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P2P Architecture Case Study: Gnutella NetworkMatei Rpeanu The University of Chicago
Unprecedented scale up to 100k nodes, 100TB data, 10M files todaySelf-organizing networkStaggering growth more than 50 times during first half of 2001Open architecture, simple and flexible protocolInteresting mix of social and technical issuesWhy analyze Gnutella network?
OverviewGnutella protocolTools for exploring the networkNetwork growthStructural graph analysisIs Gnutella a power-law network? Generated (overhead) network trafficTraffic estimatesOverlay network topology mapping
Gnutella protocol overviewP2P file sharing application on top of an overlay networkNodes maintain open TCP connectionsMessages are broadcasted (flooded) or back-propagated
Protocol:
Broadcast(Flooding)Back-propagatedNode to nodeMembership PINGPONGQueryQUERYQUERY HITFile downloadGET, PUSH
Gnutella search mechanism1234567Steps:Node 2 initiates search for file A
Gnutella search mechanism1234567Steps:Node 2 initiates search for file ASends message to all neighbors
Gnutella search mechanism1234567Steps:Node 2 initiates search for file ASends message to all neighborsNeighbors forward message
Gnutella search mechanism1234567Steps:Node 2 initiates search for file ASends message to all neighborsNeighbors forward messageNodes that have file A initiate a reply message
Gnutella search mechanism1234567Steps:Node 2 initiates search for file ASends message to all neighborsNeighbors forward messageNodes that have file A initiate a reply messageQuery reply message is back-propagated
Gnutella search mechanism1234567Steps:Node 2 initiates search for file ASends message to all neighborsNeighbors forward messageNodes that have file A initiate a reply messageQuery reply message is back-propagated
Gnutella search mechanism1234567Steps:Node 2 initiates search for file ASends message to all neighborsNeighbors forward messageNodes that have file A initiate a reply messageQuery reply message is back-propagatedFile download
download A
Tools for network explorationEavesdropper - insert modified nodes into the network to eavesdrop traffic.Crawler - connects to all active nodes and uses the membership protocol to discover graph topology. Client-server approach.Graph analysis tools high-volume offline computations.
Network growth High user interestUsers tolerate high latency, low quality resultsBetter resourcesDSL and cable modem nodes grew from 24% to 41% over first 6 months. Today >50%.Open architecture / open-source environmentCompeting implementationsLower overhead network traffic, improved resource utilization, better structure
Chart1
1.471
1.629
1.174
2.063
1.023
1.398
1.094
1.457
5.4
4.151
4.88
3.997
4.288
3.989
5.254
5.461
6.528
6.052
8.29
6.738
10.787
13.432
12.683
10.931
12.547
13.867
11.74
23
24.234
17.635
46.381
21.068
20.852
36.66
48.195
35.183
44.006
Number of nodes in the largest network component ('000)
Gnutella Network Growth .
Sheet1
Date# of nodes# of CCsize of largest CCdiameter of largest CCSearch time (hours)
11/20/0011471314748
11/21/0021629416257
11/21/00111744711177
11/22/00220633720247
11/25/0011023279908
11/27/00113982813707
11/28/00110942910607
11/30/0011457614527
02/25/015540053982:44:16
02/27/014415141211:27:27
02/28/015488048591:28:44
03/01/014399739791:20:36
03/02/014428831021:22:40
03/05/014398938961:20:46
03/07/015525451651:31:35
03/09/015546153701:25:52
03/11/017652864281:53:31
03/13/016605259631:41:57
03/16/018829078914:24:53
03/16/017673866741:50:59
03/18/01111078795763:18:40
03/19/011313432126523:52:35
03/20/011312683120843:45:07
03/22/011110931103643:51:19
03/23/011312547118474:21:14
03/24/011413867131714:57:34
03/26/011211740109144:20:00
05/09/012323000163972:00:00
05/12/0124242342423412:00:00
05/14/01181763517635
05/16/01464638146381
05/18/01212106821068
05/22/01212085220852
05/22/01373666036660
05/24/01484819548195
05/25/0135351833518343May2922:15:372001
05/29/0144440064400645May315:27:472001
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Sheet1
Number of nodes in the largest network component ('000)
Gnutella Network Growth .
Sheet2
Sheet3
Growth invariants (1): avg. node connectivity 3.4 links per node on average
Chart1
71.513
78.63
154.177
118.241
172.744
123.119
67.633
68.119
160.345
59.432
83.637
50.459
31.466
40.414
36.166
31.111
36.245
40.625
30.829
46.533
24.632
22.79
21.147
23.134
18.7
19.413
18.419
14.265
14.833
11.791
15.93
20.06
16.533
22.67
Number of nodes
Number of links ('000)
Sheet1
NodesConnectionsLinear PredictionConnect ('000)
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35183236482241575-2.15118.24
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36660246238251717-2.22123.12
20852135266143175-5.8567.63
21068136238144658-6.1868.12
463813206903184640.69160.35
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16397100918112586-11.5650.46
109146293274938-19.0831.47
131718082890435-11.8940.41
118477233281344-12.4636.17
103646222271162-14.3731.11
120847249082972-14.4636.25
126528125086872-6.9240.63
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142229306697652-4.9346.53
78914926454182-9.9824.63
66744558045825-0.5422.79
596342294409433.1921.15
642846268441366.86625023684.6123.13
513037400352245.8218.70
537038826368725.0319.41
516536838354643.7318.42
389628530267516.2414.27
420729666288862.6314.83
310223582212999.6811.79
3979318602732114.2515.93
4859401203336316.8420.06
4121330662829614.4316.53
5398453403706418.2522.67
Sheet1
71.513
157.26
308.354
236.482
345.488
246.238
135.266
136.238
320.69
118.864
167.274
100.918
62.932
80.828
72.332
62.222
72.49
81.25
61.658
93.066
49.264
45.58
42.294
46.268
37.4
38.826
36.838
28.53
29.666
23.582
31.86
40.12
33.066
45.34
Number of nodes
Number of conections '000)
Node Connectivity .
Sheet2
Sheet3
Growth invariants (2): network diameterNode-to-node distance maintains similar distributionAverage node-to-node distance grew 25% while the network grew 50 times over 6 months
Chart1
0.00245138410.00016952230.00061469050.00028671320.00051364590.0018522330.0021180275
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graph 8 (3102 nodes)
graph 43: 44006 nodes
graph22: (10362 nodes)
graph47? (on detroit) about 20000
graph 23? (on birch)
graph 6? (oak) (4859 nodes)
graph7 ?(on buda)
Node-to-node shortest path (hops)
Percent of node pairs (%)
explainations
46 22787 Thu May 31 19:53:39 2001
45 21728 Thu May 31 05:27:47 2001
43 44006 Tue May 29 22:15:37 2001
41 35183 Fri May 25 17:31:52 2001
40 48195 Thu May 24 15:52:56 2001
38 36660 Tue May 22 23:29:19 2001
37 20852 Tue May 22 04:40:49 2001
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18 14222 Sun Mar 18 19:29:56 2001
17 7891 Fri Mar 16 22:39:55 2001
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14 6428 Sun Mar 11 19:22:54 2001
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7 3979 Thu Mar 1 11:41:47 2001
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May
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May
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Point-to-point
graph 8 (3102 nodes)graph 43: 44006 nodesgraph22: (10362 nodes)graph47? (on detroit) about 20000graph 23? (on birch)graph 6? (oak) (4859 nodes)graph7 ?(on buda)
only 50 nodesafter 920 nodesafter 180 nodesafter 290after 10after 1520
031000.03%500.00%9200.01%1800.00%2900.01%12800.02%15200.03%
1235730.25%3730.02%58610.06%11760.03%18000.05%115200.19%128100.21%
23053213.18%44380.20%510030.53%104520.25%242650.69%1151871.85%1255922.08%
3163543317.01%459612.09%4110814.31%865152.11%2118546.05%92809514.92%94219915.58%
4379040239.42%36668816.67%217383322.80%56571913.79%91630126.15%303423748.79%283730246.91%
5285870029.73%97834244.46%400163541.97%161913039.47%142943540.79%182684029.37%179189829.63%
68774909.13%64699629.40%236406824.79%132319232.26%75670521.59%2816594.53%3125725.17%
71145451.19%1456366.62%4892865.13%42573110.38%1525014.35%199860.32%229910.38%
873780.08%115220.52%355200.37%640001.56%109690.31%7030.01%11510.02%
92540.00%2810.01%15870.02%51270.12%2380.01%130.00%450.00%
1040.00%120.00%840.00%4010.01%20.00%00
11010.00%20.00%340.00%000
1200030.00%000
Sum9616200220030095348804101660350436062195206048080
01280
111520
2115187
3928095
43034237
51826840
6281659
719986
8703
913
Point-to-point
0000000
0000000
0000000
0000000
0000000
0000000
0000000
0000000
0000000
0000000
0000000
0000000
graph 8 (3102 nodes)
graph 43: 44006 nodes
graph22: (10362 nodes)
graph47? (on detroit) about 20000
graph 23? (on birch)
graph 6? (oak) (4859 nodes)
graph7 ?(on buda)
Node-to-node shortest path (hops)
Percent of pairs (%)
Search characteristichs
Traffic.2
PingPongQueryOtherOK : 24.41.86.201 Wed Jun 27 17:19:36 2001
17:20:002400000272780119311414
17:21:00530000048713817193000
17:22:00520000075323464193000
17:23:00510000052015703214000
17:24:00510000048713015193000
17:25:37370000043810823214000
17:26:00530000047413244214000
17:27:00470000038410113214000
17:28:00540000053213590141000
17:29:00520000043210397114000
17:30:0135000002987027141000
17:31:0053000003217340193000
17:32:0041000003919286141000
17:33:00450000040211816189000
17:34:0043000002867066189000
17:35:0040000002947569148000
17:36:00520000049213274229000
17:37:00450000046012683189000
17:38:00470000061017342148000
17:39:00440000042611830141000
17:40:00450000039411250214000
17:41:00470000043312417229000
17:42:02480000048313393214000
17:43:01490000067020571162000
17:44:0049000004089993102000
17:45:00460000044811051148000
17:46:00430000044711944211000
17:47:01460000045412802214000
17:48:00560000058116666172000
17:49:00530000055615904172000
17:50:00530000063219324141000
17:51:00560000064617195107000
17:52:00490000049314976211000
17:53:00470000047913438100000
17:54:00500000058716486214000
17:55:04330000063617031189000
17:56:017900000162442443214000
17:57:00570000085120078148000
17:58:015700000108429135214000
17:59:005600000135038250189000
18:00:00550000085922563186000
18:01:00510000072920681172000
18:02:02620000076621254229000
18:03:00580000087822055172000
18:04:00560000085122107211000
18:05:00550000075217597141000
18:06:00590000087523222214000
18:07:00530000069619578189000
18:08:07350000051914653193000
18:09:03660000078120901141000
18:10:00530000049412070148000
18:11:0044000003628743141000
18:12:0040000003547767162000
18:13:0043000002585954211000
18:14:00440000049110299148000
18:15:0143000003307814102000
18:16:0045000003427776141000
18:17:0046000003567829141000
18:18:0048000003628189141000
18:19:0846000003559015141000
18:20:00480000049814290148000
18:21:0151000003539709192000
18:22:01470000049012101148000
18:23:00530000064717678148000
18:24:00550000052914395148000
18:25:00450000044111528141000
18:26:00540000054213703148000
18:27:00520000058916106214000
18:28:00530000063715764141000
18:29:00550000056513238141000
18:30:00520000059014452193000
18:31:00540000056714841193000
18:32:00470000043311456193000
18:33:01480000058115528141000
18:34:00530000064017163193000
18:35:00540000052013086193000
18:36:00500000048913238193000
18:37:00440000037911477193000
18:38:0142000003279017193000
18:39:00450000036211277193000
18:40:00380000034911036193000
18:41:01470000049814993193000
18:42:0048000002848653193000
18:43:0445000003159382193000
18:44:0035000002979993193000
18:45:003000000265844797000
18:46:0127000002878595189000
18:47:0417000001434684107000
18:48:0110000001193763141000
18:49:0012000001374538141000
18:50:0021000003219991148000
Avgs46.950.00.00.00.00.0512.3013,799.30172.690.010.15
whois
same, diff, undetermined
e inmultit cu 2!
GraphsSame ASDiff ASUndetTotal LinksSameDifTotal
4315012245332480102843495%86%17%
141882391765210436634%90%12%
13916332403244357783%93%9%
121174328344818364173%90%13%
11862322823694349912%92%11%
10652255282350273552%93%9%
9964256443058281373%91%11%
8554214401588227882%94%7%
7742287982320307002%94%8%
6924350464150380452%92%11%
5698299762392318702%94%8%
41176397224442431193%92%10%
151066374183810403893%93%9%
192130520487480579184%90%13%
1831587853611372873804%90%13%
171994410846186461714%89%13%
161244400744262434493%92%10%
Is Gnutella a power-law network?November 2000Power-law networks: the number of links per node follows a power-law distributionExamples: the Internet, in/out links to/from HTML pages, citation network, US power grid, social networks.
Implications: High tolerance to random node failure but low reliability when facing of an intelligent adversary
Chart3
1841427666695271119
1391378273776461113
9087656887786596
4847455761586769
5038294360444541
2827393443544538
2333382838253328
2222322931362532
1112132322312815
1313151514172812
1213202323212516
71316121922167
6714121318218
51216121015139
71210151671414
351396181410
3413585127
4610711121410
61081251179
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12515373
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3811111382
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118118118118118118118118
119119119119119119119119
120120120120120120120120
121121121121121121121121
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123123123123123123123123
124124124124124124124124
125125125125125125125125
126126126126126126126126
127127127127127127127127
128128128128128128128128
129129129129129129129129
130130130130130130130130
131131131131131131131131
132132132132132132132132
133133133133133133133133
134134134134134134134134
135135135135135135135135
136136136136136136136136
137137137137137137137137
138138138138138138138138
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141141141141141141141141
142142142142142142142142
143143143143143143143143
144144144144144144144144
145145145145145145145145
146146146146146146146146
1471471471147147147147
Number of links (log scale)
Num. of nodes (log scale)
tbl
89111718192021114671151514121613
118414275766669527111913713713718914820196109
213913771827377646111391831502111341746796
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9111261323223128151213276926311014
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1112135202323212516111015552820411
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1846610711121410499277952
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41121522111811
4214212362
4331211111
4421322211251
45121113231
46111116311
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481221161
491111262
502251
5112121521
52131211
5312612
5412121232
553141121
56111111711
5712111132
58111
5911115
6012322
6161
621
6311111
641111
6511131
662
671222
68115
69111
70111
71111
7212211
7311
7411
75112
76111
7711
7811
7921
8012
8121
8212
831
8411
8511
86
871
883
89112
90
9112
92
931
941
95
96
972
981
9912
100
10111
102
1031
1041
1051
1061
107
108
109
1101
1111
112
113
114
1151
116
117
1181
1191
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
1361
137
138
139
140
141
142
143
144
145
146
14711
148
149
150
151
152
153
154
155
1561
157
1581
7177183396716367537417588725175511001209510941159448536
tbl
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00000000
00000000
00000000
00000000
00000000
Number of links (log scale)
Num. of nodes (log scale)
Node connectivity distribution .
MBD0011CD50.xls
Chart1
34792233306225362207252227142392
16601113151914801304149115711373
10456928859107729101036805
668538583651585606712633
593504582602508565662611
675555662675525643680599
848627780788641738834758
893600818906694815892806
945597822855687780920686
804555759784642711817622
784473532561517577601472
498303413424373400501356
315191291278279319373246
191102218199188221240174
14375123139134143185132
925297819713013678
6025666154848951
5329503151585126
4628363029343931
2924351822312424
3718242012232310
26111361081812
27142481310164
1718149310113
2371875654
1714941224
1751011343
16818136328
1062322912
11652301230
1431222211
479321125
959331321
1053234343434
4752235235
7510114136
653373737371
28123838383838
358393913939
55711404040
10334141414141
6211424242242
331143434311
959144444444
39104545454545
371464614646
7634747474747
678148484848
53614949491
7275050505050
1585151515151
1545252525252
676535353153
2235454545454
4425555555555
5425656565656
7525757575757
1415858585858
2715959595959
1546060606060
1416161616161
2326262626262
1416363636363
264646464646464
61656565656565
11666666666666
16716767676767
686816868686868
31696969696969
1117070707070
171717171717171
372727272727272
273737373737373
27417474747474
375757575757575
476767676767676
377777777777777
67817878787878
7979797979797979
8080808080808080
181818181818181
182828282828282
383838383838383
284848484848484
8585858585858585
8686868686868686
8787878787878787
8888888888888888
18918989898989
9090909090909090
9191919191919191
9292929292929292
9393939393939393
194949494949494
9595959595959595
9696969696969696
9797979797979797
198989898989898
9999999999999999
100100100100100100100100
101101101101101101101101
1102102102102102102102
103103103103103103103103
104104104104104104104104
105105105105105105105105
106106106106106106106106
107107107107107107107107
108108108108108108108108
109109109109109109109109
110110110110110110110110
111111111111111111111111
112112112112112112112112
113113113113113113113113
114114114114114114114114
115115115115115115115115
116116116116116116116116
117117117117117117117117
118118118118118118118118
119119119119119119119119
120120120120120120120120
121121121121121121121121
122122122122122122122122
123123123123123123123123
124124124124124124124124
125125125125125125125125
126126126126126126126126
127127127127127127127127
128128128128128128128128
129129129129129129129129
130130130130130130130130
131131131131131131131131
132132132132132132132132
133133133133133133133133
134134134134134134134134
135135135135135135135135
136136136136136136136136
137137137137137137137137
138138138138138138138138
139139139139139139139139
140140140140140140140140
141141141141141141141141
142142142142142142142142
143143143143143143143143
144144144144144144144144
145145145145145145145145
146146146146146146146146
147147147147147147147147
148148148148148148148148
149149149149149149149149
150150150150150150150150
151151151151151151151151
152152152152152152152152
153153153153153153153153
1541541154154154154154
155155155155155155155155
156156156156156156156156
1571571571571571157157
158158158158158158158158
159159159159159159159159
160160160160160160160160
161161161161161161161161
162162162162162162162162
163163163163163163163163
164164164164164164164164
165165165165165165165165
1661661661166166166166
167167167167167167167167
168168168168168168168168
169169169169169169169169
170170170170170170170170
171171171171171171171171
172172172172172172172172
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174174174174174174174174
175175175175175175175175
1761761761761176176176
177177177177177177177177
178178178178178178178178
179179179179179179179179
180180180180180180180180
181181181181181181181181
182182182182182182182182
183183183183183183183183
184184184184184184184184
185185185185185185185185
186186186186186186186186
187187187187187187187187
188188188188188188188188
189189189189189189189189
190190190190190190190190
191191191191191191191191
192192192192192192192192
193193193193193193193193
194194194194194194194194
195195195195195195195195
196196196196196196196196
197197197197197197197197
198198198198198198198198
199199199199199199199199
Number of links (log scale)
Number of nodes (log scale)
Node connectivity distribution .
Sheet1
1422895881266112082103681186013174109271640627110
18192021222324253031
13479223330622536220725222714239236605760
21660111315191480130414911571137317032900
31045692885910772910103680511511900
46685385836515856067126339081509
55935045826025085656626119571547
66755556626755256436805999951658
784862778078864173883475811161970
889360081890669481589280611922016
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50727
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542231
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56542
577521
58141
59271
60154
61141
62232
63141
642
6561
6611
6711
6811
6931
70111
711
723
732
7421
753
764
773
7861
79
80
811
821
833
842
85
86
87
88
8911
90
91
92
93
941
95
96
97
981
99
100
101
1021
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
1541
155
156
1571
158
159
160
161
162
163
164
165
1661
167
168
169
170
171
172
173
174
175
1761
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
Sheet1
3242412532314717578391121116911721496143317061676
427299307299266413327511484498657599763896
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111325
11123332
238521
212531
23111421
122211
131132
12211412
241255
11122
1112
11211
111221
62212
11112
31111
212
111
1213
31223
2221
14512
1312
212
11211
12
12
1
221
12221
1
12
21
11
1
21
11
2
12
1
1
1
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
t
Number of links (log scale)
Number of nodes (log scale)
Node connectivity distribution
Is Gnutella a power-law network? Later, larger networks display a bimodal distribution Implications: High tolerance to random node failures preservedIncreased reliability when facing an attack.May 2001
Chart1
34792233306225362207252227142392
16601113151914801304149115711373
10456928859107729101036805
668538583651585606712633
593504582602508565662611
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315191291278279319373246
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5329503151585126
4628363029343931
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3718242012232310
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27142481310164
1718149310113
2371875654
1714941224
1751011343
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1062322912
11652301230
1431222211
479321125
959331321
1053234343434
4752235235
7510114136
653373737371
28123838383838
358393913939
55711404040
10334141414141
6211424242242
331143434311
959144444444
39104545454545
371464614646
7634747474747
678148484848
53614949491
7275050505050
1585151515151
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2235454545454
4425555555555
5425656565656
7525757575757
1415858585858
2715959595959
1546060606060
1416161616161
2326262626262
1416363636363
264646464646464
61656565656565
11666666666666
16716767676767
686816868686868
31696969696969
1117070707070
171717171717171
372727272727272
273737373737373
27417474747474
375757575757575
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377777777777777
67817878787878
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8080808080808080
181818181818181
182828282828282
383838383838383
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8585858585858585
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9191919191919191
9292929292929292
9393939393939393
194949494949494
9595959595959595
9696969696969696
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198989898989898
9999999999999999
100100100100100100100100
101101101101101101101101
1102102102102102102102
103103103103103103103103
104104104104104104104104
105105105105105105105105
106106106106106106106106
107107107107107107107107
108108108108108108108108
109109109109109109109109
110110110110110110110110
111111111111111111111111
112112112112112112112112
113113113113113113113113
114114114114114114114114
115115115115115115115115
116116116116116116116116
117117117117117117117117
118118118118118118118118
119119119119119119119119
120120120120120120120120
121121121121121121121121
122122122122122122122122
123123123123123123123123
124124124124124124124124
125125125125125125125125
126126126126126126126126
127127127127127127127127
128128128128128128128128
129129129129129129129129
130130130130130130130130
131131131131131131131131
132132132132132132132132
133133133133133133133133
134134134134134134134134
135135135135135135135135
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137137137137137137137137
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139139139139139139139139
140140140140140140140140
141141141141141141141141
142142142142142142142142
143143143143143143143143
144144144144144144144144
145145145145145145145145
146146146146146146146146
147147147147147147147147
148148148148148148148148
149149149149149149149149
150150150150150150150150
151151151151151151151151
152152152152152152152152
153153153153153153153153
1541541154154154154154
155155155155155155155155
156156156156156156156156
1571571571571571157157
158158158158158158158158
159159159159159159159159
160160160160160160160160
161161161161161161161161
162162162162162162162162
163163163163163163163163
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165165165165165165165165
1661661661166166166166
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168168168168168168168168
169169169169169169169169
170170170170170170170170
171171171171171171171171
172172172172172172172172
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174174174174174174174174
175175175175175175175175
1761761761761176176176
177177177177177177177177
178178178178178178178178
179179179179179179179179
180180180180180180180180
181181181181181181181181
182182182182182182182182
183183183183183183183183
184184184184184184184184
185185185185185185185185
186186186186186186186186
187187187187187187187187
188188188188188188188188
189189189189189189189189
190190190190190190190190
191191191191191191191191
192192192192192192192192
193193193193193193193193
194194194194194194194194
195195195195195195195195
196196196196196196196196
197197197197197197197197
198198198198198198198198
199199199199199199199199
Number of links (log scale)
Number of nodes (log scale)
Sheet1
1422895881266112082103681186013174109271640627110
18192021222324253031
13479223330622536220725222714239236605760
21660111315191480130414911571137317032900
31045692885910772910103680511511900
46685385836515856067126339081509
55935045826025085656626119571547
66755556626755256436805999951658
784862778078864173883475811161970
889360081890669481589280611922016
994559782285568778092068611201961
108045557597846427118176228771572
117844735325615175776014726711164
12498303413424373400501356445802
13315191291278279319373246359563
14191102218199188221240174253355
1514375123139134143185132185263
16925297819713013678170208
176025666154848951105156
185329503151585126106133
19462836302934393192105
2029243518223124247497
2137182420122323106481
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50727
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542231
55442
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577521
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59271
60154
61141
62232
63141
642
6561
6611
6711
6811
6931
70111
711
723
732
7421
753
764
773
7861
79
80
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8911
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1021
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