Club Certificate2025
PAMELAITA-PAME7
FEDERAZIONE ITALIANA VELA
Distr.:UVAI  www.uvai.it
Tel. + 39068841273
E-mail  segreteria@uvai.it
Rated boat velocities in knots
Wind Velocity 4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Beat Angles42.7°42.7°40.8°38.0°37.4°37.5°37.8°38.8°41.5°
Beat VMG2.323.163.764.104.224.254.254.214.04
52°3.634.775.455.725.855.905.935.965.89
60°3.874.985.595.856.006.076.126.186.14
75°3.995.095.675.976.176.336.426.556.61
90°3.855.035.726.026.236.476.666.927.10
110°3.915.095.806.206.526.797.017.397.76
120°3.744.945.706.146.546.917.297.988.76
135°3.284.465.345.916.316.717.178.6510.77
150°2.643.764.755.515.996.366.747.7110.07
Run VMG2.283.264.124.835.455.866.206.898.73
Gybe Angles147.6°147.6°152.1°158.6°166.0°174.5°176.3°170.3°146.2°
APH ToD:653.6CDL: 6.063APH ToT: 0.9180CertNo:25/1
BOAT
ClassMalù 7DesignerBuilderCantieri MaraiAge date01/1990Series date01/1981Offset filePAMELACL.OFFData filePAME7
HULL
Length Overall7.320 mMaximum Beam2.500 mDraft1.236 mDisplacement1,100 kgDLR6.5567IMS DivisionSportboatDynamic Allowance0.000%Age Allowance0.487%
PROPELLER
InstallationNo PropellerTypeN/ADiameterN/A
CREW
Maximum weight350 kg(declared)Minimum weight220 kg ✱ when appliedNon Manual PowerCrew Arm Extension
SAIL AREAS (m²)
MeasuredRatedMainsail14.9115.15Headsail Luffed14.9914.99Headsail FlyingSymmetric41.4141.41Asymmetric
STORM SAIL AREAS (m²)
Trysail4.49Storm Jib3.85Heavy Weather Jib10.40
SAIL LIMITS
Headsails5Spinnakers4
STABILITY
Righting MomentN/AStability IndexN/A
The owner and any other person in charge is responsible that boat is complying with her certificate in accordance with RRS 78.1 and ORC Rule 304.
Club Certificate2025
PAMELAITA-PAME7
FEDERAZIONE ITALIANA VELA
Distr.:UVAI  www.uvai.it
Tel. + 39068841273
E-mail  segreteria@uvai.it
Time Allowances in secs/NM
Wind Velocity 4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Beat VMG1548.91140.6957.3877.0854.1847.8846.2854.4891.7
52°991.1755.0660.9629.2615.6610.2606.7604.5610.8
60°931.4722.4644.4615.9600.5593.1588.2582.8586.1
75°902.3706.6635.5603.5583.0568.8560.4549.4545.0
90°935.1716.1629.8597.6577.5556.8540.9520.5507.3
110°921.7706.8620.7580.7551.8530.2513.9487.3464.2
120°962.8728.8631.3586.5550.9520.6494.0451.1411.2
135°1098.5806.8674.2608.7570.6536.6502.1416.2334.3
150°1366.1957.2758.6653.3600.7565.9534.5466.7357.3
Run VMG1580.21105.2874.3744.8661.1614.6580.6522.3412.6
Selected Courses
Windward / Leeward1562.81122.9915.8810.9757.6731.2713.4688.4652.1
All purpose1175.2869.8733.6669.6636.5616.0600.1573.0545.8
Single Number Scoring Options
CourseTime On
Distance
Time On
Time
Windward / Leeward789.20.7603
All purpose653.60.9180
 
Custom scoring options for Australia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low801.70.7484
Triple Number Coastal/Long Distance Medium650.50.9224
Triple Number Coastal/Long Distance High593.91.0103
Triple Number Windward/Leeward Low1019.40.5886
Triple Number Windward/Leeward Medium782.00.7673
Triple Number Windward/Leeward High708.50.8469
Custom scoring options for Austria
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance705.70.8502
Triple Number Coastal/Long Distance Low801.70.7484
Triple Number Coastal/Long Distance Medium650.50.9224
Triple Number Coastal/Long Distance High593.91.0103
Triple Number Windward/Leeward Low1019.40.5886
Triple Number Windward/Leeward Medium782.00.7673
Triple Number Windward/Leeward High708.50.8469
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1652.21121.1865.9742.1676.0638.2605.1546.9516.9
Custom scoring options for Brazil
Scoring OptionTime On
Time
Upwind "bolina"0.6586
Downwind "popa"0.8231
70% up, 30% down "Ilhabela"0.7006
30% up, 70% down "Ilhabela-inverso"0.7657
Custom scoring options for Bulgaria
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low801.70.7484
Triple Number Coastal/Long Distance Medium650.50.9224
Triple Number Coastal/Long Distance High593.91.0103
Triple Number Windward/Leeward Low1019.40.5886
Triple Number Windward/Leeward Medium782.00.7673
Triple Number Windward/Leeward High708.50.8469
Predominantly Upwind708.30.8471
Predominantly Downwind654.30.9170
Custom scoring options for Canada
Scoring OptionTODTOT
Triple Number AP Low801.70.7484
Triple Number AP Medium650.60.9223
Triple Number AP High593.91.0103
Triple Number Windward/Leeward Low1063.40.5642
Triple Number Windward/Leeward Medium782.00.7673
Triple Number Windward/Leeward High708.50.8469
Single Number Predominant Upwind732.70.8189
Single Number Predominant Reaching647.10.9272
Single Number Predominant Downwind677.80.8852
Predominant Upwind - Low950.60.6312
Predominant Upwind - Low/Med756.50.7932
Predominant Upwind - Medium691.70.8675
Predominant Upwind - Med/High661.20.9074
Predominant Upwind - High646.20.9284
Predominant Downwind Low956.10.6275
Predominant Downwind Low/Med729.80.8221
Predominant Downwind Medium636.40.9427
Predominant Downwind Med/High572.61.0479
Predominant Downwind High519.71.1545
Predominant Reaching Low853.10.7033
Predominant Reaching Low/Med680.40.8819
Predominant Reaching Medium615.60.9746
Predominant Reaching Med/High570.11.0524
Predominant Reaching High533.91.1239
SA/DSPL Upwind28.06SA/DSPL Downwind52.85
Scoring OptionTODTOT
5-Band Windward/Leeward Low1181.50.5078
5-Band Windward/Leeward Low/Med886.00.6772
5-Band Windward/Leeward Medium771.50.7777
5-Band Windward/Leeward Med/High715.90.8381
5-Band Windward/Leeward High686.40.8741
Windward/Leeward 60-40 Low1184.60.5065
Windward/Leeward 60-40 Low/Med896.90.6690
Windward/Leeward 60-40 Medium790.20.7593
Windward/Leeward 60-40 Med/High742.40.8082
Windward/Leeward 60-40 High721.00.8321
5-Band AP Low875.50.6853
5-Band AP Low/Med716.80.8371
5-Band AP Medium643.60.9323
5-Band AP Med/High601.20.9980
5-Band AP High572.91.0472
5-Band SF Bay Tour - Low1022.60.5868
5-Band SF Bay Tour - Low/Med851.00.7050
5-Band SF Bay Tour - Medium750.50.7995
5-Band SF Bay Tour - Med/High700.50.8566
5-Band SF Bay Tour - High671.40.8937
Chicago-Mac Upwind0.7998
Chicago-Mac All Purpose0.8291
Chicago-Mac Downwind0.8554
Bayview-Mac Cove Island0.6280
Bayview-Mac Shore0.6325
Harvest Moon Regatta571.21.0504
Custom scoring options for Cyprus
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance705.70.8502
Triple Number Coastal/Long Distance Low801.70.7484
Triple Number Coastal/Long Distance Medium650.50.9224
Triple Number Coastal/Long Distance High593.91.0103
Triple Number Windward/Leeward Low1019.40.5886
Triple Number Windward/Leeward Medium782.00.7673
Triple Number Windward/Leeward High708.50.8469
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1652.21121.1865.9742.1676.0638.2605.1546.9516.9
Custom scoring options for Denmark
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance705.70.8502
Triple Number Coastal/Long Distance Low801.70.7484
Triple Number Coastal/Long Distance Medium650.50.9224
Triple Number Coastal/Long Distance High593.91.0103
Triple Number Windward/Leeward Low1019.40.5886
Triple Number Windward/Leeward Medium782.00.7673
Triple Number Windward/Leeward High708.50.8469
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1652.21121.1865.9742.1676.0638.2605.1546.9516.9
Custom scoring options for Spain
Scoring OptionTime On
Distance
Coastal/Long Distance705.7
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1652.21121.1865.9742.1676.0638.2605.1546.9516.9
Custom scoring options for Estonia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low801.70.7484
Triple Number Coastal/Long Distance Medium650.50.9224
Triple Number Coastal/Long Distance High593.91.0103
Triple Number Windward/Leeward Low1019.40.5886
Triple Number Windward/Leeward Medium782.00.7673
Triple Number Windward/Leeward High708.50.8469
Custom scoring options for Finland
Scoring OptionTime On
Distance
Time On
Time
FinRating705.70.8502
FinRating, kevyt tuuli1160.00.8621
FinRating, kova tuuli573.80.8714
Custom scoring options for France
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low801.70.7484
Triple Number Coastal/Long Distance Medium650.50.9224
Triple Number Coastal/Long Distance High593.91.0103
Triple Number Windward/Leeward Low1019.40.5886
Triple Number Windward/Leeward Medium782.00.7673
Triple Number Windward/Leeward High708.50.8469
Custom scoring options for Germany
Scoring OptionTime On
Time
Coastal/Long Distance0.8502
Triple Number Coastal/Long Distance Low0.7484
Triple Number Coastal/Long Distance Medium0.9224
Triple Number Coastal/Long Distance High1.0103
Triple Number Windward/Leeward Low0.5886
Triple Number Windward/Leeward Medium0.7673
Triple Number Windward/Leeward High0.8469
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1652.21121.1865.9742.1676.0638.2605.1546.9516.9
For information
General Purpose Handicap (GPH)724.8
Custom scoring options for Greece
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance705.70.8502
Triple Number Coastal/Long Distance Low801.70.7484
Triple Number Coastal/Long Distance Medium650.50.9224
Triple Number Coastal/Long Distance High593.91.0103
Triple Number Windward/Leeward Low1019.40.5886
Triple Number Windward/Leeward Medium782.00.7673
Triple Number Windward/Leeward High708.50.8469
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1652.21121.1865.9742.1676.0638.2605.1546.9516.9
Custom scoring options for Hungary
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low801.70.7484
Triple Number Coastal/Long Distance Medium650.50.9224
Triple Number Coastal/Long Distance High593.91.0103
Triple Number Windward/Leeward Low1019.40.5886
Triple Number Windward/Leeward Medium782.00.7673
Triple Number Windward/Leeward High708.50.8469
Custom scoring options for Israel
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance705.70.8502
Triple Number Coastal/Long Distance Low801.70.7484
Triple Number Coastal/Long Distance Medium650.50.9224
Triple Number Coastal/Long Distance High593.91.0103
Triple Number Windward/Leeward Low1019.40.5886
Triple Number Windward/Leeward Medium782.00.7673
Triple Number Windward/Leeward High708.50.8469
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1652.21121.1865.9742.1676.0638.2605.1546.9516.9
Custom scoring options for Japan
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance705.70.8502
Triple Number Coastal/Long Distance Low801.70.7484
Triple Number Coastal/Long Distance Medium650.50.9224
Triple Number Coastal/Long Distance High593.91.0103
Triple Number Windward/Leeward Low1019.40.5886
Triple Number Windward/Leeward Medium782.00.7673
Triple Number Windward/Leeward High708.50.8469
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1652.21121.1865.9742.1676.0638.2605.1546.9516.9
Custom scoring options for Korea
Scoring OptionTime On
Distance
Triple Number Coastal/Long Distance Low801.7
Triple Number Coastal/Long Distance Medium650.5
Triple Number Coastal/Long Distance High593.9
Triple Number Windward/Leeward Low1019.4
Triple Number Windward/Leeward Medium782.0
Triple Number Windward/Leeward High708.5
Predominantly Upwind708.3
Predominantly Downwind654.3
Predominantly Reaching634.5
Custom scoring options for Lithuania
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance705.70.8502
Triple Number Coastal/Long Distance Low801.70.7484
Triple Number Coastal/Long Distance Medium650.50.9224
Triple Number Coastal/Long Distance High593.91.0103
Triple Number Windward/Leeward Low1019.40.5886
Triple Number Windward/Leeward Medium782.00.7673
Triple Number Windward/Leeward High708.50.8469
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1652.21121.1865.9742.1676.0638.2605.1546.9516.9
Custom scoring options for Netherlands
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.7484
Triple Number Coastal/Long Distance Medium0.9224
Triple Number Coastal/Long Distance High1.0103
Triple Number Windward/Leeward Low0.5886
Triple Number Windward/Leeward Medium0.7673
Triple Number Windward/Leeward High0.8469
Coastal/Long Distance0.8502
Predominantly Upwind0.8471
Predominantly Downwind0.9170
For information
General Purpose Handicap (GPH)724.8
Custom scoring options for Norway
Scoring OptionTime On
Time
Distanseseilas Singeltall  (APH)0.9180
Distanseseilas Trippeltall svak vind0.7484
Distanseseilas Trippeltall mellomvind0.9224
Distanseseilas Trippeltall sterk vind1.0103
Pølsebane Trippeltall svak vind0.5886
Pølsebane Trippeltall mellomvind0.7673
Pølsebane Trippeltall sterk vind0.8469
Motvind Singeltall0.8471
Medvind Singeltall0.9170
Custom scoring options for Portugal
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low801.70.7484
Triple Number Coastal/Long Distance Medium650.50.9224
Triple Number Coastal/Long Distance High593.91.0103
Triple Number Windward/Leeward Low1019.40.5886
Triple Number Windward/Leeward Medium782.00.7673
Triple Number Windward/Leeward High708.50.8469
Coastal/Long Distance705.70.8502
Custom scoring options for Russia
Scoring OptionTime On
Distance
Time On
Time
Predominantly Upwind708.30.8471
Predominantly Downwind654.30.9170
Custom scoring options for South Africa
Scoring OptionTime On
Distance
Time On
Time
Cape Doctor Inshore663.00.9050
Cape Doctor Coastal554.01.0831
Triple Number Coastal/Long Distance Low801.70.7484
Triple Number Coastal/Long Distance Medium650.50.9224
Triple Number Coastal/Long Distance High593.91.0103
Triple Number Windward/Leeward Low1019.40.5886
Triple Number Windward/Leeward Medium782.00.7673
Triple Number Windward/Leeward High708.50.8469
Custom scoring options for Slovenia
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.7484
Triple Number Coastal/Long Distance Medium0.9224
Triple Number Coastal/Long Distance High1.0103
Triple Number Windward/Leeward Low0.5886
Triple Number Windward/Leeward Medium0.7673
Triple Number Windward/Leeward High0.8469
Custom scoring options for Switzerland
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.7484
Triple Number Coastal/Long Distance Medium0.9224
Triple Number Coastal/Long Distance High1.0103
Triple Number Windward/Leeward Low0.5886
Triple Number Windward/Leeward Medium0.7673
Triple Number Windward/Leeward High0.8469
Custom scoring options for Sweden
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance705.70.8502
Triple Number Coastal/Long Distance Low801.70.7484
Triple Number Coastal/Long Distance Medium650.50.9224
Triple Number Coastal/Long Distance High593.91.0103
Triple Number Windward/Leeward Low1019.40.5886
Triple Number Windward/Leeward Medium782.00.7673
Triple Number Windward/Leeward High708.50.8469
Predominantly Upwind708.30.8471
Predominantly Downwind654.30.9170
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1652.21121.1865.9742.1676.0638.2605.1546.9516.9
Custom scoring options for Ukraine
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance705.70.8502
Triple Number Coastal/Long Distance Low801.70.7484
Triple Number Coastal/Long Distance Medium650.50.9224
Triple Number Coastal/Long Distance High593.91.0103
Triple Number Windward/Leeward Low1019.40.5886
Triple Number Windward/Leeward Medium782.00.7673
Triple Number Windward/Leeward High708.50.8469
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1652.21121.1865.9742.1676.0638.2605.1546.9516.9
Custom scoring options for United States of America
Scoring OptionTODTOT
Triple Number AP Low801.70.7484
Triple Number AP Medium650.60.9223
Triple Number AP High593.91.0103
Triple Number Windward/Leeward Low1063.40.5642
Triple Number Windward/Leeward Medium782.00.7673
Triple Number Windward/Leeward High708.50.8469
Single Number Predominant Upwind732.70.8189
Single Number Predominant Reaching647.10.9272
Single Number Predominant Downwind677.80.8852
Predominant Upwind - Low950.60.6312
Predominant Upwind - Low/Med756.50.7932
Predominant Upwind - Medium691.70.8675
Predominant Upwind - Med/High661.20.9074
Predominant Upwind - High646.20.9284
Predominant Downwind Low956.10.6275
Predominant Downwind Low/Med729.80.8221
Predominant Downwind Medium636.40.9427
Predominant Downwind Med/High572.61.0479
Predominant Downwind High519.71.1545
Predominant Reaching Low853.10.7033
Predominant Reaching Low/Med680.40.8819
Predominant Reaching Medium615.60.9746
Predominant Reaching Med/High570.11.0524
Predominant Reaching High533.91.1239
SA/DSPL Upwind28.06SA/DSPL Downwind52.85
Scoring OptionTODTOT
5-Band Windward/Leeward Low1181.50.5078
5-Band Windward/Leeward Low/Med886.00.6772
5-Band Windward/Leeward Medium771.50.7777
5-Band Windward/Leeward Med/High715.90.8381
5-Band Windward/Leeward High686.40.8741
Windward/Leeward 60-40 Low1184.60.5065
Windward/Leeward 60-40 Low/Med896.90.6690
Windward/Leeward 60-40 Medium790.20.7593
Windward/Leeward 60-40 Med/High742.40.8082
Windward/Leeward 60-40 High721.00.8321
5-Band AP Low875.50.6853
5-Band AP Low/Med716.80.8371
5-Band AP Medium643.60.9323
5-Band AP Med/High601.20.9980
5-Band AP High572.91.0472
5-Band SF Bay Tour - Low1022.60.5868
5-Band SF Bay Tour - Low/Med851.00.7050
5-Band SF Bay Tour - Medium750.50.7995
5-Band SF Bay Tour - Med/High700.50.8566
5-Band SF Bay Tour - High671.40.8937
Chicago-Mac Upwind0.7998
Chicago-Mac All Purpose0.8291
Chicago-Mac Downwind0.8554
Bayview-Mac Cove Island0.6280
Bayview-Mac Shore0.6325
Harvest Moon Regatta571.21.0504
Club Certificate2025
PAMELAITA-PAME7
FEDERAZIONE ITALIANA VELA
Distr.:UVAI  www.uvai.it
Tel. + 39068841273
E-mail  segreteria@uvai.it
Data in meters/kilograms (Metric)
HULL AND APPENDAGES (Lightship Trim)
ClassMalù 7Measurement01/01/1990HINPlan reviewHull constructionCoredCarbon rudderNoLight stanchionsNoTrim tabNo
LOA7.320Max. Beam2.500Draft1.236Displacement1,100Wetted area8.84IMS L6.012LSM05.514Acc. length7.319Sink (kg/mm) 6.63
VCGD-0.075VCGM0.000RM Rated (kg·m) 16.2Limit of positive stability(°) N/AStability IndexN/ADefault crew weight295Declared crew weight350
PROPELLER
Propeller TypeNo Propeller
Hydro generatorNo
RIG
Forestay tensionAftInner stayNone FittedMast materialAluminumSingle headsail furlerNoMainsail furlerNoArticulated bowspritNoNon-circular riggingNoFiber riggingNoAdjustable mast footNoRunning backstays0Checkstays0Spreaders1Rotating mastNo
P8.550IG8.700ISP8.780MDT10.075MDL10.110MDT20.075MDL20.070TL1.150MW0.110GO0.130
E3.000J2.400BAS1.380FSD0.035SFJ0.070SPL2.780WPLTPSBD0.100MWTMCG
Flying Headsail Foretriangles IdISPTPS
FLOTATION AND STABILITY
Calculation methodVCG entered directlyVCG entered-0.075Flotation Date23/07/2025
BALLAST
TANKS
INVENTORY
INVENTORY
Fixed Ballast Total0
Total deductible
Total deductible
Club Certificate2025
PAMELAITA-PAME7
FEDERAZIONE ITALIANA VELA
Distr.:UVAI  www.uvai.it
Tel. + 39068841273
E-mail  segreteria@uvai.it
MAINSAIL
IdMHBMUWMTWMHWMQWAreaMeas.DateCommentORC0.130.570.971.852.5814.91* Copied from legacy *
HEADSAIL
IdHHBHUWHTWHHWHQWHLPHLUBtnFlyingFTAreaMeas.DateCommentA0.050.000.000.000.003.428.65NoNo 14.99
SYMMETRIC SPINNAKER
IdSLUSLESLSHWSFLAreaMeas.DateCommentORC9.109.109.105.505.3041.41* Copied from legacy *
CRUISER/RACER REQUIREMENTS*
Accommodation length7.3 mTable area0.22 m²Headroom1.40 mMinimum number of berths2Personal gear stowage0.08 m³Fresh water capacity13 lMinimum number of seats in cockpit2Food stowage0.12 m³Fuel capacity20 lCabin soleStovesSinksGalley gear stowageToiletWash basinNavigation areaHanging locker
*This list is a summary of the requirements. See IMS Appendix 1 for details.