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Endpoints","\u002Fconnector-development\u002Fconcepts\u002Fsila-endpoints\u002F","20.connector-development\u002F30.concepts\u002F15.sila-endpoints",{"title":862,"path":863,"stem":864,"device":6},"Designing Data Types","\u002Fconnector-development\u002Fconcepts\u002Fdata-types\u002F","20.connector-development\u002F30.concepts\u002F20.data-types",{"title":866,"path":867,"stem":868,"device":6},"Connector Architecture","\u002Fconnector-development\u002Fconcepts\u002Farchitecture\u002F","20.connector-development\u002F30.concepts\u002F30.architecture",{"title":870,"path":871,"stem":872,"children":873,"page":47},"Guides","\u002Fconnector-development\u002Fguides\u002F","20.connector-development\u002F40.guides",[874,878,882,886,890,894,898,902,906,910,914,917,921],{"title":875,"path":876,"stem":877,"device":6},"Project Structure","\u002Fconnector-development\u002Fguides\u002Fproject-structure\u002F","20.connector-development\u002F40.guides\u002F10.project-structure",{"title":879,"path":880,"stem":881,"device":6},"Configuration","\u002Fconnector-development\u002Fguides\u002Fconfiguration\u002F","20.connector-development\u002F40.guides\u002F20.configuration",{"title":883,"path":884,"stem":885,"device":6},"Logging","\u002Fconnector-development\u002Fguides\u002Flogging\u002F","20.connector-development\u002F40.guides\u002F21.logging",{"title":887,"path":888,"stem":889,"device":6},"Deployment","\u002Fconnector-development\u002Fguides\u002Fdeployment\u002F","20.connector-development\u002F40.guides\u002F30.deployment",{"title":891,"path":892,"stem":893,"device":6},"Security","\u002Fconnector-development\u002Fguides\u002Fsecurity\u002F","20.connector-development\u002F40.guides\u002F40.security",{"title":895,"path":896,"stem":897,"device":6},"Subscriptions","\u002Fconnector-development\u002Fguides\u002Fsubscriptions\u002F","20.connector-development\u002F40.guides\u002F45.subscriptions",{"title":899,"path":900,"stem":901,"device":6},"Execution Modes","\u002Fconnector-development\u002Fguides\u002Fexecution-modes\u002F","20.connector-development\u002F40.guides\u002F46.execution-modes",{"title":903,"path":904,"stem":905,"device":6},"Constraints and Units","\u002Fconnector-development\u002Fguides\u002Fconstraints-and-units\u002F","20.connector-development\u002F40.guides\u002F47.constraints-and-units",{"title":907,"path":908,"stem":909,"device":6},"Device Variants","\u002Fconnector-development\u002Fguides\u002Fdevice-variants\u002F","20.connector-development\u002F40.guides\u002F48.device-variants",{"title":911,"path":912,"stem":913,"device":6},"Repeated Modules","\u002Fconnector-development\u002Fguides\u002Frepeated-modules\u002F","20.connector-development\u002F40.guides\u002F49.repeated-modules",{"title":310,"path":915,"stem":916,"device":6},"\u002Fconnector-development\u002Fguides\u002Ferror-handling\u002F","20.connector-development\u002F40.guides\u002F50.error-handling",{"title":918,"path":919,"stem":920,"device":6},"Serial Troubleshooting","\u002Fconnector-development\u002Fguides\u002Fserial-troubleshooting\u002F","20.connector-development\u002F40.guides\u002F70.serial-troubleshooting",{"title":922,"path":923,"stem":924,"device":6},"Testing","\u002Fconnector-development\u002Fguides\u002Ftesting\u002F","20.connector-development\u002F40.guides\u002F80.testing",{"title":926,"device":6,"path":927,"stem":928,"children":929},"References","\u002Fconnector-development\u002Freference\u002F","20.connector-development\u002F50.reference\u002Findex",[930,931,935,939,943],{"title":926,"path":927,"stem":928,"device":6},{"title":932,"path":933,"stem":934,"device":6},"Naming Conventions","\u002Fconnector-development\u002Freference\u002Fnaming-conventions\u002F","20.connector-development\u002F50.reference\u002F10.naming-conventions",{"title":936,"path":937,"stem":938,"device":6},"Docstring Format","\u002Fconnector-development\u002Freference\u002Fdocstrings\u002F","20.connector-development\u002F50.reference\u002F20.docstrings",{"title":940,"path":941,"stem":942,"device":6},"Feature Metadata","\u002Fconnector-development\u002Freference\u002Ffeature-metadata\u002F","20.connector-development\u002F50.reference\u002F30.feature-metadata",{"title":944,"path":945,"stem":946,"device":6},"Review Checklist","\u002Fconnector-development\u002Freference\u002Freview-checklist\u002F","20.connector-development\u002F50.reference\u002F90.review-checklist",{"title":948,"device":6,"path":949,"stem":950,"children":951},"Blog","\u002Fblog\u002F","30.blog",[952,955],{"title":953,"path":949,"stem":954,"device":6},"UniteLabs Blog","30.blog\u002Findex",{"title":956,"path":957,"stem":958,"children":959,"page":47},"Python","\u002Fblog\u002Fpython\u002F","30.blog\u002F01.python",[960],{"title":961,"path":962,"stem":963,"device":6},"Python Environment and Project Management","\u002Fblog\u002Fpython\u002Fpython-environment-management\u002F","30.blog\u002F01.python\u002F10.python-environment-management",{"id":965,"title":782,"body":966,"description":1794,"device":6,"extension":1795,"links":6,"meta":1796,"navigation":1041,"path":1797,"seo":1798,"stem":784,"type":1799,"__hash__":1800},"docs\u002F07.labware\u002F80.shapes.md",{"type":967,"value":968,"toc":1789},"minimark",[969,1008,1166,1171,1174,1196,1202,1227,1231,1242,1518,1522,1533,1760,1785],[970,971,972,973,977,978,977,981,977,984,977,987,977,990,977,993,977,996,999,1000,1003,1004,1007],"p",{},"Every container in the labware library, whether a plate well, a tube, a trough, or a tip, is built from one or more shape sections: ",[974,975,976],"code",{},"Cylinder",", ",[974,979,980],{},"Cuboid",[974,982,983],{},"Cone",[974,985,986],{},"ConicalFrustum",[974,988,989],{},"Pyramid",[974,991,992],{},"PyramidalFrustum",[974,994,995],{},"SphericalCap",[974,997,998],{},"HalfSphere",", and ",[974,1001,1002],{},"SphericalSegment",". A ",[974,1005,1006],{},"Container"," stacks them from top to bottom, and the library uses that model to turn a volume into a liquid level and back.",[1009,1010,1015],"pre",{"className":1011,"code":1012,"language":1013,"meta":1014,"style":1014},"language-python shiki shiki-themes github-light-high-contrast github-light-high-contrast github-dark-default","from unitelabs.labware import Container, ConicalFrustum, Cylinder\n\n# The container of a 50 mL conical tube: a cylinder on top of a conical bottom\ncontainer = Container(\n    max_volume=50_000,\n    sections=[\n        Cylinder(radius=13.89, height=98.77),  # top section first\n        ConicalFrustum(radius_lower=3.6, radius_upper=13.89, height=14.88),\n    ],\n)\n","python","",[974,1016,1017,1036,1043,1050,1062,1078,1089,1119,1154,1160],{"__ignoreMap":1014},[1018,1019,1022,1026,1030,1033],"span",{"class":1020,"line":1021},"line",1,[1018,1023,1025],{"class":1024},"sxkbv","from",[1018,1027,1029],{"class":1028},"sc-9e"," unitelabs.labware ",[1018,1031,1032],{"class":1024},"import",[1018,1034,1035],{"class":1028}," Container, ConicalFrustum, Cylinder\n",[1018,1037,1039],{"class":1020,"line":1038},2,[1018,1040,1042],{"emptyLinePlaceholder":1041},true,"\n",[1018,1044,1046],{"class":1020,"line":1045},3,[1018,1047,1049],{"class":1048},"sIsDC","# The container of a 50 mL conical tube: a cylinder on top of a conical bottom\n",[1018,1051,1053,1056,1059],{"class":1020,"line":1052},4,[1018,1054,1055],{"class":1028},"container ",[1018,1057,1058],{"class":1024},"=",[1018,1060,1061],{"class":1028}," Container(\n",[1018,1063,1065,1069,1071,1075],{"class":1020,"line":1064},5,[1018,1066,1068],{"class":1067},"sNqAu","    max_volume",[1018,1070,1058],{"class":1024},[1018,1072,1074],{"class":1073},"sOiAX","50_000",[1018,1076,1077],{"class":1028},",\n",[1018,1079,1081,1084,1086],{"class":1020,"line":1080},6,[1018,1082,1083],{"class":1067},"    sections",[1018,1085,1058],{"class":1024},[1018,1087,1088],{"class":1028},"[\n",[1018,1090,1092,1095,1098,1100,1103,1105,1108,1110,1113,1116],{"class":1020,"line":1091},7,[1018,1093,1094],{"class":1028},"        Cylinder(",[1018,1096,1097],{"class":1067},"radius",[1018,1099,1058],{"class":1024},[1018,1101,1102],{"class":1073},"13.89",[1018,1104,977],{"class":1028},[1018,1106,1107],{"class":1067},"height",[1018,1109,1058],{"class":1024},[1018,1111,1112],{"class":1073},"98.77",[1018,1114,1115],{"class":1028},"),  ",[1018,1117,1118],{"class":1048},"# top section first\n",[1018,1120,1122,1125,1128,1130,1133,1135,1138,1140,1142,1144,1146,1148,1151],{"class":1020,"line":1121},8,[1018,1123,1124],{"class":1028},"        ConicalFrustum(",[1018,1126,1127],{"class":1067},"radius_lower",[1018,1129,1058],{"class":1024},[1018,1131,1132],{"class":1073},"3.6",[1018,1134,977],{"class":1028},[1018,1136,1137],{"class":1067},"radius_upper",[1018,1139,1058],{"class":1024},[1018,1141,1102],{"class":1073},[1018,1143,977],{"class":1028},[1018,1145,1107],{"class":1067},[1018,1147,1058],{"class":1024},[1018,1149,1150],{"class":1073},"14.88",[1018,1152,1153],{"class":1028},"),\n",[1018,1155,1157],{"class":1020,"line":1156},9,[1018,1158,1159],{"class":1028},"    ],\n",[1018,1161,1163],{"class":1020,"line":1162},10,[1018,1164,1165],{"class":1028},")\n",[1167,1168,1170],"h2",{"id":1169},"dimensions-at-height","Dimensions at Height",[970,1172,1173],{},"When an operation needs the width of a container at a specific height, for example to move a pipetting channel to the side of a well, the answer depends on the shape. Three methods give the same answer for every concrete shape class, so your code doesn't have to handle each shape type separately:",[1175,1176,1177,1184,1190],"ul",{},[1178,1179,1180,1183],"li",{},[974,1181,1182],{},"width_at_height(height)"," returns the x-axis extent of the cross-section at a given height.",[1178,1185,1186,1189],{},[974,1187,1188],{},"depth_at_height(height)"," returns the y-axis extent of the cross-section at a given height. For circular shapes this equals the width.",[1178,1191,1192,1195],{},[974,1193,1194],{},"area_at_height(height)"," returns the cross-sectional area at a given height.",[970,1197,1198,1199,1201],{},"For stacked containers (any ",[974,1200,1006],{}," with multiple sections), one more method is available:",[1175,1203,1204],{},[1178,1205,1206,1209,1210,1213,1214,1216,1217,977,1220,999,1223,1226],{},[974,1207,1208],{},"section_at_height(height)"," returns a ",[974,1211,1212],{},"tuple[Shape, Decimal]"," containing the shape section and the local height within that section. ",[974,1215,1006],{}," delegates ",[974,1218,1219],{},"width_at_height",[974,1221,1222],{},"depth_at_height",[974,1224,1225],{},"area_at_height"," through this method.",[1167,1228,1230],{"id":1229},"usage-example","Usage Example",[970,1232,1233,1234,1237,1238,1241],{},"Given the ",[974,1235,1236],{},"Standard50mLTube"," defined in ",[1239,1240,761],"a",{"href":762},", a tube with a cylindrical upper section and a conical frustum at the bottom, you can query the width at any height without caring which section you are in:",[1009,1243,1245],{"className":1011,"code":1244,"language":1013,"meta":1014,"style":1014},"from unitelabs.labware import Decimal\n\ntube = Standard50mLTube()\n\n# Width at the middle of the cylindrical section (e.g. 50 mm from bottom)\nwidth_mid = tube.container.width_at_height(Decimal(\"50\"))\nprint(f\"Width at 50 mm: {width_mid} mm\")  # 27.78 mm (2 × 13.89)\n\n# Width near the tip of the conical frustum (e.g. 5 mm from bottom)\nwidth_tip = tube.container.width_at_height(Decimal(\"5\"))\nprint(f\"Width at 5 mm: {width_tip} mm\")  # interpolated between 7.2 mm and 27.78 mm\n\n# Cross-sectional area at 50 mm\narea = tube.container.area_at_height(Decimal(\"50\"))\nprint(f\"Area at 50 mm: {round(area, 3)} mm²\")  # π × 13.89²\n\n# Inspect which section and local offset a given height falls into\nsection, local_height = tube.container.section_at_height(Decimal(\"5\"))\nprint(f\"Section: {section}\")          # ConicalFrustum(...)\nprint(f\"Local height: {local_height} mm\")\n",[974,1246,1247,1258,1262,1272,1276,1281,1298,1330,1334,1339,1353,1379,1384,1390,1405,1441,1446,1452,1467,1495],{"__ignoreMap":1014},[1018,1248,1249,1251,1253,1255],{"class":1020,"line":1021},[1018,1250,1025],{"class":1024},[1018,1252,1029],{"class":1028},[1018,1254,1032],{"class":1024},[1018,1256,1257],{"class":1028}," Decimal\n",[1018,1259,1260],{"class":1020,"line":1038},[1018,1261,1042],{"emptyLinePlaceholder":1041},[1018,1263,1264,1267,1269],{"class":1020,"line":1045},[1018,1265,1266],{"class":1028},"tube ",[1018,1268,1058],{"class":1024},[1018,1270,1271],{"class":1028}," Standard50mLTube()\n",[1018,1273,1274],{"class":1020,"line":1052},[1018,1275,1042],{"emptyLinePlaceholder":1041},[1018,1277,1278],{"class":1020,"line":1064},[1018,1279,1280],{"class":1048},"# Width at the middle of the cylindrical section (e.g. 50 mm from bottom)\n",[1018,1282,1283,1286,1288,1291,1295],{"class":1020,"line":1080},[1018,1284,1285],{"class":1028},"width_mid ",[1018,1287,1058],{"class":1024},[1018,1289,1290],{"class":1028}," tube.container.width_at_height(Decimal(",[1018,1292,1294],{"class":1293},"sCx38","\"50\"",[1018,1296,1297],{"class":1028},"))\n",[1018,1299,1300,1303,1306,1309,1312,1315,1318,1321,1324,1327],{"class":1020,"line":1091},[1018,1301,1302],{"class":1073},"print",[1018,1304,1305],{"class":1028},"(",[1018,1307,1308],{"class":1024},"f",[1018,1310,1311],{"class":1293},"\"Width at 50 mm: ",[1018,1313,1314],{"class":1024},"{",[1018,1316,1317],{"class":1028},"width_mid",[1018,1319,1320],{"class":1024},"}",[1018,1322,1323],{"class":1293}," mm\"",[1018,1325,1326],{"class":1028},")  ",[1018,1328,1329],{"class":1048},"# 27.78 mm (2 × 13.89)\n",[1018,1331,1332],{"class":1020,"line":1121},[1018,1333,1042],{"emptyLinePlaceholder":1041},[1018,1335,1336],{"class":1020,"line":1156},[1018,1337,1338],{"class":1048},"# Width near the tip of the conical frustum (e.g. 5 mm from bottom)\n",[1018,1340,1341,1344,1346,1348,1351],{"class":1020,"line":1162},[1018,1342,1343],{"class":1028},"width_tip ",[1018,1345,1058],{"class":1024},[1018,1347,1290],{"class":1028},[1018,1349,1350],{"class":1293},"\"5\"",[1018,1352,1297],{"class":1028},[1018,1354,1356,1358,1360,1362,1365,1367,1370,1372,1374,1376],{"class":1020,"line":1355},11,[1018,1357,1302],{"class":1073},[1018,1359,1305],{"class":1028},[1018,1361,1308],{"class":1024},[1018,1363,1364],{"class":1293},"\"Width at 5 mm: ",[1018,1366,1314],{"class":1024},[1018,1368,1369],{"class":1028},"width_tip",[1018,1371,1320],{"class":1024},[1018,1373,1323],{"class":1293},[1018,1375,1326],{"class":1028},[1018,1377,1378],{"class":1048},"# interpolated between 7.2 mm and 27.78 mm\n",[1018,1380,1382],{"class":1020,"line":1381},12,[1018,1383,1042],{"emptyLinePlaceholder":1041},[1018,1385,1387],{"class":1020,"line":1386},13,[1018,1388,1389],{"class":1048},"# Cross-sectional area at 50 mm\n",[1018,1391,1393,1396,1398,1401,1403],{"class":1020,"line":1392},14,[1018,1394,1395],{"class":1028},"area ",[1018,1397,1058],{"class":1024},[1018,1399,1400],{"class":1028}," tube.container.area_at_height(Decimal(",[1018,1402,1294],{"class":1293},[1018,1404,1297],{"class":1028},[1018,1406,1408,1410,1412,1414,1417,1419,1422,1425,1428,1431,1433,1436,1438],{"class":1020,"line":1407},15,[1018,1409,1302],{"class":1073},[1018,1411,1305],{"class":1028},[1018,1413,1308],{"class":1024},[1018,1415,1416],{"class":1293},"\"Area at 50 mm: ",[1018,1418,1314],{"class":1024},[1018,1420,1421],{"class":1073},"round",[1018,1423,1424],{"class":1028},"(area, ",[1018,1426,1427],{"class":1073},"3",[1018,1429,1430],{"class":1028},")",[1018,1432,1320],{"class":1024},[1018,1434,1435],{"class":1293}," mm²\"",[1018,1437,1326],{"class":1028},[1018,1439,1440],{"class":1048},"# π × 13.89²\n",[1018,1442,1444],{"class":1020,"line":1443},16,[1018,1445,1042],{"emptyLinePlaceholder":1041},[1018,1447,1449],{"class":1020,"line":1448},17,[1018,1450,1451],{"class":1048},"# Inspect which section and local offset a given height falls into\n",[1018,1453,1455,1458,1460,1463,1465],{"class":1020,"line":1454},18,[1018,1456,1457],{"class":1028},"section, local_height ",[1018,1459,1058],{"class":1024},[1018,1461,1462],{"class":1028}," tube.container.section_at_height(Decimal(",[1018,1464,1350],{"class":1293},[1018,1466,1297],{"class":1028},[1018,1468,1470,1472,1474,1476,1479,1481,1484,1486,1489,1492],{"class":1020,"line":1469},19,[1018,1471,1302],{"class":1073},[1018,1473,1305],{"class":1028},[1018,1475,1308],{"class":1024},[1018,1477,1478],{"class":1293},"\"Section: ",[1018,1480,1314],{"class":1024},[1018,1482,1483],{"class":1028},"section",[1018,1485,1320],{"class":1024},[1018,1487,1488],{"class":1293},"\"",[1018,1490,1491],{"class":1028},")          ",[1018,1493,1494],{"class":1048},"# ConicalFrustum(...)\n",[1018,1496,1498,1500,1502,1504,1507,1509,1512,1514,1516],{"class":1020,"line":1497},20,[1018,1499,1302],{"class":1073},[1018,1501,1305],{"class":1028},[1018,1503,1308],{"class":1024},[1018,1505,1506],{"class":1293},"\"Local height: ",[1018,1508,1314],{"class":1024},[1018,1510,1511],{"class":1028},"local_height",[1018,1513,1320],{"class":1024},[1018,1515,1323],{"class":1293},[1018,1517,1165],{"class":1028},[1167,1519,1521],{"id":1520},"shape-reference","Shape Reference",[970,1523,1524,1525,1528,1529,1532],{},"The table below shows how each concrete shape implements the three methods, where ",[974,1526,1527],{},"h"," is the queried height and ",[974,1530,1531],{},"H"," is the total height of the shape:",[1534,1535,1536,1561],"table",{},[1537,1538,1539],"thead",{},[1540,1541,1542,1546,1551,1556],"tr",{},[1543,1544,1545],"th",{},"Shape",[1543,1547,1548],{},[974,1549,1550],{},"width_at_height(h)",[1543,1552,1553],{},[974,1554,1555],{},"depth_at_height(h)",[1543,1557,1558],{},[974,1559,1560],{},"area_at_height(h)",[1562,1563,1564,1588,1609,1638,1658,1677,1700,1718,1737],"tbody",{},[1540,1565,1566,1572,1578,1583],{},[1567,1568,1569],"td",{},[1570,1571,980],"strong",{},[1567,1573,1574,1577],{},[974,1575,1576],{},"width"," (constant)",[1567,1579,1580,1577],{},[974,1581,1582],{},"depth",[1567,1584,1585],{},[974,1586,1587],{},"width × depth",[1540,1589,1590,1594,1599,1604],{},[1567,1591,1592],{},[1570,1593,989],{},[1567,1595,1596],{},[974,1597,1598],{},"(h\u002FH) × width",[1567,1600,1601],{},[974,1602,1603],{},"(h\u002FH) × depth",[1567,1605,1606],{},[974,1607,1608],{},"(h\u002FH)² × width × depth",[1540,1610,1611,1615,1625,1633],{},[1567,1612,1613],{},[1570,1614,992],{},[1567,1616,1617,1618,1621,1622],{},"linear interpolation between ",[974,1619,1620],{},"width_lower"," and ",[974,1623,1624],{},"width_upper",[1567,1626,1617,1627,1621,1630],{},[974,1628,1629],{},"depth_lower",[974,1631,1632],{},"depth_upper",[1567,1634,1635],{},[974,1636,1637],{},"w(h) × d(h)",[1540,1639,1640,1644,1649,1653],{},[1567,1641,1642],{},[1570,1643,976],{},[1567,1645,1646,1577],{},[974,1647,1648],{},"2 × radius",[1567,1650,1651,1577],{},[974,1652,1648],{},[1567,1654,1655],{},[974,1656,1657],{},"π × r²",[1540,1659,1660,1664,1669,1672],{},[1567,1661,1662],{},[1570,1663,983],{},[1567,1665,1666],{},[974,1667,1668],{},"2 × (h\u002FH) × radius",[1567,1670,1671],{},"same as width",[1567,1673,1674],{},[974,1675,1676],{},"π × ((h\u002FH) × r)²",[1540,1678,1679,1683,1693,1695],{},[1567,1680,1681],{},[1570,1682,986],{},[1567,1684,1685,1688,1689,1621,1691],{},[974,1686,1687],{},"2 × r(h)",", linear interpolation between ",[974,1690,1127],{},[974,1692,1137],{},[1567,1694,1671],{},[1567,1696,1697],{},[974,1698,1699],{},"π × r(h)²",[1540,1701,1702,1706,1711,1713],{},[1567,1703,1704],{},[1570,1705,995],{},[1567,1707,1708],{},[974,1709,1710],{},"2 × √(2Rh − h²)",[1567,1712,1671],{},[1567,1714,1715],{},[974,1716,1717],{},"π × (2Rh − h²)",[1540,1719,1720,1724,1729,1733],{},[1567,1721,1722],{},[1570,1723,998],{},[1567,1725,1726,1727],{},"inherits from ",[974,1728,995],{},[1567,1730,1726,1731],{},[974,1732,995],{},[1567,1734,1726,1735],{},[974,1736,995],{},[1540,1738,1739,1743,1753,1755],{},[1567,1740,1741],{},[1570,1742,1002],{},[1567,1744,1745,1748,1749,1752],{},[974,1746,1747],{},"2 × √(2R·h' − h'²)"," where ",[974,1750,1751],{},"h'"," is height from sphere bottom",[1567,1754,1671],{},[1567,1756,1757],{},[974,1758,1759],{},"π × (2R·h' − h'²)",[1761,1762,1765],"callout",{"color":1763,"icon":1764},"info","i-heroicons-information-circle",[970,1766,1767,1770,1771,1773,1774,977,1776,999,1778,1780,1781,1784],{},[1570,1768,1769],{},"Stacked containers",": When a ",[974,1772,1006],{}," has multiple sections, ",[974,1775,1219],{},[974,1777,1222],{},[974,1779,1225],{}," automatically resolve the correct section via ",[974,1782,1783],{},"section_at_height",". 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