707:
175:) "necessary" and "sufficient" indicate relations between conditions or states of affairs, not statements. For example, being a male is a necessary condition for being a brother, but it is not sufficient—while being a male sibling is a necessary and sufficient condition for being a brother. Any conditional statement consists of at least one sufficient condition and at least one necessary condition.
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That a train runs on schedule can be a sufficient condition for arriving on time (if one boards the train and it departs on time, then one will arrive on time); but it is not always a necessary condition, since there are other ways to travel (if the train does not run to time, one could still arrive
1456:
Psychologically speaking, necessity and sufficiency are both key aspects of the classical view of concepts. Under the classical theory of concepts, how human minds represent a category X, gives rise to a set of individually necessary conditions that define X. Together, these individually necessary
1214:
should be marked with a single large spade (♠) is sufficient for the card to be an ace. Three other sufficient conditions are that the center of the card be marked with a single diamond (♦), heart (♥), or club (♣). None of these conditions is necessary to the card's being an ace, but their
1378:". Another facet of this duality is that, as illustrated above, conjunctions (using "and") of necessary conditions may achieve sufficiency, while disjunctions (using "or") of sufficient conditions may achieve necessity. For a third facet, identify every mathematical
155:
In general, a necessary condition is one (possibly one of several conditions) that must be present in order for another condition to occur, while a sufficient condition is one that produces the said condition. The assertion that a statement is a "necessary
1743:. Thus, discovering whether a graph has any odd cycles tells one whether it is bipartite and conversely. A philosopher might characterize this state of affairs thus: "Although the concepts of bipartiteness and absence of odd cycles differ in
1232:
Being in the purple region is sufficient for being in A, but not necessary. Being in A is necessary for being in the purple region, but not sufficient. Being in A and being in B is necessary and sufficient for being in the purple
1161:" or several other variants. It may be the case that several sufficient conditions, when taken together, constitute a single necessary condition (i.e., individually sufficient and jointly necessary), as illustrated in example 5.
869:
Being at least 30 years old is necessary for serving in the U.S. Senate. If you are under 30 years old, then it is impossible for you to be a senator. That is, if you are a senator, it follows that you must be at least 30 years
815:". One often finds, in mathematical prose for instance, several necessary conditions that, taken together, constitute a sufficient condition (i.e., individually necessary and jointly sufficient), as shown in Example 5.
1457:
conditions are sufficient to be X. This contrasts with the probabilistic theory of concepts which states that no defining feature is necessary or sufficient, rather that categories resemble a family tree structure.
1184:
An occurrence of thunder is a sufficient condition for the occurrence of lightning in the sense that hearing thunder, and unambiguously recognizing it as such, justifies concluding that there has been a lightning
861:
the lightning (since lightning causes thunder), but because lightning always comes with thunder, we say that thunder is necessary for lightning. (That is, in its formal sense, necessity doesn't imply causality.)
1193:
If the U.S. Congress passes a bill, the president's signing of the bill is sufficient to make it law. Note that the case whereby the president did not sign the bill, e.g. through exercising a presidential
856:
Consider thunder, the sound caused by lightning. One says that thunder is necessary for lightning, since lightning never occurs without thunder. Whenever there is lightning, there is thunder. The thunder
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1598:
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The sun being above the horizon is a necessary condition for direct sunlight; but it is not a sufficient condition, as something else may be casting a shadow, e.g., the moon in the case of an
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A number's being divisible by 4 is sufficient (but not necessary) for it to be even, but being divisible by 2 is both sufficient and necessary for it to be even.
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For the whole numbers greater than two, being odd is necessary to being prime, since two is the only whole number that is both even and prime.
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has one endpoint of each color. And for any graph to be bipartite, it is a necessary and sufficient condition that it contain no odd-length
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Because, as explained in previous section, necessity of one for the other is equivalent to sufficiency of the other for the first one, e.g.
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2134:"Necessary conditions in international business research–Advancing the field with a new perspective on causality and data analysis"
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can be used as analytical techniques for examining necessity and sufficiency of conditions for a particular outcome of interest.
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301:. In common language, this is equivalent to saying that if the conditional statement is a true statement, then the consequent
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1168:"John is a king" implies that John is male. So knowing that John is a king is sufficient to knowing that he is a male.
351:(refer again to the third column of the truth table immediately below). If the conditional statement is true, then if
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the latter is true. That is, the two statements must be either simultaneously true, or simultaneously false.
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2105:
Asnina, Erika; Osis, Janis & Jansone, Asnate (2013). "Formal
Specification of Topological Relations".
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This article is about the formal terminology in logic. For causal meanings of the terms, see
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A condition can be either necessary or sufficient without being the other. For instance,
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A condition can be both necessary and sufficient. For example, at present, "today is the
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41:"Necessary But Not Sufficient" redirects here. For the novel by Eliyahu Goldratt, see
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since to state "John is a bachelor" implies John has each of those three additional
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1080:. None of these three necessary conditions by itself is sufficient, but the
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2264:. Contexts in which extension is all that matters are, naturally, called
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One may summarize any, and thus all, of these cases by the statement "
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Sets, Functions and Logic / An
Introduction to Abstract Mathematics
27:
Terms to describe a conditional relationship between two statements
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2334:
1092:
705:
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1195:
2307:
2208:"The Concept of Necessary Conditions and Sufficient Conditions"
2007:
Proofs and
Fundamentals: A First Course in Abstract Mathematics
1727:
if it is possible to assign to each of its vertices the color
1867:{\displaystyle P\Leftrightarrow Q\equiv Q\Leftrightarrow P}
324:
being true. For example, in order for someone to be called
2057:
Managing
Science: Methodology and Organization of Research
1122:
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1320:" is a necessary and sufficient condition for "today is
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2739:
1754:
In mathematics, theorems are often stated in the form "
1350:
Mathematically speaking, necessity and sufficiency are
2268:, while contexts in which extension is not enough are
2132:
Richter, Nicole
Franziska; Hauff, Sven (2022-08-01).
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The logical relation is, as before, expressed as "if
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2180:(3rd ed.), Chapman & Hall, pp. 22–23,
2032:"Confusion of Necessary with a Sufficient Condition"
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182:, necessity and sufficiency can refer to different
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1554:equivalently, it may be understood to say that
2113:(Databases and Information Systems VII): 175.
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1224:Relationship between necessity and sufficiency
2319:
1909:Biological tests of necessity and sufficiency
474:, while the second implication suggests that
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440:(the latter of which can also be written as
2256:"Meanings, in this sense, are often called
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1098:on time through other means of transport).
289:In the above situation of "N whenever S,"
148:not being true does not always imply that
108:. (Equivalently, it is impossible to have
68:or implicational relationship between two
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1982:"[M06] Necessity and sufficiency"
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1461:Simultaneous necessity and sufficiency
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738:, this is the same thing as "whenever
34:. For the concepts in statistics, see
2107:Databases and Information Systems VII
2084:. East Sussex, UK: Psychology Press.
2030:Confusion-of-Necessary (2019-05-15).
1934:Material implication (disambiguation)
1283:) is sufficient but not necessary to
1248:) is necessary but not sufficient to
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1354:to one another. For any statements
1020:there exist a corresponding element
312:is to be true (see third column of "
218:, and the expression represented by
43:Necessary But Not Sufficient (novel)
2501:Analytic and synthetic propositions
2372:Formal semantics (natural language)
2292:Necessary and Sufficient Conditions
2059:. New York: Springer. p. 247.
1600:, which can also be stated as each
1667:{\displaystyle P\Leftrightarrow Q}
1641:{\displaystyle P\Leftrightarrow Q}
1145:". This can also be expressed as "
621:{\displaystyle S\Leftrightarrow N}
519:{\displaystyle S\Leftrightarrow N}
202:In the conditional statement, "if
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1735:in such a way that every edge of
210:", the expression represented by
2713:
2289:Critical thinking web tutorial:
2274:Stanford University primer, 2006
2245:Stanford University primer, 2006
1832:is necessary and sufficient for
1824:is necessary and sufficient for
1475:is necessary and sufficient for
486:is necessary and sufficient for
192:qualitative comparative analysis
1433:is equivalent to claiming that
1405:is equivalent to claiming that
726:is colloquially equivalent to "
140:being true always implies that
1939:Principle of sufficient reason
1858:
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2119:10.3233/978-1-61499-161-8-175
1874:and say that the statements "
1784:{\displaystyle P\Leftarrow Q}
1648:, whereas cases tell us that
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749:The logical relation between
594:{\displaystyle S\Leftarrow N}
478:is a necessary condition for
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64:are terms used to describe a
1562:is necessary for the other,
940:. It is also necessary that
188:necessary condition analysis
2792:
2009:. Springer. pp. 8–9.
1464:
1118:is true; however, knowing
1076:equal the special element
944:include a special element
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2761:Necessity and sufficiency
2708:
2585:Necessity and sufficiency
2341:
2297:Simon Fraser University:
2260:, and things designated,
2154:10.1016/j.jwb.2022.101310
2141:Journal of World Business
2080:Manktelow, K. I. (1999).
1893:is true" are equivalent.
602:
575:
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541:
534:
2776:Mathematical terminology
2055:Betz, Frederick (2011).
2005:Bloch, Ethan D. (2011).
1904:Affirming the consequent
482:. This is expressed as "
385:necessary and sufficient
363:guarantees the truth of
2771:Metaphysical properties
1889:is true if and only if
1758:is true if and only if
1622:", which is denoted by
916:, it is necessary that
320:cannot be true without
120:ensures the falsity of
2299:Concepts with examples
2176:Devlin, Keith (2004),
2082:Reasoning and Thinking
1924:Denying the antecedent
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2650:Mathematical logic
2392:Semantics of logic
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2187:978-1-58488-449-1
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2016:978-1-4419-7126-5
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1929:If and only if
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1919:Closed concept
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1880:if and only if
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1343:has a nonzero
1318:Fourth of July
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495:if and only if
455:
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347:condition for
297:condition for
254:is implied by
222:is called the
214:is called the
199:
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186:logics, where
180:data analytics
162:if and only if
124:.) Similarly,
96:, because the
26:
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14:
13:
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2696:Logic symbols
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2575:Logical truth
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2516:Contradiction
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2502:
2499:
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2464:
2462:
2461:Argumentation
2459:
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2445:Philosophical
2443:
2441:
2440:Non-classical
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2147:(5): 101310.
2146:
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2135:
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2112:
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2101:
2098:
2093:
2091:0-86377-708-2
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2051:
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2026:
2023:
2018:
2012:
2008:
2001:
1998:
1987:
1983:
1977:
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1971:
1964:
1959:
1958:
1957:Modus tollens
1954:
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1793:equivalent to
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1396:
1392:
1388:
1385:with the set
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1361:
1357:
1353:
1348:
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1342:
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1330:invertibility
1327:
1326:United States
1323:
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1125:
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209:
205:
197:
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189:
185:
181:
176:
174:
170:
165:
163:
159:
153:
152:is not true.
144:is true, but
131:
99:
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71:
67:
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55:
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2615:Substitution
2584:
2435:Mathematical
2360:Major fields
2291:
2269:
2265:
2261:
2257:
2252:
2240:
2226:
2215:. Retrieved
2211:
2177:
2171:
2144:
2140:
2127:
2110:
2106:
2100:
2081:
2075:
2056:
2050:
2039:. Retrieved
2035:
2025:
2006:
2000:
1989:. Retrieved
1985:
1955:
1950:Modus ponens
1948:
1890:
1886:
1882:
1875:
1833:
1829:
1825:
1821:
1764:
1759:
1755:
1753:
1736:
1732:
1728:
1720:
1717:graph theory
1714:
1619:
1613:
1611:
1605:
1601:
1559:
1555:
1522:
1518:
1488:
1484:
1476:
1472:
1471:To say that
1470:
1455:
1450:
1446:
1438:
1434:
1430:
1426:
1422:
1418:
1410:
1406:
1402:
1398:
1394:
1390:
1386:
1382:
1375:
1371:
1367:
1363:
1359:
1355:
1349:
1340:
1336:
1315:
1310:
1303:
1280:
1276:
1253:
1249:
1245:
1238:
1236:
1212:playing card
1158:
1154:
1150:
1146:
1142:
1138:
1134:
1130:
1128:
1123:
1119:
1115:
1111:
1107:
1103:
1101:
1077:
1073:
1051:
1047:
1025:
1021:
1017:
1013:
1009:
1005:
983:
979:
957:
953:
949:
945:
941:
886:
858:
812:
808:
804:
800:
796:
792:
788:
784:
780:
774:
770:
766:
762:
758:
754:
750:
748:
743:
739:
731:
727:
723:
719:
717:
530:Truth table
497:
491:
487:
483:
479:
475:
471:
467:
384:
383:
381:
375:
374:
369:
368:
364:
360:
356:
352:
348:
344:
340:
338:
332:
331:
326:
325:
321:
317:
309:
305:
302:
298:
294:
290:
288:
283:
279:
274:
270:
264:
260:
255:
251:
247:
243:
239:
235:
231:
227:
219:
211:
207:
203:
201:
177:
166:
157:
154:
129:
89:
61:
57:
47:
2730:WikiProject
2600:Proposition
2595:Probability
2548:Description
2489:Foundations
2270:intensional
2266:extensional
1762:is true".
1517:, and that
1345:determinant
1306:real number
1277:is rational
1250:being human
1217:disjunction
1089:Sufficiency
1082:conjunction
1008:both equal
938:associative
882:, for some
314:truth table
308:be true—if
198:Definitions
66:conditional
62:sufficiency
54:mathematics
2755:Categories
2660:Set theory
2558:Linguistic
2553:Entailment
2543:Definition
2511:Consequent
2506:Antecedent
2262:extensions
2258:intensions
2217:2019-12-02
2212:www.sfu.ca
2041:2019-12-02
1991:2019-12-02
1965:References
1723:is called
1608:the other.
1465:See also:
1126:is false.
912:to form a
838:predicates
825:unmarried,
345:sufficient
224:consequent
216:antecedent
136:, because
130:sufficient
70:statements
2691:Fallacies
2686:Paradoxes
2676:Logicians
2610:Statement
2605:Reference
2570:Induction
2533:Deduction
2496:Abduction
2466:Metalogic
2413:Classical
2377:Inference
2163:1090-9516
1914:Causality
1859:⇔
1853:≡
1847:⇔
1805:⇒
1776:⇐
1749:extension
1745:intension
1725:bipartite
1697:⇒
1691:∧
1685:⇒
1659:⇔
1633:⇔
1585:⇒
1579:∧
1573:⇒
1536:⇒
1502:⇐
1380:predicate
1207:Example 5
1190:Example 4
1181:Example 3
1173:Example 2
1165:Example 1
1061:⋆
1035:⋆
993:⋆
967:⋆
924:⋆
900:⋆
891:operation
875:Example 5
866:Example 4
853:Example 3
845:Example 2
819:Example 1
803:whenever
702:Necessity
613:⇔
586:⇐
559:⇒
511:⇔
451:⇐
425:⇒
399:⇒
355:is true,
295:necessary
282:whenever
90:necessary
58:necessity
32:Causality
2725:Category
2625:Validity
2526:Antinomy
2454:Theories
2418:Informal
1897:See also
1878:is true
1719:a graph
1415:superset
1339:is that
1304:being a
1239:being a
1200:override
1157:implies
1149:only if
1052:x″
1048:x″
1022:x″
807:", and "
787:only if
246:implies
238:only if
112:without
2740:changes
2732: (
2590:Premise
2521:Paradox
2351:History
2346:Outline
1828:, then
1606:implies
1441:) is a
1413:) is a
1324:in the
1233:region.
1133:, then
880:algebra
778:implies
761:, then
712:eclipse
206:, then
2642:topics
2428:Reason
2406:Logics
2397:Syntax
2184:
2161:
2088:
2063:
2013:
1741:cycles
1443:subset
1334:matrix
1241:mammal
1137:" or "
831:adult,
500:", or
184:causal
171:(also
76:: "If
2669:other
2634:Lists
2620:Truth
2387:Proof
2335:Logic
2137:(PDF)
1820:, if
1733:white
1729:black
1483:that
1332:of a
1185:bolt.
914:group
828:male,
811:when
795:, if
379:ame.
343:is a
278:and "
98:truth
80:then
50:logic
2734:talk
2580:Name
2565:Form
2182:ISBN
2159:ISSN
2086:ISBN
2061:ISBN
2011:ISBN
1558:and
1429:for
1401:for
1358:and
1352:dual
1196:veto
1153:", "
1050:and
982:and
870:old.
799:", "
791:", "
753:and
490:", "
414:and
306:must
250:", "
242:", "
234:", "
190:and
132:for
92:for
60:and
52:and
2476:Set
2149:doi
2115:doi
2111:249
1791:is
1731:or
1604:or
1491:,
1453:).
1445:of
1417:of
1102:If
1016:in
952:in
936:be
884:set
878:In
773:" (
746:".
286:".
258:",
230:if
178:In
167:In
158:and
128:is
100:of
88:is
84:",
48:In
2757::
2210:.
2195:^
2157:.
2145:57
2143:.
2139:.
2109:.
2034:.
1984:.
1973:^
1751:.
1712:.
1525:,
1347:.
1202:).
1141:⇒
769:⇒
695:T
678:F
661:F
644:T
526:.
382:A
273:⇒
268:,
263:→
56:,
2736:)
2327:e
2320:t
2313:v
2276:.
2247:.
2234:.
2220:.
2165:.
2151::
2121:.
2117::
2094:.
2069:.
2044:.
2019:.
1994:.
1891:P
1887:Q
1883:Q
1876:P
1862:P
1856:Q
1850:Q
1844:P
1834:P
1830:Q
1826:Q
1822:P
1808:P
1802:Q
1779:Q
1773:P
1760:Q
1756:P
1737:G
1721:G
1700:P
1694:Q
1688:Q
1682:P
1662:Q
1656:P
1636:Q
1630:P
1620:Q
1614:P
1588:P
1582:Q
1576:Q
1570:P
1560:Q
1556:P
1551:.
1539:Q
1533:P
1523:Q
1519:P
1505:Q
1499:P
1489:Q
1485:P
1477:Q
1473:P
1451:N
1449:(
1447:T
1439:S
1437:(
1435:T
1431:N
1427:S
1423:S
1421:(
1419:T
1411:N
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1407:T
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1399:N
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1264:x
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1159:Q
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1135:Q
1131:P
1124:Q
1120:P
1116:Q
1112:P
1108:Q
1104:P
1078:e
1074:x
1026:x
1018:S
1014:x
1010:x
1006:e
984:x
980:x
958:e
954:S
950:x
946:e
942:S
887:S
840:.
813:P
809:Q
805:P
801:Q
797:P
793:Q
789:Q
785:P
781:Q
775:P
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767:P
763:Q
759:P
755:Q
751:P
744:Q
740:P
732:Q
728:P
724:P
720:Q
714:.
692:T
689:T
686:F
683:F
675:F
672:T
669:T
666:F
658:T
655:F
652:F
649:T
641:T
638:T
635:T
632:T
616:N
610:S
589:N
583:S
562:N
556:S
544:N
537:S
514:N
508:S
498:N
492:S
488:N
484:S
480:N
476:S
472:N
468:S
454:N
448:S
428:S
422:N
402:N
396:S
376:N
370:S
365:N
361:S
357:N
353:S
349:N
341:S
333:N
327:S
322:N
318:S
310:S
303:N
299:S
291:N
284:S
280:N
275:N
271:S
265:N
261:S
256:S
252:N
248:N
244:S
240:N
236:S
232:S
228:N
220:N
212:S
208:N
204:S
150:Q
146:P
142:Q
138:P
134:Q
126:P
122:P
118:Q
114:Q
110:P
106:P
102:Q
94:P
86:Q
82:Q
78:P
45:.
38:.
20:)
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