63:
1650:
1227:
79:
1932:
1455:
790:
1734:
522:
1277:
927:
This method is a practical procedure to reduce celestial sights with the needed accuracy, without using electronic tools such as calculator or a computer. And it could serve as a backup in case of malfunction of the positioning system aboard.
914:
H.O. 211 (Dead
Reckoning Altitude and Azimuth Table, known as Ageton, 1931, 36pg. And 2 variants of H.O. 211: Compact Sight Reduction Table, also known as Ageton–Bayless, 1980, 9+ pg. S-Table, also known as Pepperday, 1992, 9+
470:
1927:{\displaystyle \operatorname {hav} (Z)={\frac {\operatorname {hav} (90^{\circ }\pm \vert Dec\vert )-\operatorname {hav} (\vert Lat\vert -Hc)}{1-\operatorname {hav} (\vert Lat\vert -Hc)-\operatorname {hav} (\vert Lat\vert +Hc)}}}
1704:
1159:
1003:
1272:
1537:
1450:{\displaystyle \operatorname {hav} (ZD)=\operatorname {hav} (Lat-Dec)+\left(1-\operatorname {hav} (Lat-Dec)-\operatorname {hav} (Lat+Dec)\right)\cdot \operatorname {hav} (LHA)}
317:
1115:
1059:
275:
785:{\displaystyle \cos(Z)={\frac {\sin(Dec)-\sin(Hc)\cdot \sin(Lat)}{\cos(Hc)\cdot \cos(Lat)}}={\frac {\sin(Dec)}{\cos(Hc)\cdot \cos(Lat)}}-\tan(Hc)\cdot \tan(Lat).}
219:
187:
155:
125:
1480:
881:
838:
815:
515:
306:
1724:
858:
492:
1726:
is E↔W as the name of the meridian angle, but the N↕S name is not determined. In most situations azimuth ambiguities are resolved simply by observation.
887:(Marcq St Hilaire method), which uses the difference in observed and calculated altitudes to ascertain one's relative location to the assumed point.
2073:
This computation of the altitude and the azimuth needs a haversine table. For a precision of 1 minute of arc, a four figure table is enough.
2205:
1663:
2407:
A Community
Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Position-Finding
2327:
2257:
2253:
2249:
2245:
2241:
2237:
2445:
2270:
899:
The
Nautical Almanac Sight Reduction (NASR, originally known as Concise Tables for Sight Reduction or Davies, 1984, 22pg)
902:
Pub. 249 (formerly H.O. 249, Sight
Reduction Tables for Air Navigation, A.P. 3270 in the UK, 1947–53, 1+2 volumes)
905:
Pub. 229 (formerly H.O. 229, Sight
Reduction Tables for Marine Navigation, H.D. 605/NP 401 in the UK, 1970, 6 volumes.
2339:
1120:
2363:
2351:
2315:
2180:
1646:
For the azimuth a diagram was developed for a faster solution without calculation, and with an accuracy of 1°.
309:
51:
943:
1248:
908:
The variant of HO-229: Sight
Reduction Tables for Small Boat Navigation, known as Schlereth, 1983, 1 volume)
2425:
1491:
2393:
2218:
62:
2269:
Table de point miniature (Hauteur et azimut), by R. Doniol, Navigation IFN Vol. III Nº 10, Avril 1955
1729:
When there are reasons for doubt or for the purpose of checking the following formula should be used:
2175:
1064:
1008:
222:
2440:
2420:
2283:
936:
The first approach of a compact and concise method was published by R. Doniol in 1955 and involved
2399:
230:
54:. The calculation can be done by computer, or by hand via tabular methods and longhand methods.
2226:
2222:
2291:
1649:
911:
H.O. 214 (Tables of
Computed Altitude and Azimuth, H.D. 486 in the UK, 1936–46, 9 vol.)
2426:
Vector
Solution for the intersection of two Circles of Equal Altitude - free App for android
2185:
884:
278:
37:
33:
2328:
http://fer3.com/arc/m2.aspx/Gregs-article-havDoniol-Ocean-Navigator-HannoIx-jun-2015-g31689
1226:
1483:
918:
H.O. 208 (Navigation Tables for
Mariners and Aviators, known as Dreisonstok, 1928, 113pg.)
465:{\displaystyle \sin(Hc)=\sin(Lat)\cdot \sin(Dec)+\cos(Lat)\cdot \cos(Dec)\cdot \cos(LHA).}
17:
198:
166:
134:
104:
1462:
863:
820:
797:
497:
288:
47:, of a celestial body for a line of position; or the data obtained by such observation.
1937:
1709:
1543:
843:
477:
25:
2434:
78:
190:
2340:
http://fer3.com/arc/m2.aspx/Hc-Azimuth-Diagram-finally-HannoIx-aug-2013-g24772
2170:
2295:
2352:
http://fer3.com/arc/m2.aspx/Longhand-Sight-Reduction-Bergman-nov-2014-g29441
2316:
http://fer3.com/arc/m2.aspx/Longhand-Sight-Reduction-HannoIx-nov-2014-g29121
1235:
937:
158:
43:
Sight is defined as the observation of the altitude, and sometimes also the
128:
71:
44:
29:
2415:
2290:(227). Ix, Hanno. Portland, ME, USA: Navigator Publishing LLC: 42–43.
1943:
if same name for latitude and declination (both are North or South)
1549:
if same name for latitude and declination (both are North or South)
2015:= archav() -> inverse look-up at the haversine tables if Latitude
1660:
An ambiguity in the value of azimuth may arise since in the diagram
1245:
A compact expression for the altitude was derived using haversines,
2376:
2410:
1648:
1225:
77:
61:
161:(East - positive, West - negative), both approximate (assumed);
1951:|) if contrary name (one is North the other is South)
1573:|) if contrary name (one is North the other is South)
1699:{\displaystyle 0^{\circ }\leqslant Z\leqslant 90^{\circ }}
517:(Zn=0 at North, measured eastward) is then calculated by:
1657:
This diagram could be used also for star identification.
1636:= archav() -> inverse look-up at the haversine tables
2404:
1239:
794:
These values are contrasted with the observed altitude
1238:
was developed between 2014 and 2015, and published in
1737:
1712:
1666:
1494:
1465:
1280:
1251:
1123:
1067:
1011:
946:
866:
846:
823:
800:
525:
500:
480:
320:
291:
233:
201:
169:
137:
107:
285:First calculate the altitude of the celestial body
1926:
1718:
1698:
1531:
1474:
1449:
1266:
1153:
1109:
1053:
997:
875:
852:
832:
809:
784:
509:
486:
464:
300:
269:
213:
181:
149:
119:
28:(in celestial navigation usually obtained using a
50:The mathematical basis of sight reduction is the
2400:resources for Longhand Haversine Sight Reduction
2364:"NavList: Re: Longhand Sight Reduction (129172)"
2411:Celestial Tools for the USPS/CPS JN/N Student
8:
1906:
1894:
1867:
1855:
1823:
1811:
1793:
1781:
32:) the information needed for establishing a
1234:A practical and friendly method using only
1154:{\displaystyle a=\operatorname {hav} (LHA)}
2350:Azimuth haversine formula by Lars Bergman
1772:
1756:
1736:
1711:
1690:
1671:
1665:
1511:
1493:
1464:
1279:
1250:
1122:
1066:
1010:
945:
865:
845:
822:
799:
663:
544:
524:
499:
479:
319:
290:
232:
200:
168:
136:
106:
2314:Altitude haversine formula by Hanno Ix
2258:Pub. 229 Volume 6. Latitudes 75° to 90°
2254:Pub. 229 Volume 5. Latitudes 60° to 75°
2250:Pub. 229 Volume 4. Latitudes 45° to 60°
2246:Pub. 229 Volume 3. Latitudes 30° to 45°
2242:Pub. 229 Volume 2. Latitudes 15° to 30°
2238:Pub. 229 Volume 1. Latitudes 0° to 15°
2227:Pub. 249 Volume 3. Latitudes 40° to 89°
2197:
998:{\displaystyle \sin(Hc)=n-a\cdot (m+n)}
2421:Sight Reduction - free App for android
2394:AstroNavigation - Free App for Windows
2223:Pub. 249 Volume 2. Latitudes 0° to 39°
1267:{\displaystyle \operatorname {hav} ()}
131:(North - positive, South - negative),
1274:, for all the terms of the equation:
7:
2416:Graphical all-haversine Hc reduction
2145:= archav(0.7979) = 126.6° Because
1532:{\displaystyle Hc=(90^{\circ }-ZD)}
1230:Haversine Sight Reduction algorithm
66:Steps for measuring and correcting
2121:= 90° - 77° 39′ = 12° 21′ Azimuth
923:Longhand haversine sight reduction
24:is the process of deriving from a
14:
2206:The American Practical Navigator
2377:Natural-Haversine 4-place Table
2284:"Ultra compact sight reduction"
1110:{\displaystyle m=\cos(Lat+Dec)}
1054:{\displaystyle n=\cos(Lat-Dec)}
940:. The altitude is derived from
2080:
1942:
1918:
1891:
1879:
1852:
1835:
1808:
1796:
1765:
1750:
1744:
1548:
1526:
1504:
1444:
1432:
1415:
1391:
1379:
1355:
1332:
1308:
1296:
1287:
1261:
1258:
1148:
1136:
1104:
1080:
1048:
1024:
992:
980:
962:
953:
776:
764:
752:
743:
728:
716:
704:
695:
684:
672:
654:
642:
630:
621:
610:
598:
586:
577:
565:
553:
538:
532:
456:
444:
432:
420:
408:
396:
384:
372:
360:
348:
336:
327:
1:
2326:Azimuth diagram by Hanno Ix.
2282:Rudzinski, Greg (July 2015).
2117:= archav(0.3930) = 77° 39′
1222:Ultra compact sight reduction
1539:is the calculated altitude.
883:are the three inputs to the
1653:Azimuth diagram by Hanno Ix
270:{\displaystyle LHA=GHA+Lon}
2462:
2149:< 180° and Latitude is
895:The methods included are:
2398:Navigational Algorithms:
2392:Navigational Algorithms:
2219:Pub. 249 Volume 1. Stars
2181:Circle of equal altitude
310:circle of equal altitude
52:circle of equal altitude
891:Tabular sight reduction
2338:Hc by Azimuth Diagram
1928:
1720:
1700:
1654:
1533:
1476:
1451:
1268:
1231:
1155:
1111:
1055:
999:
877:
854:
834:
811:
786:
511:
488:
466:
308:using the equation of
302:
271:
215:
183:
151:
121:
95:
75:
2093:= 57° 17.0′ Altitude
1929:
1721:
1701:
1652:
1534:
1477:
1452:
1269:
1229:
1156:
1112:
1056:
1000:
878:
855:
835:
812:
787:
512:
489:
467:
303:
281:of the body observed.
272:
225:of the body observed;
216:
193:of the body observed;
184:
152:
122:
81:
65:
2446:Celestial navigation
2176:Celestial navigation
2089:= 21° 11.0′ S (−)
2085:= 34° 10.0′ N (+)
1735:
1710:
1664:
1492:
1463:
1278:
1249:
1164:The calculation is:
1121:
1065:
1009:
944:
864:
844:
821:
798:
523:
498:
478:
318:
289:
231:
223:Greenwich hour angle
199:
167:
135:
105:
94:in intercept method.
214:{\displaystyle GHA}
182:{\displaystyle Dec}
150:{\displaystyle Lon}
120:{\displaystyle Lat}
1955:= hav(90° + |
1947:= hav(90° − |
1924:
1716:
1696:
1655:
1529:
1475:{\displaystyle ZD}
1472:
1447:
1264:
1232:
1151:
1107:
1051:
995:
876:{\displaystyle Hc}
873:
850:
833:{\displaystyle Ho}
830:
810:{\displaystyle Ho}
807:
782:
510:{\displaystyle Zn}
507:
484:
462:
301:{\displaystyle Hc}
298:
267:
211:
179:
147:
117:
96:
76:
1936:The algorithm if
1922:
1719:{\displaystyle Z}
1542:The algorithm if
853:{\displaystyle Z}
732:
658:
487:{\displaystyle Z}
2453:
2380:
2374:
2368:
2367:
2360:
2354:
2348:
2342:
2336:
2330:
2324:
2318:
2312:
2306:
2305:
2303:
2302:
2279:
2273:
2267:
2261:
2235:
2229:
2216:
2210:
2202:
2186:Intercept method
1978:
1966:
1958:
1950:
1933:
1931:
1930:
1925:
1923:
1921:
1838:
1777:
1776:
1757:
1725:
1723:
1722:
1717:
1705:
1703:
1702:
1697:
1695:
1694:
1676:
1675:
1596:
1592:
1584:
1580:
1572:
1568:
1560:
1556:
1538:
1536:
1535:
1530:
1516:
1515:
1481:
1479:
1478:
1473:
1456:
1454:
1453:
1448:
1422:
1418:
1273:
1271:
1270:
1265:
1160:
1158:
1157:
1152:
1116:
1114:
1113:
1108:
1060:
1058:
1057:
1052:
1004:
1002:
1001:
996:
885:intercept method
882:
880:
879:
874:
859:
857:
856:
851:
839:
837:
836:
831:
816:
814:
813:
808:
791:
789:
788:
783:
733:
731:
687:
664:
659:
657:
613:
545:
516:
514:
513:
508:
493:
491:
490:
485:
471:
469:
468:
463:
307:
305:
304:
299:
279:local hour angle
276:
274:
273:
268:
220:
218:
217:
212:
188:
186:
185:
180:
156:
154:
153:
148:
126:
124:
123:
118:
93:
89:
85:
69:
38:intercept method
34:line of position
2461:
2460:
2456:
2455:
2454:
2452:
2451:
2450:
2431:
2430:
2389:
2384:
2383:
2375:
2371:
2362:
2361:
2357:
2349:
2345:
2337:
2333:
2325:
2321:
2313:
2309:
2300:
2298:
2288:Ocean Navigator
2281:
2280:
2276:
2268:
2264:
2236:
2232:
2217:
2213:
2203:
2199:
2194:
2167:
2162:
2137:= 0.0358 hav(
2109:= 0.2157 hav(
2079:
2071:
1976:
1964:
1956:
1948:
1938:absolute values
1839:
1768:
1758:
1733:
1732:
1708:
1707:
1686:
1667:
1662:
1661:
1644:
1594:
1593:| − |
1590:
1582:
1581:| + |
1578:
1570:
1569:| + |
1566:
1558:
1557:| − |
1554:
1544:absolute values
1507:
1490:
1489:
1484:zenith distance
1461:
1460:
1342:
1338:
1276:
1275:
1247:
1246:
1224:
1219:
1119:
1118:
1063:
1062:
1007:
1006:
942:
941:
934:
925:
893:
862:
861:
842:
841:
819:
818:
796:
795:
688:
665:
614:
546:
521:
520:
496:
495:
476:
475:
316:
315:
287:
286:
229:
228:
197:
196:
165:
164:
133:
132:
103:
102:
91:
87:
83:
67:
60:
36:, generally by
22:sight reduction
18:astronavigation
12:
11:
5:
2459:
2457:
2449:
2448:
2443:
2433:
2432:
2429:
2428:
2423:
2418:
2413:
2408:
2402:
2396:
2388:
2387:External links
2385:
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2311:
2308:
2297:
2293:
2289:
2285:
2278:
2275:
2272:
2266:
2263:
2259:
2255:
2251:
2247:
2243:
2239:
2234:
2231:
2228:
2224:
2220:
2215:
2212:
2208:
2207:
2201:
2198:
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2184:
2182:
2179:
2177:
2174:
2172:
2169:
2168:
2164:
2160:
2156:
2152:
2148:
2144:
2141:) = 0.7979
2140:
2136:
2132:
2128:
2124:
2120:
2116:
2113:) = 0.3930
2112:
2108:
2104:
2100:
2096:
2092:
2088:
2084:
2076:
2074:
2070:
2066:
2062:
2058:
2054:
2050:
2046:
2042:
2038:
2034:
2030:
2026:
2022:
2018:
2014:
2010:
2006:
2002:
1998:
1994:
1990:
1986:
1982:
1974:
1970:
1962:
1954:
1946:
1941:
1940:are used is:
1939:
1934:
1915:
1912:
1909:
1903:
1900:
1897:
1888:
1885:
1882:
1876:
1873:
1870:
1864:
1861:
1858:
1849:
1846:
1843:
1840:
1832:
1829:
1826:
1820:
1817:
1814:
1805:
1802:
1799:
1790:
1787:
1784:
1778:
1773:
1769:
1762:
1759:
1753:
1747:
1741:
1738:
1730:
1727:
1713:
1691:
1687:
1683:
1680:
1677:
1672:
1668:
1658:
1651:
1647:
1643:
1639:
1635:
1631:
1627:
1623:
1619:
1615:
1611:
1608:
1604:
1600:
1588:
1576:
1564:
1552:
1547:
1546:are used is:
1545:
1540:
1523:
1520:
1517:
1512:
1508:
1501:
1498:
1495:
1487:
1485:
1469:
1466:
1457:
1441:
1438:
1435:
1429:
1426:
1423:
1419:
1412:
1409:
1406:
1403:
1400:
1397:
1394:
1388:
1385:
1382:
1376:
1373:
1370:
1367:
1364:
1361:
1358:
1352:
1349:
1346:
1343:
1339:
1335:
1329:
1326:
1323:
1320:
1317:
1314:
1311:
1305:
1302:
1299:
1293:
1290:
1284:
1281:
1255:
1252:
1243:
1241:
1237:
1228:
1221:
1217:
1213:
1209:
1205:
1201:
1197:
1193:
1189:
1185:
1181:
1177:
1173:
1169:
1165:
1162:
1145:
1142:
1139:
1133:
1130:
1127:
1124:
1101:
1098:
1095:
1092:
1089:
1086:
1083:
1077:
1074:
1071:
1068:
1045:
1042:
1039:
1036:
1033:
1030:
1027:
1021:
1018:
1015:
1012:
989:
986:
983:
977:
974:
971:
968:
965:
959:
956:
950:
947:
939:
931:
929:
922:
917:
913:
910:
907:
904:
901:
898:
897:
896:
890:
888:
886:
870:
867:
847:
827:
824:
804:
801:
792:
779:
773:
770:
767:
761:
758:
755:
749:
746:
740:
737:
734:
725:
722:
719:
713:
710:
707:
701:
698:
692:
689:
681:
678:
675:
669:
666:
660:
651:
648:
645:
639:
636:
633:
627:
624:
618:
615:
607:
604:
601:
595:
592:
589:
583:
580:
574:
571:
568:
562:
559:
556:
550:
547:
541:
535:
529:
526:
518:
504:
501:
481:
472:
459:
453:
450:
447:
441:
438:
435:
429:
426:
423:
417:
414:
411:
405:
402:
399:
393:
390:
387:
381:
378:
375:
369:
366:
363:
357:
354:
351:
345:
342:
339:
333:
330:
324:
321:
313:
311:
295:
292:
280:
264:
261:
258:
255:
252:
249:
246:
243:
240:
237:
234:
227:
224:
208:
205:
202:
195:
192:
176:
173:
170:
163:
160:
144:
141:
138:
130:
114:
111:
108:
101:
100:
99:
80:
73:
64:
57:
55:
53:
48:
46:
41:
39:
35:
31:
27:
23:
19:
2372:
2358:
2346:
2334:
2322:
2310:
2299:. Retrieved
2287:
2277:
2265:
2233:
2214:
2204:
2200:
2158:
2154:
2150:
2146:
2142:
2138:
2134:
2130:
2126:
2122:
2118:
2114:
2110:
2106:
2102:
2098:
2094:
2090:
2086:
2082:
2072:
2068:
2064:
2060:
2056:
2052:
2048:
2044:
2043:if Latitude
2040:
2036:
2032:
2028:
2024:
2020:
2016:
2012:
2008:
2004:
2000:
1996:
1992:
1988:
1984:
1980:
1975:= hav(|
1972:
1968:
1963:= hav(|
1960:
1952:
1944:
1935:
1731:
1728:
1659:
1656:
1645:
1641:
1637:
1633:
1629:
1625:
1621:
1617:
1613:
1609:
1606:
1602:
1598:
1589:= hav(|
1586:
1577:= hav(|
1574:
1565:= hav(|
1562:
1553:= hav(|
1550:
1541:
1488:
1458:
1244:
1233:
1215:
1211:
1207:
1203:
1199:
1195:
1191:
1187:
1183:
1179:
1175:
1171:
1167:
1163:
935:
926:
894:
793:
519:
474:The azimuth
473:
314:
284:
97:
49:
42:
21:
15:
2379:; PDF; 51kB
2133:= 0.1560
2129:= 0.6807
2105:= 0.0128
2101:= 0.2298
2063:< 180°,
2051:> 180°,
2035:< 180°,
2023:> 180°,
1005:, in which
191:declination
2441:Navigation
2435:Categories
2301:2015-11-07
2192:References
2171:Navigation
2077:An example
1585:|)
1561:|)
1236:haversines
938:haversines
2296:0886-0149
2157:= 360° -
2067:= 180° +
2055:= 180° −
2039:= 360° −
2007:) / (1 −
1979:| −
1967:| +
1889:
1883:−
1871:−
1850:
1844:−
1827:−
1806:
1800:−
1779:±
1774:∘
1763:
1742:
1692:∘
1684:⩽
1678:⩽
1673:∘
1518:−
1513:∘
1430:
1424:⋅
1389:
1383:−
1368:−
1353:
1347:−
1321:−
1306:
1285:
1256:
1202:= arcsin(
1134:
1078:
1037:−
1022:
978:⋅
972:−
951:
762:
756:⋅
741:
735:−
714:
708:⋅
693:
670:
640:
634:⋅
619:
596:
590:⋅
575:
569:−
551:
530:
442:
436:⋅
418:
412:⋅
394:
370:
364:⋅
346:
325:
159:longitude
58:Algorithm
2165:See also
2161:= 233.4°
2081:Data:
1959:|)
1640:= 90° −
1597:|)
129:latitude
70:using a
2405:NavList
2047:: if
2019:: if
1628:· (1 −
1482:is the
1240:NavList
98:Given:
72:sextant
45:azimuth
30:sextant
2294:
2209:(2002)
1616:) hav(
1612:= hav(
1459:where
1194:= hav(
1182:= cos(
1170:= cos(
932:Doniol
860:, and
277:, the
221:, the
189:, the
127:, the
82:Using
2271:Paper
2151:North
1999:) = (
26:sight
2292:ISSN
2125::
2097::
1995:hav(
1620:) =
915:pg.)
157:the
2147:LHA
2091:LHA
2087:Dec
2083:Lat
2061:LHA
2059:if
2049:LHA
2033:LHA
2031:if
2021:LHA
1977:Lat
1965:Lat
1957:Dec
1949:Dec
1886:hav
1847:hav
1803:hav
1760:hav
1739:hav
1614:LHA
1595:Dec
1591:Lat
1583:Dec
1579:Lat
1571:Dec
1567:Lat
1559:Dec
1555:Lat
1427:hav
1386:hav
1350:hav
1303:hav
1282:hav
1253:hav
1218:))
1210:⋅ (
1196:LHA
1188:Dec
1184:Lat
1176:Dec
1172:Lat
1161:.
1131:hav
1075:cos
1019:cos
948:sin
759:tan
738:tan
711:cos
690:cos
667:sin
637:cos
616:cos
593:sin
572:sin
548:sin
527:cos
494:or
439:cos
415:cos
391:cos
367:sin
343:sin
322:sin
16:In
2437::
2286:.
2256:;
2252:;
2248:;
2244:;
2240:;
2225:;
2221:;
2155:Zn
2153::
2123:Zn
2119:Hc
2115:ZD
2111:ZD
2095:Hc
2065:Zn
2053:Zn
2037:Zn
2027:=
2025:Zn
2011:)
2003:−
1991:+
1987:=
1983:)
1981:Hc
1971:)
1969:Hc
1770:90
1706:.
1688:90
1642:ZD
1638:Hc
1634:ZD
1632:)
1624:+
1618:ZD
1605:+
1601:=
1509:90
1486:,
1242:.
1214:+
1206:−
1200:Hc
1198:)
1190:)
1186:+
1178:)
1174:−
1117:,
1061:,
840:,
817:.
312::
92:Hc
90:,
86:,
84:Ho
68:Ho
40:.
20:,
2366:.
2304:.
2260:.
2159:Z
2143:Z
2139:Z
2135:n
2131:m
2127:a
2107:n
2103:m
2099:a
2069:Z
2057:Z
2045:S
2041:Z
2029:Z
2017:N
2013:Z
2009:q
2005:n
2001:a
1997:Z
1993:m
1989:n
1985:q
1973:n
1961:m
1953:a
1945:a
1919:)
1916:c
1913:H
1910:+
1907:|
1904:t
1901:a
1898:L
1895:|
1892:(
1880:)
1877:c
1874:H
1868:|
1865:t
1862:a
1859:L
1856:|
1853:(
1841:1
1836:)
1833:c
1830:H
1824:|
1821:t
1818:a
1815:L
1812:|
1809:(
1797:)
1794:|
1791:c
1788:e
1785:D
1782:|
1766:(
1754:=
1751:)
1748:Z
1745:(
1714:Z
1681:Z
1669:0
1630:q
1626:a
1622:n
1610:a
1607:m
1603:n
1599:q
1587:m
1575:n
1563:m
1551:n
1527:)
1524:D
1521:Z
1505:(
1502:=
1499:c
1496:H
1470:D
1467:Z
1445:)
1442:A
1439:H
1436:L
1433:(
1420:)
1416:)
1413:c
1410:e
1407:D
1404:+
1401:t
1398:a
1395:L
1392:(
1380:)
1377:c
1374:e
1371:D
1365:t
1362:a
1359:L
1356:(
1344:1
1340:(
1336:+
1333:)
1330:c
1327:e
1324:D
1318:t
1315:a
1312:L
1309:(
1300:=
1297:)
1294:D
1291:Z
1288:(
1262:)
1259:(
1216:n
1212:m
1208:a
1204:n
1192:a
1180:m
1168:n
1149:)
1146:A
1143:H
1140:L
1137:(
1128:=
1125:a
1105:)
1102:c
1099:e
1096:D
1093:+
1090:t
1087:a
1084:L
1081:(
1072:=
1069:m
1049:)
1046:c
1043:e
1040:D
1034:t
1031:a
1028:L
1025:(
1016:=
1013:n
993:)
990:n
987:+
984:m
981:(
975:a
969:n
966:=
963:)
960:c
957:H
954:(
871:c
868:H
848:Z
828:o
825:H
805:o
802:H
780:.
777:)
774:t
771:a
768:L
765:(
753:)
750:c
747:H
744:(
729:)
726:t
723:a
720:L
717:(
705:)
702:c
699:H
696:(
685:)
682:c
679:e
676:D
673:(
661:=
655:)
652:t
649:a
646:L
643:(
631:)
628:c
625:H
622:(
611:)
608:t
605:a
602:L
599:(
587:)
584:c
581:H
578:(
566:)
563:c
560:e
557:D
554:(
542:=
539:)
536:Z
533:(
505:n
502:Z
482:Z
460:.
457:)
454:A
451:H
448:L
445:(
433:)
430:c
427:e
424:D
421:(
409:)
406:t
403:a
400:L
397:(
388:+
385:)
382:c
379:e
376:D
373:(
361:)
358:t
355:a
352:L
349:(
340:=
337:)
334:c
331:H
328:(
296:c
293:H
265:n
262:o
259:L
256:+
253:A
250:H
247:G
244:=
241:A
238:H
235:L
209:A
206:H
203:G
177:c
174:e
171:D
145:n
142:o
139:L
115:t
112:a
109:L
88:Z
74:.
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