Club Certificate2025
KING for ONE dayNOR 3410
Norges Seilforbund
Sognsveien 73
0854 OSLO
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 Angles41.9°41.9°40.1°38.2°38.2°38.2°38.3°39.2°42.0°
Beat VMG2.503.394.024.364.474.524.544.514.33
52°3.905.105.806.136.286.356.396.426.36
60°4.145.325.966.276.446.546.596.666.64
75°4.275.456.066.396.636.806.927.067.12
90°4.145.356.046.456.716.947.147.437.61
110°3.925.226.076.526.897.217.497.878.19
120°3.725.035.936.426.817.197.558.328.91
135°3.244.505.496.166.576.947.328.2910.04
150°2.663.814.835.686.246.626.987.759.08
Run VMG2.293.304.194.975.646.136.507.177.93
Gybe Angles146.9°146.9°151.9°155.6°164.6°173.6°178.1°178.1°167.6°
APH ToD:619.2CDL: 6.971APH ToT: 0.9689CertNo:5719
BOAT
Class1/2 TON ONE OFFDesignerBerretBuilderBeneteauAge date01/1980Series date01/1980Offset filefrstsevo.OFFData file5719
HULL
Length Overall9.190 mMaximum Beam3.230 mDraft1.634 mDisplacement2,321 kgDLR7.3021IMS DivisionCruiser/RacerDynamic Allowance0.000%Age Allowance0.487%
PROPELLER
InstallationShaft exposedTypeFolding 2 bladesDiameter0.340m
CREW
Maximum weight399 kg(default)Minimum weight269 kg ✱ when appliedNon Manual PowerNoCrew Arm Extension
SAIL AREAS (m²)
MeasuredRatedMainsail27.5628.21Headsail Luffed22.3722.37Headsail FlyingSymmetric49.7149.71Asymmetric
STORM SAIL AREAS (m²)
Trysail7.97Storm Jib5.32Heavy Weather Jib14.34
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
KING for ONE dayNOR 3410
Norges Seilforbund
Sognsveien 73
0854 OSLO
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 VMG1438.31061.8895.2826.4804.8796.1792.4797.6832.2
52°922.9706.4620.3587.2573.2567.1563.5561.0566.3
60°869.1676.2604.1574.2558.6550.9546.0540.6542.3
75°842.3660.1593.8563.2543.1529.1520.6510.2505.9
90°869.3672.9596.0558.5536.8518.8504.0484.8473.1
110°917.3689.0592.7552.1522.8499.4480.7457.6439.4
120°967.4716.3606.7560.4528.6501.0476.6432.7404.2
135°1110.8800.4655.4584.7548.3518.8491.7434.5358.5
150°1355.8945.9744.7633.3576.7543.7516.1464.5396.6
Run VMG1569.01092.2858.6724.8638.6587.6553.4502.0453.7
Selected Courses
Windward / Leeward1501.71077.0876.9775.6721.7691.8672.9649.8642.9
All purpose1129.1832.5699.1635.4602.0581.2565.9543.5528.1
Single Number Scoring Options
CourseTime On
Distance
Time On
Time
Windward / Leeward751.30.7986
All purpose619.20.9689
 
Custom scoring options for Australia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low765.80.7835
Triple Number Coastal/Long Distance Medium616.00.9740
Triple Number Coastal/Long Distance High561.31.0689
Triple Number Windward/Leeward Low976.90.6142
Triple Number Windward/Leeward Medium745.20.8052
Triple Number Windward/Leeward High669.00.8969
Custom scoring options for Austria
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance670.40.8951
Triple Number Coastal/Long Distance Low765.80.7835
Triple Number Coastal/Long Distance Medium616.00.9740
Triple Number Coastal/Long Distance High561.31.0689
Triple Number Windward/Leeward Low976.90.6142
Triple Number Windward/Leeward Medium745.20.8052
Triple Number Windward/Leeward High669.00.8969
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1596.91078.5829.1707.2640.5603.0571.3516.7499.5
Custom scoring options for Brazil
Scoring OptionTime On
Time
Upwind "bolina"0.7030
Downwind "popa"0.8473
70% up, 30% down "Ilhabela"0.7409
30% up, 70% down "Ilhabela-inverso"0.7981
Custom scoring options for Bulgaria
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low765.80.7835
Triple Number Coastal/Long Distance Medium616.00.9740
Triple Number Coastal/Long Distance High561.31.0689
Triple Number Windward/Leeward Low976.90.6142
Triple Number Windward/Leeward Medium745.20.8052
Triple Number Windward/Leeward High669.00.8969
Predominantly Upwind667.20.8992
Predominantly Downwind626.60.9575
Custom scoring options for Canada
Scoring OptionTODTOT
Triple Number AP Low765.80.7835
Triple Number AP Medium616.10.9739
Triple Number AP High561.41.0689
Triple Number Windward/Leeward Low1019.50.5885
Triple Number Windward/Leeward Medium745.20.8052
Triple Number Windward/Leeward High669.00.8969
Single Number Predominant Upwind690.20.8694
Single Number Predominant Reaching614.30.9767
Single Number Predominant Downwind651.90.9204
Predominant Upwind - Low898.10.6681
Predominant Upwind - Low/Med714.00.8403
Predominant Upwind - Medium650.90.9218
Predominant Upwind - Med/High620.90.9664
Predominant Upwind - High608.60.9858
Predominant Downwind Low931.00.6445
Predominant Downwind Low/Med702.50.8541
Predominant Downwind Medium607.60.9876
Predominant Downwind Med/High547.11.0967
Predominant Downwind High506.41.1848
Predominant Reaching Low817.10.7343
Predominant Reaching Low/Med646.70.9277
Predominant Reaching Medium581.51.0318
Predominant Reaching Med/High539.71.1117
Predominant Reaching High511.11.1739
SA/DSPL Upwind28.40SA/DSPL Downwind43.95
Scoring OptionTODTOT
5-Band Windward/Leeward Low1133.60.5293
5-Band Windward/Leeward Low/Med847.70.7078
5-Band Windward/Leeward Medium734.50.8169
5-Band Windward/Leeward Med/High676.30.8872
5-Band Windward/Leeward High652.60.9194
Windward/Leeward 60-40 Low1129.80.5311
Windward/Leeward 60-40 Low/Med854.60.7021
Windward/Leeward 60-40 Medium750.20.7997
Windward/Leeward 60-40 Med/High700.00.8571
Windward/Leeward 60-40 High682.60.8789
5-Band AP Low841.90.7127
5-Band AP Low/Med682.00.8798
5-Band AP Medium609.10.9850
5-Band AP Med/High567.81.0568
5-Band AP High544.71.1014
5-Band SF Bay Tour - Low978.50.6132
5-Band SF Bay Tour - Low/Med812.40.7386
5-Band SF Bay Tour - Medium713.50.8410
5-Band SF Bay Tour - Med/High663.10.9048
5-Band SF Bay Tour - High640.20.9373
Chicago-Mac Upwind0.8484
Chicago-Mac All Purpose0.8716
Chicago-Mac Downwind0.8893
Bayview-Mac Cove Island0.6561
Bayview-Mac Shore0.6618
Harvest Moon Regatta541.61.1078
Custom scoring options for Cyprus
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance670.40.8951
Triple Number Coastal/Long Distance Low765.80.7835
Triple Number Coastal/Long Distance Medium616.00.9740
Triple Number Coastal/Long Distance High561.31.0689
Triple Number Windward/Leeward Low976.90.6142
Triple Number Windward/Leeward Medium745.20.8052
Triple Number Windward/Leeward High669.00.8969
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1596.91078.5829.1707.2640.5603.0571.3516.7499.5
Custom scoring options for Denmark
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance670.40.8951
Triple Number Coastal/Long Distance Low765.80.7835
Triple Number Coastal/Long Distance Medium616.00.9740
Triple Number Coastal/Long Distance High561.31.0689
Triple Number Windward/Leeward Low976.90.6142
Triple Number Windward/Leeward Medium745.20.8052
Triple Number Windward/Leeward High669.00.8969
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1596.91078.5829.1707.2640.5603.0571.3516.7499.5
Custom scoring options for Spain
Scoring OptionTime On
Distance
Coastal/Long Distance670.4
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1596.91078.5829.1707.2640.5603.0571.3516.7499.5
Custom scoring options for Estonia
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low765.80.7835
Triple Number Coastal/Long Distance Medium616.00.9740
Triple Number Coastal/Long Distance High561.31.0689
Triple Number Windward/Leeward Low976.90.6142
Triple Number Windward/Leeward Medium745.20.8052
Triple Number Windward/Leeward High669.00.8969
Custom scoring options for Finland
Scoring OptionTime On
Distance
Time On
Time
FinRating664.00.9037
FinRating, kevyt tuuli1114.10.8976
FinRating, kova tuuli547.20.9137
Custom scoring options for France
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low765.80.7835
Triple Number Coastal/Long Distance Medium616.00.9740
Triple Number Coastal/Long Distance High561.31.0689
Triple Number Windward/Leeward Low976.90.6142
Triple Number Windward/Leeward Medium745.20.8052
Triple Number Windward/Leeward High669.00.8969
Custom scoring options for Germany
Scoring OptionTime On
Time
Coastal/Long Distance0.8951
Triple Number Coastal/Long Distance Low0.7835
Triple Number Coastal/Long Distance Medium0.9740
Triple Number Coastal/Long Distance High1.0689
Triple Number Windward/Leeward Low0.6142
Triple Number Windward/Leeward Medium0.8052
Triple Number Windward/Leeward High0.8969
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1596.91078.5829.1707.2640.5603.0571.3516.7499.5
For information
General Purpose Handicap (GPH)688.2
Custom scoring options for Greece
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance670.40.8951
Triple Number Coastal/Long Distance Low765.80.7835
Triple Number Coastal/Long Distance Medium616.00.9740
Triple Number Coastal/Long Distance High561.31.0689
Triple Number Windward/Leeward Low976.90.6142
Triple Number Windward/Leeward Medium745.20.8052
Triple Number Windward/Leeward High669.00.8969
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1596.91078.5829.1707.2640.5603.0571.3516.7499.5
Custom scoring options for Hungary
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low765.80.7835
Triple Number Coastal/Long Distance Medium616.00.9740
Triple Number Coastal/Long Distance High561.31.0689
Triple Number Windward/Leeward Low976.90.6142
Triple Number Windward/Leeward Medium745.20.8052
Triple Number Windward/Leeward High669.00.8969
Custom scoring options for Israel
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance670.40.8951
Triple Number Coastal/Long Distance Low765.80.7835
Triple Number Coastal/Long Distance Medium616.00.9740
Triple Number Coastal/Long Distance High561.31.0689
Triple Number Windward/Leeward Low976.90.6142
Triple Number Windward/Leeward Medium745.20.8052
Triple Number Windward/Leeward High669.00.8969
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1596.91078.5829.1707.2640.5603.0571.3516.7499.5
Custom scoring options for Japan
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance670.40.8951
Triple Number Coastal/Long Distance Low765.80.7835
Triple Number Coastal/Long Distance Medium616.00.9740
Triple Number Coastal/Long Distance High561.31.0689
Triple Number Windward/Leeward Low976.90.6142
Triple Number Windward/Leeward Medium745.20.8052
Triple Number Windward/Leeward High669.00.8969
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1596.91078.5829.1707.2640.5603.0571.3516.7499.5
Custom scoring options for Korea
Scoring OptionTime On
Distance
Triple Number Coastal/Long Distance Low765.8
Triple Number Coastal/Long Distance Medium616.0
Triple Number Coastal/Long Distance High561.3
Triple Number Windward/Leeward Low976.9
Triple Number Windward/Leeward Medium745.2
Triple Number Windward/Leeward High669.0
Predominantly Upwind667.2
Predominantly Downwind626.6
Predominantly Reaching603.6
Custom scoring options for Lithuania
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance670.40.8951
Triple Number Coastal/Long Distance Low765.80.7835
Triple Number Coastal/Long Distance Medium616.00.9740
Triple Number Coastal/Long Distance High561.31.0689
Triple Number Windward/Leeward Low976.90.6142
Triple Number Windward/Leeward Medium745.20.8052
Triple Number Windward/Leeward High669.00.8969
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1596.91078.5829.1707.2640.5603.0571.3516.7499.5
Custom scoring options for Netherlands
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.7835
Triple Number Coastal/Long Distance Medium0.9740
Triple Number Coastal/Long Distance High1.0689
Triple Number Windward/Leeward Low0.6142
Triple Number Windward/Leeward Medium0.8052
Triple Number Windward/Leeward High0.8969
Coastal/Long Distance0.8951
Predominantly Upwind0.8992
Predominantly Downwind0.9575
For information
General Purpose Handicap (GPH)688.2
Custom scoring options for Norway
Scoring OptionTime On
Time
Distanseseilas Singeltall  (APH)0.9689
Distanseseilas Trippeltall svak vind0.7835
Distanseseilas Trippeltall mellomvind0.9740
Distanseseilas Trippeltall sterk vind1.0689
Pølsebane Trippeltall svak vind0.6142
Pølsebane Trippeltall mellomvind0.8052
Pølsebane Trippeltall sterk vind0.8969
Motvind Singeltall0.8992
Medvind Singeltall0.9575
Custom scoring options for Portugal
Scoring OptionTime On
Distance
Time On
Time
Triple Number Coastal/Long Distance Low765.80.7835
Triple Number Coastal/Long Distance Medium616.00.9740
Triple Number Coastal/Long Distance High561.31.0689
Triple Number Windward/Leeward Low976.90.6142
Triple Number Windward/Leeward Medium745.20.8052
Triple Number Windward/Leeward High669.00.8969
Coastal/Long Distance670.40.8951
Custom scoring options for Russia
Scoring OptionTime On
Distance
Time On
Time
Predominantly Upwind667.20.8992
Predominantly Downwind626.60.9575
Custom scoring options for South Africa
Scoring OptionTime On
Distance
Time On
Time
Cape Doctor Inshore645.00.9302
Cape Doctor Coastal532.81.1262
Triple Number Coastal/Long Distance Low765.80.7835
Triple Number Coastal/Long Distance Medium616.00.9740
Triple Number Coastal/Long Distance High561.31.0689
Triple Number Windward/Leeward Low976.90.6142
Triple Number Windward/Leeward Medium745.20.8052
Triple Number Windward/Leeward High669.00.8969
Custom scoring options for Slovenia
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.7835
Triple Number Coastal/Long Distance Medium0.9740
Triple Number Coastal/Long Distance High1.0689
Triple Number Windward/Leeward Low0.6142
Triple Number Windward/Leeward Medium0.8052
Triple Number Windward/Leeward High0.8969
Custom scoring options for Switzerland
Scoring OptionTime On
Time
Triple Number Coastal/Long Distance Low0.7835
Triple Number Coastal/Long Distance Medium0.9740
Triple Number Coastal/Long Distance High1.0689
Triple Number Windward/Leeward Low0.6142
Triple Number Windward/Leeward Medium0.8052
Triple Number Windward/Leeward High0.8969
Custom scoring options for Sweden
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance670.40.8951
Triple Number Coastal/Long Distance Low765.80.7835
Triple Number Coastal/Long Distance Medium616.00.9740
Triple Number Coastal/Long Distance High561.31.0689
Triple Number Windward/Leeward Low976.90.6142
Triple Number Windward/Leeward Medium745.20.8052
Triple Number Windward/Leeward High669.00.8969
Predominantly Upwind667.20.8992
Predominantly Downwind626.60.9575
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1596.91078.5829.1707.2640.5603.0571.3516.7499.5
Custom scoring options for Ukraine
Scoring OptionTime On
Distance
Time On
Time
Coastal/Long Distance670.40.8951
Triple Number Coastal/Long Distance Low765.80.7835
Triple Number Coastal/Long Distance Medium616.00.9740
Triple Number Coastal/Long Distance High561.31.0689
Triple Number Windward/Leeward Low976.90.6142
Triple Number Windward/Leeward Medium745.20.8052
Triple Number Windward/Leeward High669.00.8969
Performance Curve4 kt 6 kt 8 kt 10 kt 12 kt 14 kt 16 kt 20 kt 24 kt
Coastal/Long Distance1596.91078.5829.1707.2640.5603.0571.3516.7499.5
Custom scoring options for United States of America
Scoring OptionTODTOT
Triple Number AP Low765.80.7835
Triple Number AP Medium616.10.9739
Triple Number AP High561.41.0689
Triple Number Windward/Leeward Low1019.50.5885
Triple Number Windward/Leeward Medium745.20.8052
Triple Number Windward/Leeward High669.00.8969
Single Number Predominant Upwind690.20.8694
Single Number Predominant Reaching614.30.9767
Single Number Predominant Downwind651.90.9204
Predominant Upwind - Low898.10.6681
Predominant Upwind - Low/Med714.00.8403
Predominant Upwind - Medium650.90.9218
Predominant Upwind - Med/High620.90.9664
Predominant Upwind - High608.60.9858
Predominant Downwind Low931.00.6445
Predominant Downwind Low/Med702.50.8541
Predominant Downwind Medium607.60.9876
Predominant Downwind Med/High547.11.0967
Predominant Downwind High506.41.1848
Predominant Reaching Low817.10.7343
Predominant Reaching Low/Med646.70.9277
Predominant Reaching Medium581.51.0318
Predominant Reaching Med/High539.71.1117
Predominant Reaching High511.11.1739
SA/DSPL Upwind28.40SA/DSPL Downwind43.95
Scoring OptionTODTOT
5-Band Windward/Leeward Low1133.60.5293
5-Band Windward/Leeward Low/Med847.70.7078
5-Band Windward/Leeward Medium734.50.8169
5-Band Windward/Leeward Med/High676.30.8872
5-Band Windward/Leeward High652.60.9194
Windward/Leeward 60-40 Low1129.80.5311
Windward/Leeward 60-40 Low/Med854.60.7021
Windward/Leeward 60-40 Medium750.20.7997
Windward/Leeward 60-40 Med/High700.00.8571
Windward/Leeward 60-40 High682.60.8789
5-Band AP Low841.90.7127
5-Band AP Low/Med682.00.8798
5-Band AP Medium609.10.9850
5-Band AP Med/High567.81.0568
5-Band AP High544.71.1014
5-Band SF Bay Tour - Low978.50.6132
5-Band SF Bay Tour - Low/Med812.40.7386
5-Band SF Bay Tour - Medium713.50.8410
5-Band SF Bay Tour - Med/High663.10.9048
5-Band SF Bay Tour - High640.20.9373
Chicago-Mac Upwind0.8484
Chicago-Mac All Purpose0.8716
Chicago-Mac Downwind0.8893
Bayview-Mac Cove Island0.6561
Bayview-Mac Shore0.6618
Harvest Moon Regatta541.61.1078
Club Certificate2025
KING for ONE dayNOR 3410
Norges Seilforbund
Sognsveien 73
0854 OSLO
Data in meters/kilograms (Metric)
HULL AND APPENDAGES (Lightship Trim)
Class1/2 TON ONE OFFMeasurementHINPlan reviewHull constructionSolidCarbon rudderNoLight stanchionsNoTrim tabNo
LOA9.190Max. Beam3.230Draft1.634Displacement2,321Wetted area14.71IMS L7.056LSM06.824Acc. length9.190Sink (kg/mm) 10.24
VCGD-0.303VCGM-0.148RM Rated (kg·m) 44.9Limit of positive stability(°) N/AStability IndexN/ADefault crew weight399Declared crew weightN/A
PROPELLER
Propeller TypeFolding 2 blades
InstallationShaft exposedTwin screwNoHydro generatorNo
PRD0.340PBWPIPA0.0033
PSD0.020PHD0.050PHL0.110
PSA17.8°ESL0.750
ST10.020ST20.090ST30.090
ST40.090ST50.090
RIG
Forestay tensionAftInner stayNone FittedMast materialAluminumSingle headsail furlerNoMainsail furlerArticulated bowspritNoNon-circular riggingNoFiber riggingNoAdjustable mast footNoRunning backstays1CheckstaysSpreaders2Rotating mastNo
P11.210IG10.240ISP10.170MDT10.090MDL10.110MDT20.070MDL20.080TL2.040MW0.110GO0.130
E4.060J3.110BAS1.270FSD0.030SFJ0.000SPL3.190WPLTPS0.000BD0.000MWT0.00MCG0.000
Flying Headsail Foretriangles IdISPTPS
FLOTATION AND STABILITY
Calculation methodRM estimatedFlotation Date01/01/2015
BALLAST
TANKS
INVENTORY
INVENTORY
Fixed Ballast Total0
Total deductible
Total deductible
Club Certificate2025
KING for ONE dayNOR 3410
Norges Seilforbund
Sognsveien 73
0854 OSLO
MAINSAIL
IdMHBMUWMTWMHWMQWAreaMeas.DateComment460-2022042708470.150.861.582.693.4627.5627/04/2022
HEADSAIL
IdHHBHUWHTWHHWHQWHLPHLUBtnFlyingFTAreaMeas.DateComment460-2022042708450.080.541.042.123.294.5110.21NoNo 22.3727/04/2022460-2022042708430.080.450.821.592.343.0510.15YesNo 15.9727/04/2022
SYMMETRIC SPINNAKER
IdSLUSLESLSHWSFLAreaMeas.DateComment460-20220427084610.4010.4010.405.765.6449.7127/04/2022
CRUISER/RACER REQUIREMENTS*
Accommodation length9.2 mTable area0.44 m²Headroom1.64 mMinimum number of berths4Personal gear stowage0.16 m³Fresh water capacity64 lMinimum number of seats in cockpit4Food stowage0.24 m³Fuel capacity34 lCabin soleStovesSinksGalley gear stowageToiletWash basinNavigation areaHanging locker
*This list is a summary of the requirements. See IMS Appendix 1 for details.