=2 width=55) (actual time=0.135..0.136 rows=2 loops=1)

  ->  Sort  (cost=339.48..339.73 rows=100 width=55) (actual time=0.135..0.135 rows=2 loops=1)

        Sort Key: score DESC, id DESC

        Sort Method: quicksort  Memory: 25kB

        ->  Bitmap Heap Scan on posts_lists  (cost=12.78..338.48 rows=100 width=55) (actual time=0.085..0.130 rows=4 loops=1)

              Recheck Cond: (jsonb_array_lower(tags) @> '["qui"]'::jsonb)

              Heap Blocks: exact=1

              ->  Bitmap Index Scan on posts_lists_idx_tags_func2  (cost=0.00..12.75 rows=100 width=0) (actual time=0.008..0.008 rows=4 loops=1)

                    Index Cond: (jsonb_array_lower(tags) @> '["qui"]'::jsonb)

Planning time: 0.146 ms

Execution time: 0.162 ms

EXPLAIN

SELECT pg_size_pretty(pg_table_size('posts_lists_idx_tags_func'))  AS func_idx
     , pg_size_pretty(pg_table_size('posts_lists_idx_tags_func2')) AS func2_idx
     , pg_size_pretty(pg_table_size('posts_lists_idx_tags_fts'))   AS fts_idx
     , pg_size_pretty(pg_table_size('posts_lists_idx_score_id'))   AS sort_idx
     , pg_size_pretty(pg_table_size('posts_lists_idx_score_func')) AS sort_func_idx;

func_idx
func2_idx
fts_idx
sort_idx
sort_func_idx

760 kB
768 kB
760 kB
4880 kB
4880 kB

SELECT 1

schemaname	tablename	attname	inherited	null_frac	avg_width	n_distinct	most_common_vals	most_common_freqs	histogram_bounds	correlation	most_common_elems	most_common_elem_freqs	elem_count_histogram
public	posts_lists_idx_tags_func	jsonb_array_lower	f	0	21	1001	{"["205", "b", "c"]","["897", "b", "c"]","["934", "b", "c"]","["25", "b", "c"]","["557", "b", "c"]","["987", "b", "c"]","["92", "b", "c"]","["166", "b", "c"]","["425", "b", "c"]","["604", "b", "c"]","["274", "b", "c"]","["35", "b", "c"]","["560", "b", "c"]","["860", "b", "c"]","["944", "b", "c"]","["172", "b", "c"]","["247", "b", "c"]","["579", "b", "c"]","["61", "b", "c"]","["691", "b", "c"]","["862", "b", "c"]","["880", "b", "c"]","["142", "b", "c"]","["195", "b", "c"]","["209", "b", "c"]","["275", "b", "c"]","["352", "b", "c"]","["383", "b", "c"]","["409", "b", "c"]","["463", "b", "c"]","["472", "b", "c"]","["617", "b", "c"]","["646", "b", "c"]","["651", "b", "c"]","["736", "b", "c"]","["936", "b", "c"]","["989", "b", "c"]","["105", "b", "c"]","["135", "b", "c"]","["149", "b", "c"]","["299", "b", "c"]","["441", "b", "c"]","["51", "b", "c"]","["540", "b", "c"]","["664", "b", "c"]","["702", "b", "c"]","["841", "b", "c"]","["145", "b", "c"]","["181", "b", "c"]","["289", "b", "c"]","["292", "b", "c"]","["322", "b", "c"]","["378", "b", "c"]","["386", "b", "c"]","["455", "b", "c"]","["456", "b", "c"]","["590", "b", "c"]","["607", "b", "c"]","["625", "b", "c"]","["638", "b", "c"]","["90", "b", "c"]","["910", "b", "c"]","["929", "b", "c"]","["931", "b", "c"]","["952", "b", "c"]","["965", "b", "c"]","["127", "b", "c"]","["17", "b", "c"]","["203", "b", "c"]","["26", "b", "c"]","["291", "b", "c"]","["319", "b", "c"]","["350", "b", "c"]","["356", "b", "c"]","["411", "b", "c"]","["429", "b", "c"]","["543", "b", "c"]","["614", "b", "c"]","["656", "b", "c"]","["665", "b", "c"]","["681", "b", "c"]","["708", "b", "c"]","["761", "b", "c"]","["868", "b", "c"]","["937", "b", "c"]"}	{0.00156667,0.00156667,0.00156667,0.00153333,0.00153333,0.00153333,0.0015,0.00146667,0.00146667,0.00146667,0.00143333,0.00143333,0.00143333,0.00143333,0.00143333,0.0014,0.0014,0.0014,0.0014,0.0014,0.0014,0.0014,0.00136667,0.00136667,0.00136667,0.00136667,0.00136667,0.00136667,0.00136667,0.00136667,0.00136667,0.00136667,0.00136667,0.00136667,0.00136667,0.00136667,0.00136667,0.00133333,0.00133333,0.00133333,0.00133333,0.00133333,0.00133333,0.00133333,0.00133333,0.00133333,0.00133333,0.0013,0.0013,0.0013,0.0013,0.0013,0.0013,0.0013,0.0013,0.0013,0.0013,0.0013,0.0013,0.0013,0.0013,0.0013,0.0013,0.0013,0.0013,0.0013,0.00126667,0.00126667,0.00126667,0.00126667,0.00126667,0.00126667,0.00126667,0.00126667,0.00126667,0.00126667,0.00126667,0.00126667,0.00126667,0.00126667,0.00126667,0.00126667,0.00126667,0.00126667,0.00126667}	{"["qui"]","["107", "b", "c"]","["116", "b", "c"]","["123", "b", "c"]","["133", "b", "c"]","["141", "b", "c"]","["152", "b", "c"]","["160", "b", "c"]","["170", "b", "c"]","["18", "b", "c"]","["189", "b", "c"]","["197", "b", "c"]","["207", "b", "c"]","["216", "b", "c"]","["224", "b", "c"]","["232", "b", "c"]","["240", "b", "c"]","["250", "b", "c"]","["258", "b", "c"]","["267", "b", "c"]","["278", "b", "c"]","["286", "b", "c"]","["297", "b", "c"]","["305", "b", "c"]","["313", "b", "c"]","["324", "b", "c"]","["331", "b", "c"]","["340", "b", "c"]","["349", "b", "c"]","["360", "b", "c"]","["369", "b", "c"]","["377", "b", "c"]","["388", "b", "c"]","["397", "b", "c"]","["405", "b", "c"]","["415", "b", "c"]","["423", "b", "c"]","["432", "b", "c"]","["442", "b", "c"]","["45", "b", "c"]","["460", "b", "c"]","["47", "b", "c"]","["48", "b", "c"]","["488", "b", "c"]","["497", "b", "c"]","["504", "b", "c"]","["513", "b", "c"]","["521", "b", "c"]","["530", "b", "c"]","["54", "b", "c"]","["55", "b", "c"]","["559", "b", "c"]","["567", "b", "c"]","["576", "b", "c"]","["585", "b", "c"]","["594", "b", "c"]","["602", "b", "c"]","["613", "b", "c"]","["622", "b", "c"]","["632", "b", "c"]","["641", "b", "c"]","["650", "b", "c"]","["661", "b", "c"]","["671", "b", "c"]","["680", "b", "c"]","["69", "b", "c"]","["699", "b", "c"]","["707", "b", "c"]","["717", "b", "c"]","["725", "b", "c"]","["733", "b", "c"]","["742", "b", "c"]","["751", "b", "c"]","["76", "b", "c"]","["769", "b", "c"]","["777", "b", "c"]","["785", "b", "c"]","["793", "b", "c"]","["800", "b", "c"]","["808", "b", "c"]","["817", "b", "c"]","["825", "b", "c"]","["834", "b", "c"]","["843", "b", "c"]","["851", "b", "c"]","["86", "b", "c"]","["870", "b", "c"]","["88", "b", "c"]","["888", "b", "c"]","["896", "b", "c"]","["906", "b", "c"]","["915", "b", "c"]","["924", "b", "c"]","["935", "b", "c"]","["946", "b", "c"]","["955", "b", "c"]","["963", "b", "c"]","["972", "b", "c"]","["980", "b", "c"]","["991", "b", "c"]","["999", "b", "c"]"}	0.00608567	null	null	null
public	posts_lists_idx_tags_fts	to_tsvector	f	0	39	-1	null	null	null	null	{0,1,2,3,4,5,6,7,8,9,b,c,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999}	{0.000966667,0.0011,0.000966667,0.000966667,0.0009,0.00116667,0.001,0.00106667,0.00103333,0.00106667,0.999967,0.999967,0.001,0.000933333,0.00113333,0.000966667,0.0012,0.0009,0.00123333,0.00126667,0.000833333,0.00116667,0.0009,0.0009,0.0008,0.0008,0.00103333,0.00153333,0.00126667,0.000766667,0.0012,0.000966667,0.000733333,0.000766667,0.000933333,0.000866667,0.000833333,0.00143333,0.000966667,0.00113333,0.000766667,0.000866667,0.0006,0.0011,0.000933333,0.0009,0.0008,0.000833333,0.0009,0.000866667,0.00123333,0.0011,0.0008,0.00133333,0.000633333,0.000766667,0.000966667,0.001,0.00116667,0.0007,0.000933333,0.00106667,0.000833333,0.0014,0.00123333,0.001,0.000933333,0.0009,0.0009,0.001,0.0008,0.0012,0.00103333,0.0012,0.000866667,0.0011,0.0009,0.0008,0.00113333,0.000766667,0.00106667,0.000933333,0.00106667,0.00106667,0.0009,0.001,0.0012,0.000666667,0.0009,0.00113333,0.0009,0.000833333,0.0013,0.00106667,0.0015,0.00113333,0.0009,0.000866667,0.00123333,0.000966667,0.000933333,0.000966667,0.000766667,0.001,0.000933333,0.0006,0.00076666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