id sid tid token lemma pos ejpam-4901 1 1 european european PROPN ejpam-4901 1 2 journal journal PROPN ejpam-4901 1 3 of of ADP ejpam-4901 1 4 pure pure ADJ ejpam-4901 1 5 and and CCONJ ejpam-4901 1 6 applied apply VERB ejpam-4901 1 7 mathematics mathematic NOUN ejpam-4901 1 8 vol vol NOUN ejpam-4901 1 9 . . PUNCT ejpam-4901 2 1 16 16 NUM ejpam-4901 2 2 , , PUNCT ejpam-4901 2 3 no no INTJ ejpam-4901 2 4 . . NOUN ejpam-4901 2 5 4 4 NUM ejpam-4901 2 6 , , PUNCT ejpam-4901 2 7 2023 2023 NUM ejpam-4901 2 8 , , PUNCT ejpam-4901 2 9 2751 2751 NUM ejpam-4901 2 10 - - SYM ejpam-4901 2 11 2762 2762 NUM ejpam-4901 2 12 issn issn PROPN ejpam-4901 2 13 1307 1307 NUM ejpam-4901 2 14 - - SYM ejpam-4901 2 15 5543 5543 NUM ejpam-4901 2 16 – – PUNCT ejpam-4901 2 17 ejpam.com ejpam.com X ejpam-4901 2 18 published publish VERB ejpam-4901 2 19 by by ADP ejpam-4901 2 20 new new PROPN ejpam-4901 2 21 york york PROPN ejpam-4901 2 22 business business PROPN ejpam-4901 2 23 global global PROPN ejpam-4901 2 24 on on ADP ejpam-4901 2 25 the the DET ejpam-4901 2 26 number number NOUN ejpam-4901 2 27 of of ADP ejpam-4901 2 28 restricted restrict VERB ejpam-4901 2 29 one one NUM ejpam-4901 2 30 - - PUNCT ejpam-4901 2 31 to to ADP ejpam-4901 2 32 - - PUNCT ejpam-4901 2 33 one one NUM ejpam-4901 2 34 and and CCONJ ejpam-4901 2 35 onto onto ADP ejpam-4901 2 36 functions function NOUN ejpam-4901 2 37 having have VERB ejpam-4901 2 38 integral integral ADJ ejpam-4901 2 39 coordinates coordinate NOUN ejpam-4901 2 40 mary mary PROPN ejpam-4901 2 41 joy joy PROPN ejpam-4901 2 42 r. r. PROPN ejpam-4901 2 43 latayada latayada PROPN ejpam-4901 2 44 department department PROPN ejpam-4901 2 45 of of ADP ejpam-4901 2 46 mathematics mathematic NOUN ejpam-4901 2 47 , , PUNCT ejpam-4901 2 48 caraga caraga PROPN ejpam-4901 2 49 state state PROPN ejpam-4901 2 50 university university PROPN ejpam-4901 2 51 , , PUNCT ejpam-4901 2 52 8600 8600 NUM ejpam-4901 2 53 butuan butuan PROPN ejpam-4901 2 54 city city NOUN ejpam-4901 2 55 , , PUNCT ejpam-4901 3 1 philippines philippine NOUN ejpam-4901 3 2 abstract abstract ADJ ejpam-4901 3 3 . . PUNCT ejpam-4901 4 1 let let VERB ejpam-4901 4 2 nm nm SCONJ ejpam-4901 4 3 be be AUX ejpam-4901 4 4 the the DET ejpam-4901 4 5 set set NOUN ejpam-4901 4 6 of of ADP ejpam-4901 4 7 positive positive ADJ ejpam-4901 4 8 integers integer NOUN ejpam-4901 4 9 1 1 NUM ejpam-4901 4 10 , , PUNCT ejpam-4901 4 11 2 2 NUM ejpam-4901 4 12 , , PUNCT ejpam-4901 4 13 , , PUNCT ejpam-4901 4 14 · · PUNCT ejpam-4901 4 15 · · PUNCT ejpam-4901 4 16 · · PUNCT ejpam-4901 4 17 , , PUNCT ejpam-4901 4 18 m m VERB ejpam-4901 4 19 and and CCONJ ejpam-4901 4 20 s s VERB ejpam-4901 4 21 ⊆ ⊆ NUM ejpam-4901 4 22 nm nm NOUN ejpam-4901 4 23 . . PUNCT ejpam-4901 5 1 in in ADP ejpam-4901 5 2 2000 2000 NUM ejpam-4901 5 3 , , PUNCT ejpam-4901 5 4 j. j. PROPN ejpam-4901 5 5 caumeran caumeran PROPN ejpam-4901 5 6 and and CCONJ ejpam-4901 5 7 r. r. PROPN ejpam-4901 5 8 corcino corcino PROPN ejpam-4901 5 9 made make VERB ejpam-4901 5 10 a a DET ejpam-4901 5 11 thorough thorough ADJ ejpam-4901 5 12 investigation investigation NOUN ejpam-4901 5 13 on on ADP ejpam-4901 5 14 counting count VERB ejpam-4901 5 15 restricted restrict VERB ejpam-4901 5 16 functions function NOUN ejpam-4901 5 17 f|s f|s VERB ejpam-4901 5 18 under under ADP ejpam-4901 5 19 each each PRON ejpam-4901 5 20 of of ADP ejpam-4901 5 21 the the DET ejpam-4901 5 22 following following ADJ ejpam-4901 5 23 conditions condition NOUN ejpam-4901 5 24 : : PUNCT ejpam-4901 5 25 ( ( PUNCT ejpam-4901 5 26 a a X ejpam-4901 5 27 ) ) PUNCT ejpam-4901 5 28 f(a f(a NOUN ejpam-4901 5 29 ) ) PUNCT ejpam-4901 5 30 ≤ ≤ NOUN ejpam-4901 5 31 a a PRON ejpam-4901 5 32 , , PUNCT ejpam-4901 5 33 ∀a ∀a NOUN ejpam-4901 5 34 ∈ ∈ NOUN ejpam-4901 5 35 s s X ejpam-4901 5 36 ; ; PUNCT ejpam-4901 5 37 ( ( PUNCT ejpam-4901 5 38 b b X ejpam-4901 5 39 ) ) PUNCT ejpam-4901 5 40 f(a f(a NOUN ejpam-4901 5 41 ) ) PUNCT ejpam-4901 5 42 ≤ ≤ NOUN ejpam-4901 5 43 g(a g(a PROPN ejpam-4901 5 44 ) ) PUNCT ejpam-4901 5 45 , , PUNCT ejpam-4901 5 46 ∀a ∀a NOUN ejpam-4901 5 47 ∈ ∈ NOUN ejpam-4901 5 48 s s VERB ejpam-4901 5 49 where where SCONJ ejpam-4901 5 50 g g PROPN ejpam-4901 5 51 is be AUX ejpam-4901 5 52 any any DET ejpam-4901 5 53 nonnegative nonnegative ADJ ejpam-4901 5 54 real real ADV ejpam-4901 5 55 - - PUNCT ejpam-4901 5 56 valued value VERB ejpam-4901 5 57 continuous continuous ADJ ejpam-4901 5 58 functions function NOUN ejpam-4901 5 59 ; ; PUNCT ejpam-4901 5 60 ( ( PUNCT ejpam-4901 5 61 c c X ejpam-4901 5 62 ) ) PUNCT ejpam-4901 5 63 g1(a g1(a NOUN ejpam-4901 5 64 ) ) PUNCT ejpam-4901 5 65 ≤ ≤ NUM ejpam-4901 5 66 f(a f(a NOUN ejpam-4901 5 67 ) ) PUNCT ejpam-4901 5 68 ≤ ≤ NUM ejpam-4901 6 1 g2(a g2(a NOUN ejpam-4901 6 2 ) ) PUNCT ejpam-4901 6 3 , , PUNCT ejpam-4901 6 4 ∀a ∀a VERB ejpam-4901 6 5 ∈ ∈ PROPN ejpam-4901 6 6 s s NOUN ejpam-4901 6 7 , , PUNCT ejpam-4901 6 8 where where SCONJ ejpam-4901 6 9 g1 g1 PROPN ejpam-4901 6 10 and and CCONJ ejpam-4901 6 11 g2 g2 PROPN ejpam-4901 6 12 are be AUX ejpam-4901 6 13 any any DET ejpam-4901 6 14 nonnegative nonnegative ADJ ejpam-4901 6 15 real real ADV ejpam-4901 6 16 - - PUNCT ejpam-4901 6 17 valued value VERB ejpam-4901 6 18 continuous continuous ADJ ejpam-4901 6 19 functions function NOUN ejpam-4901 6 20 . . PUNCT ejpam-4901 7 1 several several ADJ ejpam-4901 7 2 formulae formulae NOUN ejpam-4901 7 3 and and CCONJ ejpam-4901 7 4 identities identity NOUN ejpam-4901 7 5 were be AUX ejpam-4901 7 6 also also ADV ejpam-4901 7 7 obtain obtain VERB ejpam-4901 7 8 by by ADP ejpam-4901 7 9 caumeran caumeran NOUN ejpam-4901 7 10 using use VERB ejpam-4901 7 11 basic basic ADJ ejpam-4901 7 12 concepts concept NOUN ejpam-4901 7 13 in in ADP ejpam-4901 7 14 combinatorics combinatoric NOUN ejpam-4901 7 15 . . PUNCT ejpam-4901 8 1 in in ADP ejpam-4901 8 2 this this DET ejpam-4901 8 3 paper paper NOUN ejpam-4901 8 4 we we PRON ejpam-4901 8 5 count count VERB ejpam-4901 8 6 those those DET ejpam-4901 8 7 restricted restrict VERB ejpam-4901 8 8 functions function NOUN ejpam-4901 8 9 under under ADP ejpam-4901 8 10 condition condition NOUN ejpam-4901 8 11 f(a f(a NOUN ejpam-4901 8 12 ) ) PUNCT ejpam-4901 8 13 ≤ ≤ NOUN ejpam-4901 8 14 a a DET ejpam-4901 8 15 , , PUNCT ejpam-4901 8 16 ∀a ∀a NOUN ejpam-4901 8 17 ∈ ∈ NOUN ejpam-4901 8 18 s s X ejpam-4901 8 19 which which PRON ejpam-4901 8 20 is be AUX ejpam-4901 8 21 one one NUM ejpam-4901 8 22 - - PUNCT ejpam-4901 8 23 to to ADP ejpam-4901 8 24 - - PUNCT ejpam-4901 8 25 one one NUM ejpam-4901 8 26 and and CCONJ ejpam-4901 8 27 onto onto ADP ejpam-4901 8 28 and and CCONJ ejpam-4901 8 29 establish establish VERB ejpam-4901 8 30 some some DET ejpam-4901 8 31 formulas formula NOUN ejpam-4901 8 32 and and CCONJ ejpam-4901 8 33 identities identity NOUN ejpam-4901 8 34 parallel parallel ADJ ejpam-4901 8 35 to to ADP ejpam-4901 8 36 those those PRON ejpam-4901 8 37 obtained obtain VERB ejpam-4901 8 38 by by ADP ejpam-4901 8 39 j. j. PROPN ejpam-4901 8 40 caumeran caumeran PROPN ejpam-4901 8 41 and and CCONJ ejpam-4901 8 42 r. r. PROPN ejpam-4901 8 43 corcino corcino PROPN ejpam-4901 8 44 . . PUNCT ejpam-4901 9 1 2020 2020 NUM ejpam-4901 9 2 mathematics mathematics PROPN ejpam-4901 9 3 subject subject NOUN ejpam-4901 9 4 classifications classification NOUN ejpam-4901 9 5 : : PUNCT ejpam-4901 9 6 11b34 11b34 NUM ejpam-4901 9 7 , , PUNCT ejpam-4901 9 8 11b73 11b73 NUM ejpam-4901 9 9 , , PUNCT ejpam-4901 9 10 11b37 11b37 NUM ejpam-4901 9 11 , , PUNCT ejpam-4901 9 12 05a10 05a10 X ejpam-4901 9 13 key key ADJ ejpam-4901 9 14 words word NOUN ejpam-4901 9 15 and and CCONJ ejpam-4901 9 16 phrases phrase NOUN ejpam-4901 9 17 : : PUNCT ejpam-4901 9 18 restricted restricted ADJ ejpam-4901 9 19 function function NOUN ejpam-4901 9 20 , , PUNCT ejpam-4901 9 21 one one NUM ejpam-4901 9 22 - - PUNCT ejpam-4901 9 23 to to ADP ejpam-4901 9 24 - - PUNCT ejpam-4901 9 25 one one NUM ejpam-4901 9 26 function function NOUN ejpam-4901 9 27 , , PUNCT ejpam-4901 9 28 onto onto ADP ejpam-4901 9 29 function function NOUN ejpam-4901 9 30 , , PUNCT ejpam-4901 9 31 stirling stirling NOUN ejpam-4901 9 32 numbers number NOUN ejpam-4901 9 33 of of ADP ejpam-4901 9 34 the the DET ejpam-4901 9 35 second second ADJ ejpam-4901 9 36 kind kind NOUN ejpam-4901 9 37 , , PUNCT ejpam-4901 9 38 restricted restrict VERB ejpam-4901 9 39 onto onto ADP ejpam-4901 9 40 function function NOUN ejpam-4901 9 41 , , PUNCT ejpam-4901 9 42 recurrence recurrence NOUN ejpam-4901 9 43 relation relation NOUN ejpam-4901 9 44 1 1 NUM ejpam-4901 9 45 . . PUNCT ejpam-4901 10 1 introduction introduction NOUN ejpam-4901 10 2 cantor cantor NOUN ejpam-4901 10 3 [ [ X ejpam-4901 10 4 12 12 NUM ejpam-4901 10 5 ] ] PUNCT ejpam-4901 10 6 is be AUX ejpam-4901 10 7 the the DET ejpam-4901 10 8 first first ADJ ejpam-4901 10 9 to to PART ejpam-4901 10 10 consider consider VERB ejpam-4901 10 11 the the DET ejpam-4901 10 12 study study NOUN ejpam-4901 10 13 of of ADP ejpam-4901 10 14 counting counting NOUN ejpam-4901 10 15 functions function NOUN ejpam-4901 10 16 when when SCONJ ejpam-4901 10 17 he he PRON ejpam-4901 10 18 attempted attempt VERB ejpam-4901 10 19 to to PART ejpam-4901 10 20 give give VERB ejpam-4901 10 21 meaning meaning NOUN ejpam-4901 10 22 to to ADP ejpam-4901 10 23 power power NOUN ejpam-4901 10 24 of of ADP ejpam-4901 10 25 cardinal cardinal ADJ ejpam-4901 10 26 numbers number NOUN ejpam-4901 10 27 . . PUNCT ejpam-4901 11 1 cantor cantor PROPN ejpam-4901 11 2 obtained obtain VERB ejpam-4901 11 3 that that SCONJ ejpam-4901 11 4 the the DET ejpam-4901 11 5 number number NOUN ejpam-4901 11 6 of of ADP ejpam-4901 11 7 possible possible ADJ ejpam-4901 11 8 functions function NOUN ejpam-4901 11 9 from from ADP ejpam-4901 11 10 an an DET ejpam-4901 11 11 m m NOUN ejpam-4901 11 12 - - PUNCT ejpam-4901 11 13 set set VERB ejpam-4901 11 14 to to ADP ejpam-4901 11 15 an an DET ejpam-4901 11 16 n n ADV ejpam-4901 11 17 - - PUNCT ejpam-4901 11 18 set set NOUN ejpam-4901 11 19 is be AUX ejpam-4901 11 20 equal equal ADJ ejpam-4901 11 21 to to ADP ejpam-4901 11 22 nm nm NOUN ejpam-4901 11 23 in in ADP ejpam-4901 11 24 which which PRON ejpam-4901 11 25 ( ( PUNCT ejpam-4901 11 26 n)m n)m PUNCT ejpam-4901 11 27 = = PUNCT ejpam-4901 11 28 n(n n(n NOUN ejpam-4901 11 29 − − PROPN ejpam-4901 11 30 1)(n− 1)(n− NUM ejpam-4901 11 31 2 2 NUM ejpam-4901 11 32 ) ) PUNCT ejpam-4901 11 33 . . PUNCT ejpam-4901 11 34 . . PUNCT ejpam-4901 11 35 . . PUNCT ejpam-4901 12 1 ( ( PUNCT ejpam-4901 12 2 n−m+ n−m+ PROPN ejpam-4901 12 3 1 1 NUM ejpam-4901 12 4 ) ) PUNCT ejpam-4901 12 5 of of ADP ejpam-4901 12 6 these these PRON ejpam-4901 12 7 are be AUX ejpam-4901 12 8 one one NUM ejpam-4901 12 9 - - PUNCT ejpam-4901 12 10 to to ADP ejpam-4901 12 11 - - PUNCT ejpam-4901 12 12 one one NUM ejpam-4901 12 13 functions.stirling functions.stirle VERB ejpam-4901 12 14 number number NOUN ejpam-4901 12 15 of of ADP ejpam-4901 12 16 the the DET ejpam-4901 12 17 first first ADJ ejpam-4901 12 18 and and CCONJ ejpam-4901 12 19 second second ADJ ejpam-4901 12 20 kind kind NOUN ejpam-4901 12 21 was be AUX ejpam-4901 12 22 first first ADV ejpam-4901 12 23 introduced introduce VERB ejpam-4901 12 24 by by ADP ejpam-4901 12 25 james james PROPN ejpam-4901 12 26 stirling stirling PROPN ejpam-4901 12 27 published publish VERB ejpam-4901 12 28 in in ADP ejpam-4901 12 29 1730 1730 NUM ejpam-4901 12 30 in in ADP ejpam-4901 12 31 his his PRON ejpam-4901 12 32 book book NOUN ejpam-4901 12 33 methodes methode NOUN ejpam-4901 12 34 differentials differential NOUN ejpam-4901 12 35 . . PUNCT ejpam-4901 13 1 the the DET ejpam-4901 13 2 stirling stirling NOUN ejpam-4901 13 3 numbers number NOUN ejpam-4901 13 4 of of ADP ejpam-4901 13 5 the the DET ejpam-4901 13 6 second second ADJ ejpam-4901 13 7 kind kind NOUN ejpam-4901 13 8 s(n s(n PROPN ejpam-4901 13 9 , , PUNCT ejpam-4901 13 10 m m NOUN ejpam-4901 13 11 ) ) PUNCT ejpam-4901 13 12 count count VERB ejpam-4901 13 13 the the DET ejpam-4901 13 14 number number NOUN ejpam-4901 13 15 of of ADP ejpam-4901 13 16 ways way NOUN ejpam-4901 13 17 of of ADP ejpam-4901 13 18 partitioning partition VERB ejpam-4901 13 19 a a DET ejpam-4901 13 20 set set NOUN ejpam-4901 13 21 containing contain VERB ejpam-4901 13 22 n n DET ejpam-4901 13 23 elements element NOUN ejpam-4901 13 24 into into ADP ejpam-4901 13 25 m m PROPN ejpam-4901 13 26 nonempty nonempty ADJ ejpam-4901 13 27 subsets subset NOUN ejpam-4901 13 28 . . PUNCT ejpam-4901 14 1 by by ADP ejpam-4901 14 2 making make VERB ejpam-4901 14 3 use use NOUN ejpam-4901 14 4 of of ADP ejpam-4901 14 5 the the DET ejpam-4901 14 6 classical classical ADJ ejpam-4901 14 7 stirling stirling NOUN ejpam-4901 14 8 numbers number NOUN ejpam-4901 14 9 of of ADP ejpam-4901 14 10 the the DET ejpam-4901 14 11 second second ADJ ejpam-4901 14 12 kind kind NOUN ejpam-4901 14 13 s(n s(n PROPN ejpam-4901 14 14 , , PUNCT ejpam-4901 14 15 k k NOUN ejpam-4901 14 16 ) ) PUNCT ejpam-4901 14 17 , , PUNCT ejpam-4901 14 18 it it PRON ejpam-4901 14 19 is be AUX ejpam-4901 14 20 shown show VERB ejpam-4901 14 21 that that SCONJ ejpam-4901 14 22 the the DET ejpam-4901 14 23 number number NOUN ejpam-4901 14 24 of of ADP ejpam-4901 14 25 onto onto ADP ejpam-4901 14 26 functions function NOUN ejpam-4901 14 27 is be AUX ejpam-4901 14 28 n!s(m n!s(m ADJ ejpam-4901 14 29 , , PUNCT ejpam-4901 14 30 n n CCONJ ejpam-4901 14 31 ) ) PUNCT ejpam-4901 14 32 ( ( PUNCT ejpam-4901 14 33 see see VERB ejpam-4901 14 34 [ [ X ejpam-4901 14 35 3 3 NUM ejpam-4901 14 36 ] ] NUM ejpam-4901 14 37 ) ) PUNCT ejpam-4901 14 38 . . PUNCT ejpam-4901 15 1 the the DET ejpam-4901 15 2 stirling stirling NOUN ejpam-4901 15 3 numbers number NOUN ejpam-4901 15 4 of of ADP ejpam-4901 15 5 the the DET ejpam-4901 15 6 second second ADJ ejpam-4901 15 7 kind kind NOUN ejpam-4901 15 8 satisfy satisfy VERB ejpam-4901 15 9 the the DET ejpam-4901 15 10 following follow VERB ejpam-4901 15 11 recurrence recurrence NOUN ejpam-4901 15 12 relations relation NOUN ejpam-4901 15 13 and and CCONJ ejpam-4901 15 14 explicit explicit ADJ ejpam-4901 15 15 formula formula NOUN ejpam-4901 15 16 : : PUNCT ejpam-4901 15 17 doi doi NOUN ejpam-4901 15 18 : : PUNCT ejpam-4901 15 19 https://doi.org/10.29020/nybg.ejpam.v16i4.4901 https://doi.org/10.29020/nybg.ejpam.v16i4.4901 PROPN ejpam-4901 15 20 email email NOUN ejpam-4901 15 21 address address NOUN ejpam-4901 15 22 : : PUNCT ejpam-4901 15 23 mrlatayada@carsu.edu.ph(m mrlatayada@carsu.edu.ph(m PROPN ejpam-4901 15 24 . . PROPN ejpam-4901 15 25 j. j. PROPN ejpam-4901 15 26 latayada latayada PROPN ejpam-4901 15 27 ) ) PUNCT ejpam-4901 15 28 https://www.ejpam.com https://www.ejpam.com NOUN ejpam-4901 15 29 2751 2751 NUM ejpam-4901 16 1 © © ADP ejpam-4901 16 2 2023 2023 NUM ejpam-4901 16 3 ejpam ejpam NOUN ejpam-4901 16 4 all all DET ejpam-4901 16 5 rights right NOUN ejpam-4901 16 6 reserved reserve VERB ejpam-4901 16 7 . . PUNCT ejpam-4901 17 1 m. m. NOUN ejpam-4901 17 2 j. j. PROPN ejpam-4901 17 3 latayada latayada PROPN ejpam-4901 17 4 / / SYM ejpam-4901 17 5 eur eur PROPN ejpam-4901 17 6 . . PUNCT ejpam-4901 18 1 j. j. PROPN ejpam-4901 18 2 pure pure PROPN ejpam-4901 18 3 appl appl PROPN ejpam-4901 18 4 . . PROPN ejpam-4901 18 5 math math PROPN ejpam-4901 18 6 , , PUNCT ejpam-4901 18 7 16 16 NUM ejpam-4901 18 8 ( ( PUNCT ejpam-4901 18 9 4 4 NUM ejpam-4901 18 10 ) ) PUNCT ejpam-4901 18 11 ( ( PUNCT ejpam-4901 18 12 2023 2023 NUM ejpam-4901 18 13 ) ) PUNCT ejpam-4901 18 14 , , PUNCT ejpam-4901 18 15 2751 2751 NUM ejpam-4901 18 16 - - SYM ejpam-4901 18 17 2762 2762 NUM ejpam-4901 18 18 2752 2752 NUM ejpam-4901 18 19 ( ( PUNCT ejpam-4901 18 20 i i NOUN ejpam-4901 18 21 ) ) PUNCT ejpam-4901 18 22 s(n s(n PROPN ejpam-4901 18 23 , , PUNCT ejpam-4901 18 24 k k NOUN ejpam-4901 18 25 ) ) PUNCT ejpam-4901 18 26 = = SYM ejpam-4901 18 27 s(n− s(n− PROPN ejpam-4901 18 28 1 1 NUM ejpam-4901 18 29 , , PUNCT ejpam-4901 18 30 k k PROPN ejpam-4901 18 31 − − PROPN ejpam-4901 18 32 1 1 NUM ejpam-4901 18 33 ) ) PUNCT ejpam-4901 18 34 + + CCONJ ejpam-4901 19 1 ks(n− ks(n− PROPN ejpam-4901 19 2 1 1 NUM ejpam-4901 19 3 , , PUNCT ejpam-4901 19 4 k k NOUN ejpam-4901 19 5 ) ) PUNCT ejpam-4901 19 6 , , PUNCT ejpam-4901 19 7 n n CCONJ ejpam-4901 19 8 , , PUNCT ejpam-4901 19 9 k k PROPN ejpam-4901 19 10 ≥ ≥ NUM ejpam-4901 19 11 1 1 NUM ejpam-4901 19 12 . . PUNCT ejpam-4901 20 1 s(n s(n NOUN ejpam-4901 20 2 , , PUNCT ejpam-4901 20 3 0 0 NUM ejpam-4901 20 4 ) ) PUNCT ejpam-4901 20 5 = = SYM ejpam-4901 21 1 s(0 s(0 PROPN ejpam-4901 21 2 , , PUNCT ejpam-4901 21 3 k k NOUN ejpam-4901 21 4 ) ) PUNCT ejpam-4901 21 5 = = SYM ejpam-4901 21 6 0 0 PUNCT ejpam-4901 21 7 except except SCONJ ejpam-4901 21 8 s(0 s(0 PROPN ejpam-4901 21 9 , , PUNCT ejpam-4901 21 10 0 0 NUM ejpam-4901 21 11 ) ) PUNCT ejpam-4901 21 12 = = SYM ejpam-4901 21 13 1.n 1.n NUM ejpam-4901 21 14 , , PUNCT ejpam-4901 21 15 k k PROPN ejpam-4901 21 16 ≥ ≥ NUM ejpam-4901 21 17 1 1 NUM ejpam-4901 21 18 . . PUNCT ejpam-4901 21 19 ( ( PUNCT ejpam-4901 21 20 ii ii NOUN ejpam-4901 21 21 ) ) PUNCT ejpam-4901 21 22 s(n s(n PROPN ejpam-4901 21 23 , , PUNCT ejpam-4901 21 24 k k NOUN ejpam-4901 21 25 ) ) PUNCT ejpam-4901 21 26 = = SYM ejpam-4901 21 27 1 1 NUM ejpam-4901 21 28 k k X ejpam-4901 21 29 ! ! PUNCT ejpam-4901 21 30 k∑ k∑ PROPN ejpam-4901 21 31 j=0 j=0 PROPN ejpam-4901 21 32 ( ( PUNCT ejpam-4901 21 33 −1)j −1)j X ejpam-4901 21 34 ( ( PUNCT ejpam-4901 21 35 k k PROPN ejpam-4901 21 36 j j PROPN ejpam-4901 21 37 ) ) PUNCT ejpam-4901 21 38 ( ( PUNCT ejpam-4901 21 39 k k NOUN ejpam-4901 21 40 − − PROPN ejpam-4901 21 41 j)n j)n NOUN ejpam-4901 21 42 = = PUNCT ejpam-4901 21 43 1 1 NUM ejpam-4901 21 44 k k X ejpam-4901 21 45 ! ! PUNCT ejpam-4901 21 46 k∑ k∑ PROPN ejpam-4901 22 1 i=0 i=0 PROPN ejpam-4901 22 2 ( ( PUNCT ejpam-4901 22 3 −1)k−i −1)k−i X ejpam-4901 22 4 ( ( PUNCT ejpam-4901 22 5 k k NOUN ejpam-4901 22 6 i i PROPN ejpam-4901 22 7 ) ) PUNCT ejpam-4901 22 8 ( ( PUNCT ejpam-4901 22 9 i)n i)n X ejpam-4901 22 10 . . PUNCT ejpam-4901 23 1 using use VERB ejpam-4901 23 2 these these DET ejpam-4901 23 3 identities identity NOUN ejpam-4901 23 4 , , PUNCT ejpam-4901 23 5 we we PRON ejpam-4901 23 6 can can AUX ejpam-4901 23 7 easily easily ADV ejpam-4901 23 8 construct construct VERB ejpam-4901 23 9 the the DET ejpam-4901 23 10 following follow VERB ejpam-4901 23 11 table table NOUN ejpam-4901 23 12 of of ADP ejpam-4901 23 13 values value NOUN ejpam-4901 23 14 of of ADP ejpam-4901 23 15 s(n s(n PROPN ejpam-4901 23 16 , , PUNCT ejpam-4901 23 17 k k NOUN ejpam-4901 23 18 ): ): PUNCT ejpam-4901 23 19 @ @ ADP ejpam-4901 23 20 @ @ ADP ejpam-4901 23 21 @n @n NOUN ejpam-4901 23 22 k k NOUN ejpam-4901 23 23 0 0 NUM ejpam-4901 23 24 1 1 NUM ejpam-4901 23 25 2 2 NUM ejpam-4901 23 26 3 3 NUM ejpam-4901 23 27 4 4 NUM ejpam-4901 23 28 5 5 NUM ejpam-4901 23 29 6 6 NUM ejpam-4901 23 30 0 0 NUM ejpam-4901 23 31 0 0 NUM ejpam-4901 23 32 1 1 NUM ejpam-4901 23 33 0 0 NUM ejpam-4901 23 34 1 1 NUM ejpam-4901 23 35 2 2 NUM ejpam-4901 23 36 0 0 NUM ejpam-4901 23 37 1 1 NUM ejpam-4901 23 38 1 1 NUM ejpam-4901 23 39 3 3 NUM ejpam-4901 23 40 0 0 NUM ejpam-4901 23 41 1 1 NUM ejpam-4901 23 42 3 3 NUM ejpam-4901 23 43 1 1 NUM ejpam-4901 23 44 4 4 NUM ejpam-4901 23 45 0 0 NUM ejpam-4901 23 46 1 1 NUM ejpam-4901 23 47 7 7 NUM ejpam-4901 23 48 6 6 NUM ejpam-4901 23 49 1 1 NUM ejpam-4901 23 50 5 5 NUM ejpam-4901 23 51 0 0 NUM ejpam-4901 23 52 1 1 NUM ejpam-4901 23 53 15 15 NUM ejpam-4901 23 54 25 25 NUM ejpam-4901 23 55 10 10 NUM ejpam-4901 23 56 1 1 NUM ejpam-4901 23 57 6 6 NUM ejpam-4901 23 58 0 0 NUM ejpam-4901 23 59 1 1 NUM ejpam-4901 23 60 31 31 NUM ejpam-4901 23 61 90 90 NUM ejpam-4901 23 62 65 65 NUM ejpam-4901 23 63 15 15 NUM ejpam-4901 23 64 1 1 NUM ejpam-4901 23 65 table table NOUN ejpam-4901 23 66 1 1 NUM ejpam-4901 23 67 : : PUNCT ejpam-4901 23 68 values value NOUN ejpam-4901 23 69 of of ADP ejpam-4901 23 70 s(n s(n PROPN ejpam-4901 23 71 , , PUNCT ejpam-4901 23 72 k k NOUN ejpam-4901 23 73 ) ) PUNCT ejpam-4901 23 74 for for ADP ejpam-4901 23 75 0 0 NUM ejpam-4901 23 76 ≤ ≤ NUM ejpam-4901 23 77 n n DET ejpam-4901 23 78 ≤ ≤ NUM ejpam-4901 23 79 6 6 NUM ejpam-4901 23 80 the the DET ejpam-4901 23 81 stirling stirling NOUN ejpam-4901 23 82 numbers number NOUN ejpam-4901 23 83 of of ADP ejpam-4901 23 84 the the DET ejpam-4901 23 85 second second ADJ ejpam-4901 23 86 kind kind NOUN ejpam-4901 23 87 has have AUX ejpam-4901 23 88 been be AUX ejpam-4901 23 89 generalized generalize VERB ejpam-4901 23 90 by by ADP ejpam-4901 23 91 introducing introduce VERB ejpam-4901 23 92 two two NUM ejpam-4901 23 93 parameters parameter NOUN ejpam-4901 23 94 r r NOUN ejpam-4901 23 95 and and CCONJ ejpam-4901 23 96 β β NOUN ejpam-4901 23 97 . . PUNCT ejpam-4901 24 1 these these DET ejpam-4901 24 2 generalized generalized ADJ ejpam-4901 24 3 numbers number NOUN ejpam-4901 24 4 are be AUX ejpam-4901 24 5 referred refer VERB ejpam-4901 24 6 to to ADP ejpam-4901 24 7 as as ADP ejpam-4901 24 8 ( ( PUNCT ejpam-4901 24 9 r r NOUN ejpam-4901 24 10 , , PUNCT ejpam-4901 24 11 β)− β)− PUNCT ejpam-4901 24 12 stirling stirling NOUN ejpam-4901 24 13 numbers number NOUN ejpam-4901 24 14 , , PUNCT ejpam-4901 24 15 denoted denote VERB ejpam-4901 24 16 by by ADP ejpam-4901 24 17 sr sr PROPN ejpam-4901 24 18 , , PUNCT ejpam-4901 24 19 β(n β(n PROPN ejpam-4901 24 20 , , PUNCT ejpam-4901 24 21 k k NOUN ejpam-4901 24 22 ) ) PUNCT ejpam-4901 24 23 . . PUNCT ejpam-4901 25 1 they they PRON ejpam-4901 25 2 were be AUX ejpam-4901 25 3 introduced introduce VERB ejpam-4901 25 4 by by ADP ejpam-4901 25 5 r. r. PROPN ejpam-4901 25 6 corcino corcino PROPN ejpam-4901 26 1 [ [ X ejpam-4901 26 2 6 6 NUM ejpam-4901 26 3 ] ] PUNCT ejpam-4901 26 4 as as ADP ejpam-4901 26 5 coefficient coefficient NOUN ejpam-4901 26 6 of of ADP ejpam-4901 26 7 the the DET ejpam-4901 26 8 explicit explicit ADJ ejpam-4901 26 9 formula formula NOUN ejpam-4901 26 10 : : PUNCT ejpam-4901 26 11 sr sr PROPN ejpam-4901 26 12 , , PUNCT ejpam-4901 26 13 β(n β(n PROPN ejpam-4901 26 14 , , PUNCT ejpam-4901 26 15 k k NOUN ejpam-4901 26 16 ) ) PUNCT ejpam-4901 26 17 = = SYM ejpam-4901 26 18 1 1 NUM ejpam-4901 26 19 βk βk NOUN ejpam-4901 26 20 ! ! PROPN ejpam-4901 26 21 k∑ k∑ PROPN ejpam-4901 27 1 j=0 j=0 PROPN ejpam-4901 27 2 ( ( PUNCT ejpam-4901 27 3 −1)k−j −1)k−j X ejpam-4901 27 4 ( ( PUNCT ejpam-4901 27 5 k k PROPN ejpam-4901 27 6 j j PROPN ejpam-4901 27 7 ) ) PUNCT ejpam-4901 27 8 ( ( PUNCT ejpam-4901 27 9 βj βj X ejpam-4901 27 10 + + X ejpam-4901 27 11 r)n r)n X ejpam-4901 27 12 . . PUNCT ejpam-4901 28 1 in in ADP ejpam-4901 28 2 [ [ X ejpam-4901 28 3 2 2 NUM ejpam-4901 28 4 ] ] PUNCT ejpam-4901 28 5 , , PUNCT ejpam-4901 28 6 it it PRON ejpam-4901 28 7 was be AUX ejpam-4901 28 8 obtained obtain VERB ejpam-4901 28 9 that that SCONJ ejpam-4901 28 10 the the DET ejpam-4901 28 11 number number NOUN ejpam-4901 28 12 of of ADP ejpam-4901 28 13 restricted restricted ADJ ejpam-4901 28 14 functions function NOUN ejpam-4901 28 15 f f PROPN ejpam-4901 28 16 |s |s PROPN ejpam-4901 28 17 : : PUNCT ejpam-4901 28 18 nm nm ADV ejpam-4901 28 19 −→ −→ NOUN ejpam-4901 28 20 nn nn INTJ ejpam-4901 28 21 for for ADP ejpam-4901 28 22 all all PRON ejpam-4901 28 23 s s PART ejpam-4901 28 24 ⊆ ⊆ NUM ejpam-4901 28 25 nm nm NOUN ejpam-4901 28 26 where where SCONJ ejpam-4901 28 27 nm nm ADV ejpam-4901 28 28 = = PUNCT ejpam-4901 28 29 { { PUNCT ejpam-4901 28 30 1 1 NUM ejpam-4901 28 31 , , PUNCT ejpam-4901 28 32 2 2 NUM ejpam-4901 28 33 , , PUNCT ejpam-4901 28 34 . . PUNCT ejpam-4901 28 35 . . PUNCT ejpam-4901 29 1 . . PUNCT ejpam-4901 30 1 , , PUNCT ejpam-4901 30 2 m m AUX ejpam-4901 30 3 } } PUNCT ejpam-4901 30 4 is be AUX ejpam-4901 30 5 equal equal ADJ ejpam-4901 30 6 to to ADP ejpam-4901 30 7 ( ( PUNCT ejpam-4901 30 8 n+ n+ NOUN ejpam-4901 30 9 1)m 1)m NUM ejpam-4901 30 10 . . PUNCT ejpam-4901 31 1 r. r. PROPN ejpam-4901 31 2 corcino corcino PROPN ejpam-4901 31 3 et et PROPN ejpam-4901 31 4 al al PROPN ejpam-4901 31 5 . . PUNCT ejpam-4901 32 1 [ [ X ejpam-4901 32 2 7 7 X ejpam-4901 32 3 ] ] PUNCT ejpam-4901 32 4 established establish VERB ejpam-4901 32 5 some some DET ejpam-4901 32 6 formulas formula NOUN ejpam-4901 32 7 in in ADP ejpam-4901 32 8 counting count VERB ejpam-4901 32 9 restricted restrict VERB ejpam-4901 32 10 functions function NOUN ejpam-4901 32 11 f f PROPN ejpam-4901 32 12 |s |s PROPN ejpam-4901 32 13 : : PUNCT ejpam-4901 32 14 nm nm ADV ejpam-4901 32 15 −→ −→ NOUN ejpam-4901 32 16 n n NOUN ejpam-4901 32 17 , , PUNCT ejpam-4901 32 18 s s VERB ejpam-4901 32 19 ⊆ ⊆ NUM ejpam-4901 32 20 nm nm NOUN ejpam-4901 32 21 under under ADP ejpam-4901 32 22 each each PRON ejpam-4901 32 23 of of ADP ejpam-4901 32 24 the the DET ejpam-4901 32 25 following following ADJ ejpam-4901 32 26 conditions condition NOUN ejpam-4901 32 27 : : PUNCT ejpam-4901 32 28 ( ( PUNCT ejpam-4901 32 29 i i NOUN ejpam-4901 32 30 ) ) PUNCT ejpam-4901 32 31 f(a f(a PROPN ejpam-4901 32 32 ) ) PUNCT ejpam-4901 32 33 ≤ ≤ NOUN ejpam-4901 32 34 a a PRON ejpam-4901 32 35 , , PUNCT ejpam-4901 32 36 ∀a ∀a NOUN ejpam-4901 32 37 ∈ ∈ NOUN ejpam-4901 32 38 s s NOUN ejpam-4901 32 39 ; ; PUNCT ejpam-4901 32 40 ( ( PUNCT ejpam-4901 32 41 ii ii NOUN ejpam-4901 32 42 ) ) PUNCT ejpam-4901 32 43 f(a f(a PROPN ejpam-4901 32 44 ) ) PUNCT ejpam-4901 32 45 ≤ ≤ NOUN ejpam-4901 32 46 g(a g(a PROPN ejpam-4901 32 47 ) ) PUNCT ejpam-4901 32 48 , , PUNCT ejpam-4901 32 49 ∀a ∀a NOUN ejpam-4901 32 50 ∈ ∈ NOUN ejpam-4901 32 51 s s VERB ejpam-4901 32 52 where where SCONJ ejpam-4901 32 53 g g PROPN ejpam-4901 32 54 is be AUX ejpam-4901 32 55 any any DET ejpam-4901 32 56 nonnegative nonnegative ADJ ejpam-4901 32 57 real real ADV ejpam-4901 32 58 - - PUNCT ejpam-4901 32 59 valued value VERB ejpam-4901 32 60 continuous continuous ADJ ejpam-4901 32 61 functions function NOUN ejpam-4901 32 62 ; ; PUNCT ejpam-4901 32 63 ( ( PUNCT ejpam-4901 32 64 iii iii X ejpam-4901 32 65 ) ) PUNCT ejpam-4901 32 66 g1(a g1(a NOUN ejpam-4901 32 67 ) ) PUNCT ejpam-4901 32 68 ≤ ≤ NUM ejpam-4901 32 69 f(a f(a NOUN ejpam-4901 32 70 ) ) PUNCT ejpam-4901 32 71 ≤ ≤ NUM ejpam-4901 33 1 g2(a g2(a NOUN ejpam-4901 33 2 ) ) PUNCT ejpam-4901 33 3 , , PUNCT ejpam-4901 33 4 ∀a ∀a VERB ejpam-4901 33 5 ∈ ∈ PROPN ejpam-4901 33 6 s s NOUN ejpam-4901 33 7 , , PUNCT ejpam-4901 33 8 where where SCONJ ejpam-4901 33 9 g1 g1 PROPN ejpam-4901 33 10 and and CCONJ ejpam-4901 33 11 g2 g2 PROPN ejpam-4901 33 12 are be AUX ejpam-4901 33 13 any any DET ejpam-4901 33 14 nonnegative nonnegative ADJ ejpam-4901 33 15 real real ADV ejpam-4901 33 16 - - PUNCT ejpam-4901 33 17 valued value VERB ejpam-4901 33 18 continuous continuous ADJ ejpam-4901 33 19 functions function NOUN ejpam-4901 33 20 . . PUNCT ejpam-4901 34 1 in in ADP ejpam-4901 34 2 this this DET ejpam-4901 34 3 paper paper NOUN ejpam-4901 34 4 , , PUNCT ejpam-4901 34 5 we we PRON ejpam-4901 34 6 count count VERB ejpam-4901 34 7 those those DET ejpam-4901 34 8 restricted restrict VERB ejpam-4901 34 9 functions function NOUN ejpam-4901 34 10 considered consider VERB ejpam-4901 34 11 by by ADP ejpam-4901 34 12 caumeran caumeran NOUN ejpam-4901 34 13 [ [ X ejpam-4901 34 14 2 2 X ejpam-4901 34 15 ] ] PUNCT ejpam-4901 34 16 under under ADP ejpam-4901 34 17 condition condition NOUN ejpam-4901 34 18 ( ( PUNCT ejpam-4901 34 19 i i NOUN ejpam-4901 34 20 ) ) PUNCT ejpam-4901 34 21 which which PRON ejpam-4901 34 22 is be AUX ejpam-4901 34 23 one one NUM ejpam-4901 34 24 - - PUNCT ejpam-4901 34 25 to to ADP ejpam-4901 34 26 - - PUNCT ejpam-4901 34 27 one one NUM ejpam-4901 34 28 and and CCONJ ejpam-4901 34 29 also also ADV ejpam-4901 34 30 onto onto ADP ejpam-4901 34 31 . . PUNCT ejpam-4901 35 1 it it PRON ejpam-4901 35 2 is be AUX ejpam-4901 35 3 known know VERB ejpam-4901 35 4 that that SCONJ ejpam-4901 35 5 the the DET ejpam-4901 35 6 number number NOUN ejpam-4901 35 7 of of ADP ejpam-4901 35 8 one one NUM ejpam-4901 35 9 - - PUNCT ejpam-4901 35 10 to to ADP ejpam-4901 35 11 - - PUNCT ejpam-4901 35 12 one one NUM ejpam-4901 35 13 m. m. NOUN ejpam-4901 35 14 j. j. PROPN ejpam-4901 35 15 latayada latayada PROPN ejpam-4901 35 16 / / SYM ejpam-4901 35 17 eur eur PROPN ejpam-4901 35 18 . . PUNCT ejpam-4901 36 1 j. j. PROPN ejpam-4901 36 2 pure pure PROPN ejpam-4901 36 3 appl appl PROPN ejpam-4901 36 4 . . PROPN ejpam-4901 36 5 math math PROPN ejpam-4901 36 6 , , PUNCT ejpam-4901 36 7 16 16 NUM ejpam-4901 36 8 ( ( PUNCT ejpam-4901 36 9 4 4 NUM ejpam-4901 36 10 ) ) PUNCT ejpam-4901 36 11 ( ( PUNCT ejpam-4901 36 12 2023 2023 NUM ejpam-4901 36 13 ) ) PUNCT ejpam-4901 36 14 , , PUNCT ejpam-4901 36 15 2751 2751 NUM ejpam-4901 36 16 - - SYM ejpam-4901 36 17 2762 2762 NUM ejpam-4901 36 18 2753 2753 NUM ejpam-4901 36 19 functions function NOUN ejpam-4901 36 20 that that PRON ejpam-4901 36 21 can can AUX ejpam-4901 36 22 be be AUX ejpam-4901 36 23 formed form VERB ejpam-4901 36 24 from from ADP ejpam-4901 36 25 a a PRON ejpam-4901 36 26 to to ADP ejpam-4901 36 27 b b NOUN ejpam-4901 36 28 where where SCONJ ejpam-4901 36 29 |a| |a| NOUN ejpam-4901 36 30 = = PUNCT ejpam-4901 36 31 n n PROPN ejpam-4901 36 32 and and CCONJ ejpam-4901 36 33 |b| |b| PROPN ejpam-4901 37 1 = = PUNCT ejpam-4901 37 2 m m VERB ejpam-4901 37 3 is be AUX ejpam-4901 37 4 equal equal ADJ ejpam-4901 37 5 to to ADP ejpam-4901 37 6 m(m− m(m− PROPN ejpam-4901 37 7 1)(m− 1)(m− PROPN ejpam-4901 37 8 2 2 NUM ejpam-4901 37 9 ) ) PUNCT ejpam-4901 37 10 · · PUNCT ejpam-4901 37 11 · · PUNCT ejpam-4901 37 12 · · PUNCT ejpam-4901 37 13 ( ( PUNCT ejpam-4901 37 14 m− m− PROPN ejpam-4901 37 15 n+ n+ PUNCT ejpam-4901 37 16 1 1 NUM ejpam-4901 37 17 ) ) PUNCT ejpam-4901 37 18 . . PUNCT ejpam-4901 38 1 on on ADP ejpam-4901 38 2 the the DET ejpam-4901 38 3 other other ADJ ejpam-4901 38 4 hand hand NOUN ejpam-4901 38 5 , , PUNCT ejpam-4901 38 6 the the DET ejpam-4901 38 7 number number NOUN ejpam-4901 38 8 of of ADP ejpam-4901 38 9 onto onto ADP ejpam-4901 38 10 functions function NOUN ejpam-4901 38 11 f f PROPN ejpam-4901 38 12 |s |s PROPN ejpam-4901 38 13 : : PUNCT ejpam-4901 38 14 nn nn INTJ ejpam-4901 38 15 −→ −→ NOUN ejpam-4901 38 16 nm nm NOUN ejpam-4901 38 17 that that PRON ejpam-4901 38 18 can can AUX ejpam-4901 38 19 be be AUX ejpam-4901 38 20 formed form VERB ejpam-4901 38 21 is be AUX ejpam-4901 38 22 m m NOUN ejpam-4901 38 23 ! ! PUNCT ejpam-4901 38 24 · · PUNCT ejpam-4901 39 1 s(n s(n PROPN ejpam-4901 39 2 , , PUNCT ejpam-4901 39 3 m m NOUN ejpam-4901 39 4 ) ) PUNCT ejpam-4901 39 5 , , PUNCT ejpam-4901 39 6 where where SCONJ ejpam-4901 39 7 nn nn X ejpam-4901 39 8 = = SYM ejpam-4901 39 9 { { PUNCT ejpam-4901 39 10 1 1 NUM ejpam-4901 39 11 , , PUNCT ejpam-4901 39 12 2 2 NUM ejpam-4901 39 13 , , PUNCT ejpam-4901 39 14 3 3 NUM ejpam-4901 39 15 , , PUNCT ejpam-4901 39 16 · · PUNCT ejpam-4901 39 17 · · PUNCT ejpam-4901 39 18 · · PUNCT ejpam-4901 39 19 , , PUNCT ejpam-4901 39 20 n n CCONJ ejpam-4901 39 21 } } PUNCT ejpam-4901 39 22 and and CCONJ ejpam-4901 39 23 s(n s(n PROPN ejpam-4901 39 24 , , PUNCT ejpam-4901 39 25 m m NOUN ejpam-4901 39 26 ) ) PUNCT ejpam-4901 39 27 , , PUNCT ejpam-4901 39 28 denotes denote VERB ejpam-4901 39 29 the the DET ejpam-4901 39 30 stirling stirling NOUN ejpam-4901 39 31 numbers number NOUN ejpam-4901 39 32 of of ADP ejpam-4901 39 33 the the DET ejpam-4901 39 34 second second ADJ ejpam-4901 39 35 kind kind NOUN ejpam-4901 39 36 satisfying satisfy VERB ejpam-4901 39 37 the the DET ejpam-4901 39 38 relation relation NOUN ejpam-4901 39 39 xn xn PUNCT ejpam-4901 40 1 = = SYM ejpam-4901 40 2 m∑ m∑ CCONJ ejpam-4901 40 3 i=0 i=0 PROPN ejpam-4901 40 4 s(n s(n PROPN ejpam-4901 40 5 , , PUNCT ejpam-4901 40 6 i)(x)i i)(x)i ADP ejpam-4901 40 7 , , PUNCT ejpam-4901 40 8 where where SCONJ ejpam-4901 40 9 ( ( PUNCT ejpam-4901 40 10 x)i x)i PUNCT ejpam-4901 40 11 = = SYM ejpam-4901 40 12 x(x x(x PROPN ejpam-4901 41 1 − − PROPN ejpam-4901 41 2 1(x 1(x NUM ejpam-4901 41 3 − − NOUN ejpam-4901 41 4 2 2 NUM ejpam-4901 41 5 ) ) PUNCT ejpam-4901 41 6 · · PUNCT ejpam-4901 41 7 · · PUNCT ejpam-4901 41 8 · · PUNCT ejpam-4901 42 1 ( ( PUNCT ejpam-4901 42 2 x x X ejpam-4901 42 3 − − VERB ejpam-4901 42 4 i i PRON ejpam-4901 42 5 + + NOUN ejpam-4901 42 6 1 1 NUM ejpam-4901 42 7 ) ) PUNCT ejpam-4901 42 8 . . PUNCT ejpam-4901 43 1 it it PRON ejpam-4901 43 2 is be AUX ejpam-4901 43 3 observed observe VERB ejpam-4901 43 4 that that SCONJ ejpam-4901 43 5 the the DET ejpam-4901 43 6 process process NOUN ejpam-4901 43 7 of of ADP ejpam-4901 43 8 counting count VERB ejpam-4901 43 9 onto onto ADP ejpam-4901 43 10 functions function NOUN ejpam-4901 43 11 makes make VERB ejpam-4901 43 12 use use NOUN ejpam-4901 43 13 of of ADP ejpam-4901 43 14 the the DET ejpam-4901 43 15 multiplication multiplication NOUN ejpam-4901 43 16 principle principle NOUN ejpam-4901 43 17 and and CCONJ ejpam-4901 43 18 the the DET ejpam-4901 43 19 appropriate appropriate ADJ ejpam-4901 43 20 application application NOUN ejpam-4901 43 21 of of ADP ejpam-4901 43 22 stirling stirling NOUN ejpam-4901 43 23 numbers number NOUN ejpam-4901 43 24 of of ADP ejpam-4901 43 25 the the DET ejpam-4901 43 26 second second ADJ ejpam-4901 43 27 kind kind NOUN ejpam-4901 43 28 . . PUNCT ejpam-4901 44 1 the the DET ejpam-4901 44 2 process process NOUN ejpam-4901 44 3 of of ADP ejpam-4901 44 4 obtaining obtain VERB ejpam-4901 44 5 one one NUM ejpam-4901 44 6 - - PUNCT ejpam-4901 44 7 to to ADP ejpam-4901 44 8 - - PUNCT ejpam-4901 44 9 one one NUM ejpam-4901 44 10 and and CCONJ ejpam-4901 44 11 onto onto ADP ejpam-4901 44 12 functions function NOUN ejpam-4901 44 13 may may AUX ejpam-4901 44 14 be be AUX ejpam-4901 44 15 applicable applicable ADJ ejpam-4901 44 16 in in ADP ejpam-4901 44 17 counting count VERB ejpam-4901 44 18 restricted restrict VERB ejpam-4901 44 19 one one NUM ejpam-4901 44 20 - - PUNCT ejpam-4901 44 21 to to ADP ejpam-4901 44 22 - - PUNCT ejpam-4901 44 23 one one NUM ejpam-4901 44 24 and and CCONJ ejpam-4901 44 25 onto onto ADP ejpam-4901 44 26 functions function NOUN ejpam-4901 44 27 . . PUNCT ejpam-4901 45 1 recall recall VERB ejpam-4901 45 2 that that PRON ejpam-4901 45 3 , , PUNCT ejpam-4901 45 4 for for ADP ejpam-4901 45 5 a a DET ejpam-4901 45 6 finite finite NOUN ejpam-4901 45 7 sets set VERB ejpam-4901 45 8 a a DET ejpam-4901 45 9 and and CCONJ ejpam-4901 45 10 b b NOUN ejpam-4901 45 11 , , PUNCT ejpam-4901 45 12 a a DET ejpam-4901 45 13 function function NOUN ejpam-4901 45 14 f f NOUN ejpam-4901 45 15 : : PUNCT ejpam-4901 45 16 a a DET ejpam-4901 45 17 −→ −→ NOUN ejpam-4901 45 18 b b NOUN ejpam-4901 45 19 is be AUX ejpam-4901 45 20 said say VERB ejpam-4901 45 21 to to PART ejpam-4901 45 22 be be AUX ejpam-4901 45 23 onto onto ADP ejpam-4901 45 24 if if SCONJ ejpam-4901 45 25 f(a f(a NOUN ejpam-4901 45 26 ) ) PUNCT ejpam-4901 46 1 = = SYM ejpam-4901 46 2 b. b. PROPN ejpam-4901 46 3 hence hence ADV ejpam-4901 46 4 , , PUNCT ejpam-4901 46 5 in in ADP ejpam-4901 46 6 order order NOUN ejpam-4901 46 7 for for ADP ejpam-4901 46 8 the the DET ejpam-4901 46 9 function function NOUN ejpam-4901 46 10 f f PROPN ejpam-4901 46 11 to to PART ejpam-4901 46 12 be be AUX ejpam-4901 46 13 onto onto ADP ejpam-4901 46 14 , , PUNCT ejpam-4901 46 15 |a| |a| PROPN ejpam-4901 46 16 must must AUX ejpam-4901 46 17 be be AUX ejpam-4901 46 18 greater great ADJ ejpam-4901 46 19 than than ADP ejpam-4901 46 20 or or CCONJ ejpam-4901 46 21 equal equal ADJ ejpam-4901 46 22 to to ADP ejpam-4901 46 23 |b| |b| PROPN ejpam-4901 46 24 . . PROPN ejpam-4901 46 25 2 2 NUM ejpam-4901 46 26 . . X ejpam-4901 46 27 number number NOUN ejpam-4901 46 28 of of ADP ejpam-4901 46 29 restricted restrict VERB ejpam-4901 46 30 one one NUM ejpam-4901 46 31 - - PUNCT ejpam-4901 46 32 to to ADP ejpam-4901 46 33 - - PUNCT ejpam-4901 46 34 one one NUM ejpam-4901 46 35 functions function NOUN ejpam-4901 46 36 let let VERB ejpam-4901 46 37 si si PART ejpam-4901 46 38 be be AUX ejpam-4901 46 39 a a DET ejpam-4901 46 40 subset subset NOUN ejpam-4901 46 41 of of ADP ejpam-4901 46 42 nm nm NOUN ejpam-4901 46 43 and and CCONJ ejpam-4901 47 1 |si| |si| PROPN ejpam-4901 47 2 = = SYM ejpam-4901 47 3 i. i. NOUN ejpam-4901 47 4 the the DET ejpam-4901 47 5 number number NOUN ejpam-4901 47 6 of of ADP ejpam-4901 47 7 restricted restrict VERB ejpam-4901 47 8 one one NUM ejpam-4901 47 9 - - PUNCT ejpam-4901 47 10 to to ADP ejpam-4901 47 11 - - PUNCT ejpam-4901 47 12 one one NUM ejpam-4901 47 13 functions function NOUN ejpam-4901 47 14 f f PROPN ejpam-4901 47 15 |s |s PROPN ejpam-4901 47 16 : : PUNCT ejpam-4901 47 17 nm nm ADV ejpam-4901 47 18 −→ −→ NOUN ejpam-4901 47 19 nn nn INTJ ejpam-4901 47 20 for for ADP ejpam-4901 47 21 all all PRON ejpam-4901 47 22 s s PART ejpam-4901 47 23 ⊆ ⊆ NUM ejpam-4901 47 24 nm nm NOUN ejpam-4901 47 25 is be AUX ejpam-4901 47 26 n(n− n(n− PROPN ejpam-4901 47 27 1)(n− 1)(n− PROPN ejpam-4901 47 28 2 2 NUM ejpam-4901 47 29 ) ) PUNCT ejpam-4901 47 30 . . PUNCT ejpam-4901 47 31 . . PUNCT ejpam-4901 47 32 . . PUNCT ejpam-4901 48 1 ( ( PUNCT ejpam-4901 48 2 n− n− NOUN ejpam-4901 48 3 ( ( PUNCT ejpam-4901 48 4 i− i− PROPN ejpam-4901 48 5 1 1 NUM ejpam-4901 48 6 ) ) PUNCT ejpam-4901 48 7 ) ) PUNCT ejpam-4901 49 1 = = SYM ejpam-4901 49 2 ( ( PUNCT ejpam-4901 49 3 n)i n)i PUNCT ejpam-4901 49 4 . . PUNCT ejpam-4901 50 1 let let VERB ejpam-4901 50 2 îm îm ADJ ejpam-4901 50 3 = = SYM ejpam-4901 50 4 ⋃m ⋃m NOUN ejpam-4901 50 5 i=0 i=0 PROPN ejpam-4901 50 6 îi îi PROPN ejpam-4901 50 7 , , PUNCT ejpam-4901 50 8 m. m. NOUN ejpam-4901 50 9 then then ADV ejpam-4901 50 10 îm îm VERB ejpam-4901 50 11 = = SYM ejpam-4901 50 12 ⋃ ⋃ PROPN ejpam-4901 50 13 si⊆nm si⊆nm NOUN ejpam-4901 50 14 { { PUNCT ejpam-4901 50 15 f f X ejpam-4901 50 16 |si |si X ejpam-4901 50 17 : : PUNCT ejpam-4901 50 18 f f X ejpam-4901 50 19 is be AUX ejpam-4901 50 20 a a DET ejpam-4901 50 21 one one NUM ejpam-4901 50 22 - - PUNCT ejpam-4901 50 23 to to ADP ejpam-4901 50 24 - - PUNCT ejpam-4901 50 25 one one NUM ejpam-4901 50 26 function function NOUN ejpam-4901 50 27 } } PUNCT ejpam-4901 50 28 . . PUNCT ejpam-4901 51 1 the the DET ejpam-4901 51 2 number number NOUN ejpam-4901 51 3 of of ADP ejpam-4901 51 4 subsets subset NOUN ejpam-4901 51 5 of of ADP ejpam-4901 51 6 nm nm NOUN ejpam-4901 51 7 containing contain VERB ejpam-4901 51 8 i i PRON ejpam-4901 51 9 elements element NOUN ejpam-4901 51 10 is be AUX ejpam-4901 51 11 ( ( PUNCT ejpam-4901 51 12 m m VERB ejpam-4901 51 13 i i NOUN ejpam-4901 51 14 ) ) PUNCT ejpam-4901 51 15 and and CCONJ ejpam-4901 51 16 |îm| |îm| PROPN ejpam-4901 51 17 = = PROPN ejpam-4901 51 18 m∑ m∑ CCONJ ejpam-4901 51 19 i=0 i=0 PROPN ejpam-4901 51 20 ∣∣î(n)i ∣∣î(n)i PROPN ejpam-4901 51 21 , , PUNCT ejpam-4901 51 22 m m VERB ejpam-4901 51 23 ∣∣ ∣∣ NUM ejpam-4901 51 24 = = PUNCT ejpam-4901 51 25 m∑ m∑ CCONJ ejpam-4901 51 26 i=0 i=0 PROPN ejpam-4901 51 27 ∣∣∣∣ ∣∣∣∣ PROPN ejpam-4901 51 28 ⋃ ⋃ PROPN ejpam-4901 51 29 si⊆nm si⊆nm NOUN ejpam-4901 51 30 { { PUNCT ejpam-4901 51 31 f f X ejpam-4901 51 32 |si |si X ejpam-4901 51 33 : : PUNCT ejpam-4901 51 34 f f X ejpam-4901 51 35 is be AUX ejpam-4901 51 36 a a DET ejpam-4901 51 37 one one NUM ejpam-4901 51 38 - - PUNCT ejpam-4901 51 39 to to ADP ejpam-4901 51 40 - - PUNCT ejpam-4901 51 41 one one NUM ejpam-4901 51 42 function function NOUN ejpam-4901 51 43 } } PUNCT ejpam-4901 51 44 ∣∣∣∣ ∣∣∣∣ NOUN ejpam-4901 51 45 implying imply VERB ejpam-4901 51 46 that that SCONJ ejpam-4901 51 47 |îm| |îm| PROPN ejpam-4901 51 48 = = SYM ejpam-4901 51 49 m∑ m∑ NOUN ejpam-4901 51 50 i=0 i=0 PROPN ejpam-4901 51 51 ( ( PUNCT ejpam-4901 51 52 m m VERB ejpam-4901 51 53 i i NOUN ejpam-4901 51 54 ) ) PUNCT ejpam-4901 51 55 ( ( PUNCT ejpam-4901 51 56 n)i n)i X ejpam-4901 51 57 . . NOUN ejpam-4901 51 58 to to PART ejpam-4901 51 59 state state VERB ejpam-4901 51 60 this this DET ejpam-4901 51 61 result result NOUN ejpam-4901 51 62 formally formally ADV ejpam-4901 51 63 , , PUNCT ejpam-4901 51 64 we we PRON ejpam-4901 51 65 have have VERB ejpam-4901 51 66 the the DET ejpam-4901 51 67 following follow VERB ejpam-4901 51 68 proposition proposition NOUN ejpam-4901 51 69 . . PUNCT ejpam-4901 52 1 proposition proposition NOUN ejpam-4901 52 2 1 1 NUM ejpam-4901 52 3 . . PUNCT ejpam-4901 53 1 let let VERB ejpam-4901 53 2 f f PROPN ejpam-4901 53 3 |s |s PROPN ejpam-4901 53 4 : : PUNCT ejpam-4901 53 5 nm nm ADV ejpam-4901 53 6 −→ −→ NOUN ejpam-4901 53 7 nn nn INTJ ejpam-4901 53 8 such such ADJ ejpam-4901 54 1 that that SCONJ ejpam-4901 54 2 m m VERB ejpam-4901 54 3 ≤ ≤ ADJ ejpam-4901 54 4 n. n. NOUN ejpam-4901 54 5 if if SCONJ ejpam-4901 54 6 îm îm ADV ejpam-4901 54 7 = = SYM ejpam-4901 54 8 ⋃m ⋃m NOUN ejpam-4901 54 9 i=0 i=0 PROPN ejpam-4901 54 10 ŷi ŷi PROPN ejpam-4901 54 11 , , PUNCT ejpam-4901 54 12 m m VERB ejpam-4901 54 13 where where SCONJ ejpam-4901 54 14 îm îm ADV ejpam-4901 54 15 = = PUNCT ejpam-4901 54 16 { { PUNCT ejpam-4901 54 17 f f X ejpam-4901 54 18 |si |si X ejpam-4901 54 19 : : PUNCT ejpam-4901 54 20 si si PROPN ejpam-4901 54 21 ⊆ ⊆ NUM ejpam-4901 54 22 nm nm NOUN ejpam-4901 54 23 and and CCONJ ejpam-4901 54 24 f f PROPN ejpam-4901 54 25 is be AUX ejpam-4901 54 26 a a DET ejpam-4901 54 27 one one NUM ejpam-4901 54 28 - - PUNCT ejpam-4901 54 29 to to ADP ejpam-4901 54 30 - - PUNCT ejpam-4901 54 31 one one NUM ejpam-4901 54 32 function function NOUN ejpam-4901 54 33 } } PUNCT ejpam-4901 54 34 , , PUNCT ejpam-4901 54 35 then then ADV ejpam-4901 54 36 |îm| |îm| PROPN ejpam-4901 54 37 = = PUNCT ejpam-4901 54 38 m∑ m∑ VERB ejpam-4901 54 39 i=0 i=0 PROPN ejpam-4901 54 40 ( ( PUNCT ejpam-4901 54 41 m m VERB ejpam-4901 54 42 i i NOUN ejpam-4901 54 43 ) ) PUNCT ejpam-4901 54 44 ( ( PUNCT ejpam-4901 54 45 n)i n)i PROPN ejpam-4901 54 46 . . PUNCT ejpam-4901 54 47 m. m. PROPN ejpam-4901 54 48 j. j. PROPN ejpam-4901 54 49 latayada latayada PROPN ejpam-4901 54 50 / / SYM ejpam-4901 54 51 eur eur PROPN ejpam-4901 54 52 . . PUNCT ejpam-4901 55 1 j. j. PROPN ejpam-4901 55 2 pure pure PROPN ejpam-4901 55 3 appl appl PROPN ejpam-4901 55 4 . . PROPN ejpam-4901 55 5 math math PROPN ejpam-4901 55 6 , , PUNCT ejpam-4901 55 7 16 16 NUM ejpam-4901 55 8 ( ( PUNCT ejpam-4901 55 9 4 4 NUM ejpam-4901 55 10 ) ) PUNCT ejpam-4901 55 11 ( ( PUNCT ejpam-4901 55 12 2023 2023 NUM ejpam-4901 55 13 ) ) PUNCT ejpam-4901 55 14 , , PUNCT ejpam-4901 55 15 2751 2751 NUM ejpam-4901 55 16 - - SYM ejpam-4901 55 17 2762 2762 NUM ejpam-4901 55 18 2754 2754 NUM ejpam-4901 55 19 example example NOUN ejpam-4901 56 1 1 1 NUM ejpam-4901 56 2 . . PUNCT ejpam-4901 57 1 if if SCONJ ejpam-4901 57 2 m m ADV ejpam-4901 57 3 = = SYM ejpam-4901 57 4 3 3 NUM ejpam-4901 57 5 and and CCONJ ejpam-4901 57 6 n n NOUN ejpam-4901 58 1 = = NOUN ejpam-4901 58 2 4 4 NUM ejpam-4901 58 3 we we PRON ejpam-4901 58 4 have have VERB ejpam-4901 58 5 n3 n3 NOUN ejpam-4901 58 6 = = SYM ejpam-4901 58 7 1 1 NUM ejpam-4901 58 8 , , PUNCT ejpam-4901 58 9 2 2 NUM ejpam-4901 58 10 , , PUNCT ejpam-4901 58 11 3 3 NUM ejpam-4901 58 12 and and CCONJ ejpam-4901 58 13 n4 n4 PROPN ejpam-4901 58 14 = = PROPN ejpam-4901 58 15 1 1 NUM ejpam-4901 58 16 , , PUNCT ejpam-4901 58 17 2 2 NUM ejpam-4901 58 18 , , PUNCT ejpam-4901 58 19 3 3 NUM ejpam-4901 58 20 , , PUNCT ejpam-4901 58 21 4 4 NUM ejpam-4901 58 22 . . X ejpam-4901 59 1 for for ADP ejpam-4901 59 2 i i PRON ejpam-4901 59 3 = = SYM ejpam-4901 59 4 0 0 NUM ejpam-4901 59 5 , , PUNCT ejpam-4901 59 6 s0 s0 PROPN ejpam-4901 59 7 = = PUNCT ejpam-4901 59 8 { { PUNCT ejpam-4901 59 9 } } PUNCT ejpam-4901 59 10 , , PUNCT ejpam-4901 59 11 f f PROPN ejpam-4901 59 12 |s0 |s0 PROPN ejpam-4901 59 13 = = X ejpam-4901 59 14 { { PUNCT ejpam-4901 59 15 } } PUNCT ejpam-4901 59 16 is be AUX ejpam-4901 59 17 the the DET ejpam-4901 59 18 only only ADJ ejpam-4901 59 19 one one NUM ejpam-4901 59 20 - - PUNCT ejpam-4901 59 21 to to ADP ejpam-4901 59 22 - - PUNCT ejpam-4901 59 23 one one NUM ejpam-4901 59 24 function function NOUN ejpam-4901 59 25 . . PUNCT ejpam-4901 60 1 for for ADP ejpam-4901 60 2 i i PRON ejpam-4901 60 3 = = SYM ejpam-4901 60 4 1 1 NUM ejpam-4901 60 5 , , PUNCT ejpam-4901 60 6 si si X ejpam-4901 60 7 = = PUNCT ejpam-4901 60 8 { { PUNCT ejpam-4901 60 9 1 1 NUM ejpam-4901 60 10 } } PUNCT ejpam-4901 60 11 , , PUNCT ejpam-4901 60 12 { { PUNCT ejpam-4901 60 13 2 2 NUM ejpam-4901 60 14 } } PUNCT ejpam-4901 60 15 , , PUNCT ejpam-4901 60 16 { { PUNCT ejpam-4901 60 17 3 3 NUM ejpam-4901 60 18 } } PUNCT ejpam-4901 60 19 , , PUNCT ejpam-4901 60 20 the the DET ejpam-4901 60 21 one one NUM ejpam-4901 60 22 - - PUNCT ejpam-4901 60 23 to to ADP ejpam-4901 60 24 - - PUNCT ejpam-4901 60 25 one one NUM ejpam-4901 60 26 functions function NOUN ejpam-4901 60 27 are be AUX ejpam-4901 60 28 { { PUNCT ejpam-4901 60 29 ( ( PUNCT ejpam-4901 60 30 1 1 NUM ejpam-4901 60 31 , , PUNCT ejpam-4901 60 32 1 1 NUM ejpam-4901 60 33 ) ) PUNCT ejpam-4901 60 34 } } PUNCT ejpam-4901 60 35 { { PUNCT ejpam-4901 60 36 ( ( PUNCT ejpam-4901 60 37 1 1 NUM ejpam-4901 60 38 , , PUNCT ejpam-4901 60 39 2 2 NUM ejpam-4901 60 40 ) ) PUNCT ejpam-4901 60 41 } } PUNCT ejpam-4901 60 42 { { PUNCT ejpam-4901 60 43 ( ( PUNCT ejpam-4901 60 44 1 1 NUM ejpam-4901 60 45 , , PUNCT ejpam-4901 60 46 3 3 NUM ejpam-4901 60 47 ) ) PUNCT ejpam-4901 60 48 } } PUNCT ejpam-4901 60 49 { { PUNCT ejpam-4901 60 50 ( ( PUNCT ejpam-4901 60 51 1 1 NUM ejpam-4901 60 52 , , PUNCT ejpam-4901 60 53 4 4 NUM ejpam-4901 60 54 ) ) PUNCT ejpam-4901 60 55 } } PUNCT ejpam-4901 60 56 { { PUNCT ejpam-4901 60 57 ( ( PUNCT ejpam-4901 60 58 2 2 NUM ejpam-4901 60 59 , , PUNCT ejpam-4901 60 60 1 1 NUM ejpam-4901 60 61 ) ) PUNCT ejpam-4901 60 62 } } PUNCT ejpam-4901 60 63 { { PUNCT ejpam-4901 60 64 ( ( PUNCT ejpam-4901 60 65 2 2 NUM ejpam-4901 60 66 , , PUNCT ejpam-4901 60 67 2 2 NUM ejpam-4901 60 68 ) ) PUNCT ejpam-4901 60 69 } } PUNCT ejpam-4901 60 70 { { PUNCT ejpam-4901 60 71 ( ( PUNCT ejpam-4901 60 72 2 2 NUM ejpam-4901 60 73 , , PUNCT ejpam-4901 60 74 3 3 NUM ejpam-4901 60 75 ) ) PUNCT ejpam-4901 60 76 } } PUNCT ejpam-4901 60 77 { { PUNCT ejpam-4901 60 78 ( ( PUNCT ejpam-4901 60 79 2 2 NUM ejpam-4901 60 80 , , PUNCT ejpam-4901 60 81 4 4 NUM ejpam-4901 60 82 ) ) PUNCT ejpam-4901 60 83 } } PUNCT ejpam-4901 60 84 { { PUNCT ejpam-4901 60 85 ( ( PUNCT ejpam-4901 60 86 3 3 NUM ejpam-4901 60 87 , , PUNCT ejpam-4901 60 88 1 1 NUM ejpam-4901 60 89 ) ) PUNCT ejpam-4901 60 90 } } PUNCT ejpam-4901 60 91 { { PUNCT ejpam-4901 60 92 ( ( PUNCT ejpam-4901 60 93 3 3 NUM ejpam-4901 60 94 , , PUNCT ejpam-4901 60 95 2 2 NUM ejpam-4901 60 96 ) ) PUNCT ejpam-4901 60 97 } } PUNCT ejpam-4901 60 98 { { PUNCT ejpam-4901 60 99 ( ( PUNCT ejpam-4901 60 100 3 3 NUM ejpam-4901 60 101 , , PUNCT ejpam-4901 60 102 3 3 NUM ejpam-4901 60 103 ) ) PUNCT ejpam-4901 60 104 } } PUNCT ejpam-4901 60 105 { { PUNCT ejpam-4901 60 106 ( ( PUNCT ejpam-4901 60 107 3 3 NUM ejpam-4901 60 108 , , PUNCT ejpam-4901 60 109 4 4 NUM ejpam-4901 60 110 ) ) PUNCT ejpam-4901 60 111 } } PUNCT ejpam-4901 60 112 for for ADP ejpam-4901 60 113 i i PROPN ejpam-4901 60 114 = = SYM ejpam-4901 60 115 2 2 NUM ejpam-4901 60 116 , , PUNCT ejpam-4901 60 117 si si X ejpam-4901 60 118 = = SYM ejpam-4901 60 119 { { PUNCT ejpam-4901 60 120 1 1 NUM ejpam-4901 60 121 , , PUNCT ejpam-4901 60 122 2 2 NUM ejpam-4901 60 123 } } PUNCT ejpam-4901 60 124 , , PUNCT ejpam-4901 60 125 { { PUNCT ejpam-4901 60 126 1 1 NUM ejpam-4901 60 127 , , PUNCT ejpam-4901 60 128 3 3 NUM ejpam-4901 60 129 } } PUNCT ejpam-4901 60 130 , , PUNCT ejpam-4901 60 131 { { PUNCT ejpam-4901 60 132 2 2 NUM ejpam-4901 60 133 , , PUNCT ejpam-4901 60 134 3 3 NUM ejpam-4901 60 135 } } PUNCT ejpam-4901 60 136 , , PUNCT ejpam-4901 60 137 the the DET ejpam-4901 60 138 one one NUM ejpam-4901 60 139 - - PUNCT ejpam-4901 60 140 to to ADP ejpam-4901 60 141 - - PUNCT ejpam-4901 60 142 one one NUM ejpam-4901 60 143 functions function NOUN ejpam-4901 60 144 are be AUX ejpam-4901 60 145 { { PUNCT ejpam-4901 60 146 ( ( PUNCT ejpam-4901 60 147 1 1 NUM ejpam-4901 60 148 , , PUNCT ejpam-4901 60 149 1 1 NUM ejpam-4901 60 150 ) ) PUNCT ejpam-4901 60 151 , , PUNCT ejpam-4901 60 152 ( ( PUNCT ejpam-4901 60 153 2 2 NUM ejpam-4901 60 154 , , PUNCT ejpam-4901 60 155 2 2 NUM ejpam-4901 60 156 ) ) PUNCT ejpam-4901 60 157 } } PUNCT ejpam-4901 60 158 { { PUNCT ejpam-4901 60 159 ( ( PUNCT ejpam-4901 60 160 1 1 NUM ejpam-4901 60 161 , , PUNCT ejpam-4901 60 162 2 2 NUM ejpam-4901 60 163 ) ) PUNCT ejpam-4901 60 164 , , PUNCT ejpam-4901 60 165 ( ( PUNCT ejpam-4901 60 166 2 2 NUM ejpam-4901 60 167 , , PUNCT ejpam-4901 60 168 1 1 NUM ejpam-4901 60 169 ) ) PUNCT ejpam-4901 60 170 } } PUNCT ejpam-4901 60 171 { { PUNCT ejpam-4901 60 172 ( ( PUNCT ejpam-4901 60 173 1 1 NUM ejpam-4901 60 174 , , PUNCT ejpam-4901 60 175 3 3 NUM ejpam-4901 60 176 ) ) PUNCT ejpam-4901 60 177 , , PUNCT ejpam-4901 60 178 ( ( PUNCT ejpam-4901 60 179 2 2 NUM ejpam-4901 60 180 , , PUNCT ejpam-4901 60 181 1 1 NUM ejpam-4901 60 182 ) ) PUNCT ejpam-4901 60 183 } } PUNCT ejpam-4901 60 184 { { PUNCT ejpam-4901 60 185 ( ( PUNCT ejpam-4901 60 186 1 1 NUM ejpam-4901 60 187 , , PUNCT ejpam-4901 60 188 4 4 NUM ejpam-4901 60 189 ) ) PUNCT ejpam-4901 60 190 , , PUNCT ejpam-4901 60 191 ( ( PUNCT ejpam-4901 60 192 2 2 NUM ejpam-4901 60 193 , , PUNCT ejpam-4901 60 194 1 1 NUM ejpam-4901 60 195 ) ) PUNCT ejpam-4901 60 196 } } PUNCT ejpam-4901 60 197 { { PUNCT ejpam-4901 60 198 ( ( PUNCT ejpam-4901 60 199 1 1 NUM ejpam-4901 60 200 , , PUNCT ejpam-4901 60 201 1 1 NUM ejpam-4901 60 202 ) ) PUNCT ejpam-4901 60 203 , , PUNCT ejpam-4901 60 204 ( ( PUNCT ejpam-4901 60 205 2 2 NUM ejpam-4901 60 206 , , PUNCT ejpam-4901 60 207 3 3 NUM ejpam-4901 60 208 ) ) PUNCT ejpam-4901 60 209 } } PUNCT ejpam-4901 60 210 { { PUNCT ejpam-4901 60 211 ( ( PUNCT ejpam-4901 60 212 1 1 NUM ejpam-4901 60 213 , , PUNCT ejpam-4901 60 214 2 2 NUM ejpam-4901 60 215 ) ) PUNCT ejpam-4901 60 216 , , PUNCT ejpam-4901 60 217 ( ( PUNCT ejpam-4901 60 218 2 2 NUM ejpam-4901 60 219 , , PUNCT ejpam-4901 60 220 3 3 NUM ejpam-4901 60 221 ) ) PUNCT ejpam-4901 60 222 } } PUNCT ejpam-4901 60 223 { { PUNCT ejpam-4901 60 224 ( ( PUNCT ejpam-4901 60 225 1 1 NUM ejpam-4901 60 226 , , PUNCT ejpam-4901 60 227 3 3 NUM ejpam-4901 60 228 ) ) PUNCT ejpam-4901 60 229 , , PUNCT ejpam-4901 60 230 ( ( PUNCT ejpam-4901 60 231 2 2 NUM ejpam-4901 60 232 , , PUNCT ejpam-4901 60 233 2 2 NUM ejpam-4901 60 234 ) ) PUNCT ejpam-4901 60 235 } } PUNCT ejpam-4901 60 236 { { PUNCT ejpam-4901 60 237 ( ( PUNCT ejpam-4901 60 238 1 1 NUM ejpam-4901 60 239 , , PUNCT ejpam-4901 60 240 4 4 NUM ejpam-4901 60 241 ) ) PUNCT ejpam-4901 60 242 , , PUNCT ejpam-4901 60 243 ( ( PUNCT ejpam-4901 60 244 2 2 NUM ejpam-4901 60 245 , , PUNCT ejpam-4901 60 246 2 2 NUM ejpam-4901 60 247 ) ) PUNCT ejpam-4901 60 248 } } PUNCT ejpam-4901 60 249 { { PUNCT ejpam-4901 60 250 ( ( PUNCT ejpam-4901 60 251 1 1 NUM ejpam-4901 60 252 , , PUNCT ejpam-4901 60 253 1 1 NUM ejpam-4901 60 254 ) ) PUNCT ejpam-4901 60 255 , , PUNCT ejpam-4901 60 256 ( ( PUNCT ejpam-4901 60 257 2 2 NUM ejpam-4901 60 258 , , PUNCT ejpam-4901 60 259 4 4 NUM ejpam-4901 60 260 ) ) PUNCT ejpam-4901 60 261 } } PUNCT ejpam-4901 60 262 { { PUNCT ejpam-4901 60 263 ( ( PUNCT ejpam-4901 60 264 1 1 NUM ejpam-4901 60 265 , , PUNCT ejpam-4901 60 266 2 2 NUM ejpam-4901 60 267 ) ) PUNCT ejpam-4901 60 268 , , PUNCT ejpam-4901 60 269 ( ( PUNCT ejpam-4901 60 270 2 2 NUM ejpam-4901 60 271 , , PUNCT ejpam-4901 60 272 4 4 NUM ejpam-4901 60 273 ) ) PUNCT ejpam-4901 60 274 } } PUNCT ejpam-4901 60 275 { { PUNCT ejpam-4901 60 276 ( ( PUNCT ejpam-4901 60 277 1 1 NUM ejpam-4901 60 278 , , PUNCT ejpam-4901 60 279 3 3 NUM ejpam-4901 60 280 ) ) PUNCT ejpam-4901 60 281 , , PUNCT ejpam-4901 60 282 ( ( PUNCT ejpam-4901 60 283 2 2 NUM ejpam-4901 60 284 , , PUNCT ejpam-4901 60 285 4 4 NUM ejpam-4901 60 286 ) ) PUNCT ejpam-4901 60 287 } } PUNCT ejpam-4901 60 288 { { PUNCT ejpam-4901 60 289 ( ( PUNCT ejpam-4901 60 290 1 1 NUM ejpam-4901 60 291 , , PUNCT ejpam-4901 60 292 4 4 NUM ejpam-4901 60 293 ) ) PUNCT ejpam-4901 60 294 , , PUNCT ejpam-4901 60 295 ( ( PUNCT ejpam-4901 60 296 2 2 NUM ejpam-4901 60 297 , , PUNCT ejpam-4901 60 298 3 3 NUM ejpam-4901 60 299 ) ) PUNCT ejpam-4901 60 300 } } PUNCT ejpam-4901 60 301 { { PUNCT ejpam-4901 60 302 ( ( PUNCT ejpam-4901 60 303 1 1 NUM ejpam-4901 60 304 , , PUNCT ejpam-4901 60 305 1 1 NUM ejpam-4901 60 306 ) ) PUNCT ejpam-4901 60 307 , , PUNCT ejpam-4901 60 308 ( ( PUNCT ejpam-4901 60 309 3 3 NUM ejpam-4901 60 310 , , PUNCT ejpam-4901 60 311 2 2 NUM ejpam-4901 60 312 ) ) PUNCT ejpam-4901 60 313 } } PUNCT ejpam-4901 60 314 { { PUNCT ejpam-4901 60 315 ( ( PUNCT ejpam-4901 60 316 1 1 NUM ejpam-4901 60 317 , , PUNCT ejpam-4901 60 318 2 2 NUM ejpam-4901 60 319 ) ) PUNCT ejpam-4901 60 320 , , PUNCT ejpam-4901 60 321 ( ( PUNCT ejpam-4901 60 322 3 3 NUM ejpam-4901 60 323 , , PUNCT ejpam-4901 60 324 1 1 NUM ejpam-4901 60 325 ) ) PUNCT ejpam-4901 60 326 } } PUNCT ejpam-4901 60 327 { { PUNCT ejpam-4901 60 328 ( ( PUNCT ejpam-4901 60 329 1 1 NUM ejpam-4901 60 330 , , PUNCT ejpam-4901 60 331 3 3 NUM ejpam-4901 60 332 ) ) PUNCT ejpam-4901 60 333 , , PUNCT ejpam-4901 60 334 ( ( PUNCT ejpam-4901 60 335 3 3 NUM ejpam-4901 60 336 , , PUNCT ejpam-4901 60 337 1 1 NUM ejpam-4901 60 338 ) ) PUNCT ejpam-4901 60 339 } } PUNCT ejpam-4901 60 340 { { PUNCT ejpam-4901 60 341 ( ( PUNCT ejpam-4901 60 342 1 1 NUM ejpam-4901 60 343 , , PUNCT ejpam-4901 60 344 4 4 NUM ejpam-4901 60 345 ) ) PUNCT ejpam-4901 60 346 , , PUNCT ejpam-4901 60 347 ( ( PUNCT ejpam-4901 60 348 3 3 NUM ejpam-4901 60 349 , , PUNCT ejpam-4901 60 350 1 1 NUM ejpam-4901 60 351 ) ) PUNCT ejpam-4901 60 352 } } PUNCT ejpam-4901 60 353 { { PUNCT ejpam-4901 60 354 ( ( PUNCT ejpam-4901 60 355 1 1 NUM ejpam-4901 60 356 , , PUNCT ejpam-4901 60 357 1 1 NUM ejpam-4901 60 358 ) ) PUNCT ejpam-4901 60 359 , , PUNCT ejpam-4901 60 360 ( ( PUNCT ejpam-4901 60 361 3 3 NUM ejpam-4901 60 362 , , PUNCT ejpam-4901 60 363 3 3 NUM ejpam-4901 60 364 ) ) PUNCT ejpam-4901 60 365 } } PUNCT ejpam-4901 60 366 { { PUNCT ejpam-4901 60 367 ( ( PUNCT ejpam-4901 60 368 1 1 NUM ejpam-4901 60 369 , , PUNCT ejpam-4901 60 370 2 2 NUM ejpam-4901 60 371 ) ) PUNCT ejpam-4901 60 372 , , PUNCT ejpam-4901 60 373 ( ( PUNCT ejpam-4901 60 374 3 3 NUM ejpam-4901 60 375 , , PUNCT ejpam-4901 60 376 3 3 NUM ejpam-4901 60 377 ) ) PUNCT ejpam-4901 60 378 } } PUNCT ejpam-4901 60 379 { { PUNCT ejpam-4901 60 380 ( ( PUNCT ejpam-4901 60 381 1 1 NUM ejpam-4901 60 382 , , PUNCT ejpam-4901 60 383 3 3 NUM ejpam-4901 60 384 ) ) PUNCT ejpam-4901 60 385 , , PUNCT ejpam-4901 60 386 ( ( PUNCT ejpam-4901 60 387 3 3 NUM ejpam-4901 60 388 , , PUNCT ejpam-4901 60 389 2 2 NUM ejpam-4901 60 390 ) ) PUNCT ejpam-4901 60 391 } } PUNCT ejpam-4901 60 392 { { PUNCT ejpam-4901 60 393 ( ( PUNCT ejpam-4901 60 394 1 1 NUM ejpam-4901 60 395 , , PUNCT ejpam-4901 60 396 4 4 NUM ejpam-4901 60 397 ) ) PUNCT ejpam-4901 60 398 , , PUNCT ejpam-4901 60 399 ( ( PUNCT ejpam-4901 60 400 3 3 NUM ejpam-4901 60 401 , , PUNCT ejpam-4901 60 402 2 2 NUM ejpam-4901 60 403 ) ) PUNCT ejpam-4901 60 404 } } PUNCT ejpam-4901 60 405 { { PUNCT ejpam-4901 60 406 ( ( PUNCT ejpam-4901 60 407 1 1 NUM ejpam-4901 60 408 , , PUNCT ejpam-4901 60 409 1 1 NUM ejpam-4901 60 410 ) ) PUNCT ejpam-4901 60 411 , , PUNCT ejpam-4901 60 412 ( ( PUNCT ejpam-4901 60 413 3 3 NUM ejpam-4901 60 414 , , PUNCT ejpam-4901 60 415 4 4 NUM ejpam-4901 60 416 ) ) PUNCT ejpam-4901 60 417 } } PUNCT ejpam-4901 60 418 { { PUNCT ejpam-4901 60 419 ( ( PUNCT ejpam-4901 60 420 1 1 NUM ejpam-4901 60 421 , , PUNCT ejpam-4901 60 422 2 2 NUM ejpam-4901 60 423 ) ) PUNCT ejpam-4901 60 424 , , PUNCT ejpam-4901 60 425 ( ( PUNCT ejpam-4901 60 426 3 3 NUM ejpam-4901 60 427 , , PUNCT ejpam-4901 60 428 4 4 NUM ejpam-4901 60 429 ) ) PUNCT ejpam-4901 60 430 } } PUNCT ejpam-4901 60 431 { { PUNCT ejpam-4901 60 432 ( ( PUNCT ejpam-4901 60 433 1 1 NUM ejpam-4901 60 434 , , PUNCT ejpam-4901 60 435 3 3 NUM ejpam-4901 60 436 ) ) PUNCT ejpam-4901 60 437 , , PUNCT ejpam-4901 60 438 ( ( PUNCT ejpam-4901 60 439 3 3 NUM ejpam-4901 60 440 , , PUNCT ejpam-4901 60 441 4 4 NUM ejpam-4901 60 442 ) ) PUNCT ejpam-4901 60 443 } } PUNCT ejpam-4901 60 444 { { PUNCT ejpam-4901 60 445 ( ( PUNCT ejpam-4901 60 446 1 1 NUM ejpam-4901 60 447 , , PUNCT ejpam-4901 60 448 4 4 NUM ejpam-4901 60 449 ) ) PUNCT ejpam-4901 60 450 , , PUNCT ejpam-4901 60 451 ( ( PUNCT ejpam-4901 60 452 3 3 NUM ejpam-4901 60 453 , , PUNCT ejpam-4901 60 454 3 3 NUM ejpam-4901 60 455 ) ) PUNCT ejpam-4901 60 456 } } PUNCT ejpam-4901 60 457 { { PUNCT ejpam-4901 60 458 ( ( PUNCT ejpam-4901 60 459 2 2 NUM ejpam-4901 60 460 , , PUNCT ejpam-4901 60 461 1 1 NUM ejpam-4901 60 462 ) ) PUNCT ejpam-4901 60 463 , , PUNCT ejpam-4901 60 464 ( ( PUNCT ejpam-4901 60 465 3 3 NUM ejpam-4901 60 466 , , PUNCT ejpam-4901 60 467 2 2 NUM ejpam-4901 60 468 ) ) PUNCT ejpam-4901 60 469 } } PUNCT ejpam-4901 60 470 { { PUNCT ejpam-4901 60 471 ( ( PUNCT ejpam-4901 60 472 2 2 NUM ejpam-4901 60 473 , , PUNCT ejpam-4901 60 474 2 2 NUM ejpam-4901 60 475 ) ) PUNCT ejpam-4901 60 476 , , PUNCT ejpam-4901 60 477 ( ( PUNCT ejpam-4901 60 478 3 3 NUM ejpam-4901 60 479 , , PUNCT ejpam-4901 60 480 1 1 NUM ejpam-4901 60 481 ) ) PUNCT ejpam-4901 60 482 } } PUNCT ejpam-4901 60 483 { { PUNCT ejpam-4901 60 484 ( ( PUNCT ejpam-4901 60 485 2 2 NUM ejpam-4901 60 486 , , PUNCT ejpam-4901 60 487 3 3 NUM ejpam-4901 60 488 ) ) PUNCT ejpam-4901 60 489 , , PUNCT ejpam-4901 60 490 ( ( PUNCT ejpam-4901 60 491 3 3 NUM ejpam-4901 60 492 , , PUNCT ejpam-4901 60 493 1 1 NUM ejpam-4901 60 494 ) ) PUNCT ejpam-4901 60 495 } } PUNCT ejpam-4901 60 496 { { PUNCT ejpam-4901 60 497 ( ( PUNCT ejpam-4901 60 498 2 2 NUM ejpam-4901 60 499 , , PUNCT ejpam-4901 60 500 4 4 NUM ejpam-4901 60 501 ) ) PUNCT ejpam-4901 60 502 , , PUNCT ejpam-4901 60 503 ( ( PUNCT ejpam-4901 60 504 3 3 NUM ejpam-4901 60 505 , , PUNCT ejpam-4901 60 506 1 1 NUM ejpam-4901 60 507 ) ) PUNCT ejpam-4901 60 508 } } PUNCT ejpam-4901 60 509 { { PUNCT ejpam-4901 60 510 ( ( PUNCT ejpam-4901 60 511 2 2 NUM ejpam-4901 60 512 , , PUNCT ejpam-4901 60 513 1 1 NUM ejpam-4901 60 514 ) ) PUNCT ejpam-4901 60 515 , , PUNCT ejpam-4901 60 516 ( ( PUNCT ejpam-4901 60 517 3 3 NUM ejpam-4901 60 518 , , PUNCT ejpam-4901 60 519 3 3 NUM ejpam-4901 60 520 ) ) PUNCT ejpam-4901 60 521 } } PUNCT ejpam-4901 60 522 { { PUNCT ejpam-4901 60 523 ( ( PUNCT ejpam-4901 60 524 2 2 NUM ejpam-4901 60 525 , , PUNCT ejpam-4901 60 526 2 2 NUM ejpam-4901 60 527 ) ) PUNCT ejpam-4901 60 528 , , PUNCT ejpam-4901 60 529 ( ( PUNCT ejpam-4901 60 530 3 3 NUM ejpam-4901 60 531 , , PUNCT ejpam-4901 60 532 3 3 NUM ejpam-4901 60 533 ) ) PUNCT ejpam-4901 60 534 } } PUNCT ejpam-4901 60 535 { { PUNCT ejpam-4901 60 536 ( ( PUNCT ejpam-4901 60 537 2 2 NUM ejpam-4901 60 538 , , PUNCT ejpam-4901 60 539 3 3 NUM ejpam-4901 60 540 ) ) PUNCT ejpam-4901 60 541 , , PUNCT ejpam-4901 60 542 ( ( PUNCT ejpam-4901 60 543 3 3 NUM ejpam-4901 60 544 , , PUNCT ejpam-4901 60 545 2 2 NUM ejpam-4901 60 546 ) ) PUNCT ejpam-4901 60 547 } } PUNCT ejpam-4901 60 548 { { PUNCT ejpam-4901 60 549 ( ( PUNCT ejpam-4901 60 550 2 2 NUM ejpam-4901 60 551 , , PUNCT ejpam-4901 60 552 4 4 NUM ejpam-4901 60 553 ) ) PUNCT ejpam-4901 60 554 , , PUNCT ejpam-4901 60 555 ( ( PUNCT ejpam-4901 60 556 3 3 NUM ejpam-4901 60 557 , , PUNCT ejpam-4901 60 558 2 2 NUM ejpam-4901 60 559 ) ) PUNCT ejpam-4901 60 560 } } PUNCT ejpam-4901 60 561 { { PUNCT ejpam-4901 60 562 ( ( PUNCT ejpam-4901 60 563 2 2 NUM ejpam-4901 60 564 , , PUNCT ejpam-4901 60 565 1 1 NUM ejpam-4901 60 566 ) ) PUNCT ejpam-4901 60 567 , , PUNCT ejpam-4901 60 568 ( ( PUNCT ejpam-4901 60 569 3 3 NUM ejpam-4901 60 570 , , PUNCT ejpam-4901 60 571 4 4 NUM ejpam-4901 60 572 ) ) PUNCT ejpam-4901 60 573 } } PUNCT ejpam-4901 60 574 { { PUNCT ejpam-4901 60 575 ( ( PUNCT ejpam-4901 60 576 2 2 NUM ejpam-4901 60 577 , , PUNCT ejpam-4901 60 578 2 2 NUM ejpam-4901 60 579 ) ) PUNCT ejpam-4901 60 580 , , PUNCT ejpam-4901 60 581 ( ( PUNCT ejpam-4901 60 582 3 3 NUM ejpam-4901 60 583 , , PUNCT ejpam-4901 60 584 4 4 NUM ejpam-4901 60 585 ) ) PUNCT ejpam-4901 60 586 } } PUNCT ejpam-4901 60 587 { { PUNCT ejpam-4901 60 588 ( ( PUNCT ejpam-4901 60 589 3 3 NUM ejpam-4901 60 590 , , PUNCT ejpam-4901 60 591 3 3 NUM ejpam-4901 60 592 ) ) PUNCT ejpam-4901 60 593 , , PUNCT ejpam-4901 60 594 ( ( PUNCT ejpam-4901 60 595 3 3 NUM ejpam-4901 60 596 , , PUNCT ejpam-4901 60 597 4 4 NUM ejpam-4901 60 598 ) ) PUNCT ejpam-4901 60 599 } } PUNCT ejpam-4901 60 600 { { PUNCT ejpam-4901 60 601 ( ( PUNCT ejpam-4901 60 602 2 2 NUM ejpam-4901 60 603 , , PUNCT ejpam-4901 60 604 4 4 NUM ejpam-4901 60 605 ) ) PUNCT ejpam-4901 60 606 , , PUNCT ejpam-4901 60 607 ( ( PUNCT ejpam-4901 60 608 3 3 NUM ejpam-4901 60 609 , , PUNCT ejpam-4901 60 610 3 3 NUM ejpam-4901 60 611 ) ) PUNCT ejpam-4901 60 612 } } PUNCT ejpam-4901 60 613 for for ADP ejpam-4901 60 614 i i PROPN ejpam-4901 60 615 = = SYM ejpam-4901 60 616 3 3 NUM ejpam-4901 60 617 , , PUNCT ejpam-4901 60 618 si si X ejpam-4901 60 619 = = SYM ejpam-4901 60 620 { { PUNCT ejpam-4901 60 621 1 1 NUM ejpam-4901 60 622 , , PUNCT ejpam-4901 60 623 2 2 NUM ejpam-4901 60 624 , , PUNCT ejpam-4901 60 625 3 3 NUM ejpam-4901 60 626 } } PUNCT ejpam-4901 60 627 , , PUNCT ejpam-4901 60 628 { { PUNCT ejpam-4901 60 629 1 1 NUM ejpam-4901 60 630 , , PUNCT ejpam-4901 60 631 3 3 NUM ejpam-4901 60 632 } } PUNCT ejpam-4901 60 633 , , PUNCT ejpam-4901 60 634 { { PUNCT ejpam-4901 60 635 2 2 NUM ejpam-4901 60 636 , , PUNCT ejpam-4901 60 637 3 3 NUM ejpam-4901 60 638 } } PUNCT ejpam-4901 60 639 , , PUNCT ejpam-4901 60 640 the the DET ejpam-4901 60 641 one one NUM ejpam-4901 60 642 - - PUNCT ejpam-4901 60 643 to to ADP ejpam-4901 60 644 - - PUNCT ejpam-4901 60 645 one one NUM ejpam-4901 60 646 functions function NOUN ejpam-4901 60 647 are be AUX ejpam-4901 60 648 { { PUNCT ejpam-4901 60 649 ( ( PUNCT ejpam-4901 60 650 1 1 NUM ejpam-4901 60 651 , , PUNCT ejpam-4901 60 652 1 1 NUM ejpam-4901 60 653 ) ) PUNCT ejpam-4901 60 654 , , PUNCT ejpam-4901 60 655 ( ( PUNCT ejpam-4901 60 656 2 2 NUM ejpam-4901 60 657 , , PUNCT ejpam-4901 60 658 2 2 NUM ejpam-4901 60 659 ) ) PUNCT ejpam-4901 60 660 , , PUNCT ejpam-4901 60 661 ( ( PUNCT ejpam-4901 60 662 3 3 NUM ejpam-4901 60 663 , , PUNCT ejpam-4901 60 664 3 3 NUM ejpam-4901 60 665 ) ) PUNCT ejpam-4901 60 666 } } PUNCT ejpam-4901 60 667 { { PUNCT ejpam-4901 60 668 ( ( PUNCT ejpam-4901 60 669 1 1 NUM ejpam-4901 60 670 , , PUNCT ejpam-4901 60 671 2 2 NUM ejpam-4901 60 672 ) ) PUNCT ejpam-4901 60 673 , , PUNCT ejpam-4901 60 674 ( ( PUNCT ejpam-4901 60 675 2 2 NUM ejpam-4901 60 676 , , PUNCT ejpam-4901 60 677 1 1 NUM ejpam-4901 60 678 ) ) PUNCT ejpam-4901 60 679 , , PUNCT ejpam-4901 60 680 ( ( PUNCT ejpam-4901 60 681 3 3 NUM ejpam-4901 60 682 , , PUNCT ejpam-4901 60 683 3 3 NUM ejpam-4901 60 684 ) ) PUNCT ejpam-4901 60 685 } } PUNCT ejpam-4901 60 686 { { PUNCT ejpam-4901 60 687 ( ( PUNCT ejpam-4901 60 688 1 1 NUM ejpam-4901 60 689 , , PUNCT ejpam-4901 60 690 3 3 NUM ejpam-4901 60 691 ) ) PUNCT ejpam-4901 60 692 , , PUNCT ejpam-4901 60 693 ( ( PUNCT ejpam-4901 60 694 2 2 NUM ejpam-4901 60 695 , , PUNCT ejpam-4901 60 696 1 1 NUM ejpam-4901 60 697 ) ) PUNCT ejpam-4901 60 698 , , PUNCT ejpam-4901 60 699 ( ( PUNCT ejpam-4901 60 700 3 3 NUM ejpam-4901 60 701 , , PUNCT ejpam-4901 60 702 2 2 NUM ejpam-4901 60 703 ) ) PUNCT ejpam-4901 60 704 } } PUNCT ejpam-4901 60 705 { { PUNCT ejpam-4901 60 706 ( ( PUNCT ejpam-4901 60 707 1 1 NUM ejpam-4901 60 708 , , PUNCT ejpam-4901 60 709 4 4 NUM ejpam-4901 60 710 ) ) PUNCT ejpam-4901 60 711 , , PUNCT ejpam-4901 60 712 ( ( PUNCT ejpam-4901 60 713 2 2 NUM ejpam-4901 60 714 , , PUNCT ejpam-4901 60 715 1 1 NUM ejpam-4901 60 716 ) ) PUNCT ejpam-4901 60 717 , , PUNCT ejpam-4901 60 718 ( ( PUNCT ejpam-4901 60 719 3 3 NUM ejpam-4901 60 720 , , PUNCT ejpam-4901 60 721 2 2 NUM ejpam-4901 60 722 ) ) PUNCT ejpam-4901 60 723 } } PUNCT ejpam-4901 60 724 { { PUNCT ejpam-4901 60 725 ( ( PUNCT ejpam-4901 60 726 1 1 NUM ejpam-4901 60 727 , , PUNCT ejpam-4901 60 728 1 1 NUM ejpam-4901 60 729 ) ) PUNCT ejpam-4901 60 730 , , PUNCT ejpam-4901 60 731 ( ( PUNCT ejpam-4901 60 732 2 2 NUM ejpam-4901 60 733 , , PUNCT ejpam-4901 60 734 2 2 NUM ejpam-4901 60 735 ) ) PUNCT ejpam-4901 60 736 , , PUNCT ejpam-4901 60 737 ( ( PUNCT ejpam-4901 60 738 3 3 NUM ejpam-4901 60 739 , , PUNCT ejpam-4901 60 740 4 4 NUM ejpam-4901 60 741 ) ) PUNCT ejpam-4901 60 742 } } PUNCT ejpam-4901 60 743 { { PUNCT ejpam-4901 60 744 ( ( PUNCT ejpam-4901 60 745 1 1 NUM ejpam-4901 60 746 , , PUNCT ejpam-4901 60 747 2 2 NUM ejpam-4901 60 748 ) ) PUNCT ejpam-4901 60 749 , , PUNCT ejpam-4901 60 750 ( ( PUNCT ejpam-4901 60 751 2 2 NUM ejpam-4901 60 752 , , PUNCT ejpam-4901 60 753 1 1 NUM ejpam-4901 60 754 ) ) PUNCT ejpam-4901 60 755 , , PUNCT ejpam-4901 60 756 ( ( PUNCT ejpam-4901 60 757 3 3 NUM ejpam-4901 60 758 , , PUNCT ejpam-4901 60 759 4 4 NUM ejpam-4901 60 760 ) ) PUNCT ejpam-4901 60 761 } } PUNCT ejpam-4901 60 762 { { PUNCT ejpam-4901 60 763 ( ( PUNCT ejpam-4901 60 764 1 1 NUM ejpam-4901 60 765 , , PUNCT ejpam-4901 60 766 3 3 NUM ejpam-4901 60 767 ) ) PUNCT ejpam-4901 60 768 , , PUNCT ejpam-4901 60 769 ( ( PUNCT ejpam-4901 60 770 2 2 NUM ejpam-4901 60 771 , , PUNCT ejpam-4901 60 772 1 1 NUM ejpam-4901 60 773 ) ) PUNCT ejpam-4901 60 774 , , PUNCT ejpam-4901 60 775 ( ( PUNCT ejpam-4901 60 776 3 3 NUM ejpam-4901 60 777 , , PUNCT ejpam-4901 60 778 4 4 NUM ejpam-4901 60 779 ) ) PUNCT ejpam-4901 60 780 } } PUNCT ejpam-4901 60 781 { { PUNCT ejpam-4901 60 782 ( ( PUNCT ejpam-4901 60 783 1 1 NUM ejpam-4901 60 784 , , PUNCT ejpam-4901 60 785 4 4 NUM ejpam-4901 60 786 ) ) PUNCT ejpam-4901 60 787 , , PUNCT ejpam-4901 60 788 ( ( PUNCT ejpam-4901 60 789 2 2 NUM ejpam-4901 60 790 , , PUNCT ejpam-4901 60 791 1 1 NUM ejpam-4901 60 792 ) ) PUNCT ejpam-4901 60 793 , , PUNCT ejpam-4901 60 794 ( ( PUNCT ejpam-4901 60 795 3 3 NUM ejpam-4901 60 796 , , PUNCT ejpam-4901 60 797 3 3 NUM ejpam-4901 60 798 ) ) PUNCT ejpam-4901 60 799 } } PUNCT ejpam-4901 60 800 { { PUNCT ejpam-4901 60 801 ( ( PUNCT ejpam-4901 60 802 1 1 NUM ejpam-4901 60 803 , , PUNCT ejpam-4901 60 804 1 1 NUM ejpam-4901 60 805 ) ) PUNCT ejpam-4901 60 806 , , PUNCT ejpam-4901 60 807 ( ( PUNCT ejpam-4901 60 808 2 2 NUM ejpam-4901 60 809 , , PUNCT ejpam-4901 60 810 3 3 NUM ejpam-4901 60 811 ) ) PUNCT ejpam-4901 60 812 , , PUNCT ejpam-4901 60 813 ( ( PUNCT ejpam-4901 60 814 3 3 NUM ejpam-4901 60 815 , , PUNCT ejpam-4901 60 816 4 4 NUM ejpam-4901 60 817 ) ) PUNCT ejpam-4901 60 818 } } PUNCT ejpam-4901 60 819 { { PUNCT ejpam-4901 60 820 ( ( PUNCT ejpam-4901 60 821 1 1 NUM ejpam-4901 60 822 , , PUNCT ejpam-4901 60 823 2 2 NUM ejpam-4901 60 824 ) ) PUNCT ejpam-4901 60 825 , , PUNCT ejpam-4901 60 826 ( ( PUNCT ejpam-4901 60 827 2 2 NUM ejpam-4901 60 828 , , PUNCT ejpam-4901 60 829 3 3 NUM ejpam-4901 60 830 ) ) PUNCT ejpam-4901 60 831 , , PUNCT ejpam-4901 60 832 ( ( PUNCT ejpam-4901 60 833 3 3 NUM ejpam-4901 60 834 , , PUNCT ejpam-4901 60 835 1 1 NUM ejpam-4901 60 836 ) ) PUNCT ejpam-4901 60 837 } } PUNCT ejpam-4901 60 838 { { PUNCT ejpam-4901 60 839 ( ( PUNCT ejpam-4901 60 840 1 1 NUM ejpam-4901 60 841 , , PUNCT ejpam-4901 60 842 3 3 NUM ejpam-4901 60 843 ) ) PUNCT ejpam-4901 60 844 , , PUNCT ejpam-4901 60 845 ( ( PUNCT ejpam-4901 60 846 2 2 NUM ejpam-4901 60 847 , , PUNCT ejpam-4901 60 848 2 2 NUM ejpam-4901 60 849 ) ) PUNCT ejpam-4901 60 850 , , PUNCT ejpam-4901 60 851 ( ( PUNCT ejpam-4901 60 852 3 3 NUM ejpam-4901 60 853 , , PUNCT ejpam-4901 60 854 1 1 NUM ejpam-4901 60 855 ) ) PUNCT ejpam-4901 60 856 } } PUNCT ejpam-4901 60 857 { { PUNCT ejpam-4901 60 858 ( ( PUNCT ejpam-4901 60 859 1 1 NUM ejpam-4901 60 860 , , PUNCT ejpam-4901 60 861 4 4 NUM ejpam-4901 60 862 ) ) PUNCT ejpam-4901 60 863 , , PUNCT ejpam-4901 60 864 ( ( PUNCT ejpam-4901 60 865 2 2 NUM ejpam-4901 60 866 , , PUNCT ejpam-4901 60 867 2 2 NUM ejpam-4901 60 868 ) ) PUNCT ejpam-4901 60 869 , , PUNCT ejpam-4901 60 870 ( ( PUNCT ejpam-4901 60 871 3 3 NUM ejpam-4901 60 872 , , PUNCT ejpam-4901 60 873 1 1 NUM ejpam-4901 60 874 ) ) PUNCT ejpam-4901 60 875 } } PUNCT ejpam-4901 60 876 { { PUNCT ejpam-4901 60 877 ( ( PUNCT ejpam-4901 60 878 1 1 NUM ejpam-4901 60 879 , , PUNCT ejpam-4901 60 880 1 1 NUM ejpam-4901 60 881 ) ) PUNCT ejpam-4901 60 882 , , PUNCT ejpam-4901 60 883 ( ( PUNCT ejpam-4901 60 884 2 2 NUM ejpam-4901 60 885 , , PUNCT ejpam-4901 60 886 3 3 NUM ejpam-4901 60 887 ) ) PUNCT ejpam-4901 60 888 , , PUNCT ejpam-4901 60 889 ( ( PUNCT ejpam-4901 60 890 3 3 NUM ejpam-4901 60 891 , , PUNCT ejpam-4901 60 892 2 2 NUM ejpam-4901 60 893 ) ) PUNCT ejpam-4901 60 894 } } PUNCT ejpam-4901 60 895 { { PUNCT ejpam-4901 60 896 ( ( PUNCT ejpam-4901 60 897 1 1 NUM ejpam-4901 60 898 , , PUNCT ejpam-4901 60 899 2 2 NUM ejpam-4901 60 900 ) ) PUNCT ejpam-4901 60 901 , , PUNCT ejpam-4901 60 902 ( ( PUNCT ejpam-4901 60 903 2 2 NUM ejpam-4901 60 904 , , PUNCT ejpam-4901 60 905 3 3 NUM ejpam-4901 60 906 ) ) PUNCT ejpam-4901 60 907 , , PUNCT ejpam-4901 60 908 ( ( PUNCT ejpam-4901 60 909 3 3 NUM ejpam-4901 60 910 , , PUNCT ejpam-4901 60 911 4 4 NUM ejpam-4901 60 912 ) ) PUNCT ejpam-4901 60 913 } } PUNCT ejpam-4901 60 914 { { PUNCT ejpam-4901 60 915 ( ( PUNCT ejpam-4901 60 916 1 1 NUM ejpam-4901 60 917 , , PUNCT ejpam-4901 60 918 3 3 NUM ejpam-4901 60 919 ) ) PUNCT ejpam-4901 60 920 , , PUNCT ejpam-4901 60 921 ( ( PUNCT ejpam-4901 60 922 2 2 NUM ejpam-4901 60 923 , , PUNCT ejpam-4901 60 924 2 2 NUM ejpam-4901 60 925 ) ) PUNCT ejpam-4901 60 926 , , PUNCT ejpam-4901 60 927 ( ( PUNCT ejpam-4901 60 928 3 3 NUM ejpam-4901 60 929 , , PUNCT ejpam-4901 60 930 4 4 NUM ejpam-4901 60 931 ) ) PUNCT ejpam-4901 60 932 } } PUNCT ejpam-4901 60 933 { { PUNCT ejpam-4901 60 934 ( ( PUNCT ejpam-4901 60 935 1 1 NUM ejpam-4901 60 936 , , PUNCT ejpam-4901 60 937 4 4 NUM ejpam-4901 60 938 ) ) PUNCT ejpam-4901 60 939 , , PUNCT ejpam-4901 60 940 ( ( PUNCT ejpam-4901 60 941 2 2 NUM ejpam-4901 60 942 , , PUNCT ejpam-4901 60 943 2 2 NUM ejpam-4901 60 944 ) ) PUNCT ejpam-4901 60 945 , , PUNCT ejpam-4901 60 946 ( ( PUNCT ejpam-4901 60 947 3 3 NUM ejpam-4901 60 948 , , PUNCT ejpam-4901 60 949 3 3 NUM ejpam-4901 60 950 ) ) PUNCT ejpam-4901 60 951 } } PUNCT ejpam-4901 60 952 { { PUNCT ejpam-4901 60 953 ( ( PUNCT ejpam-4901 60 954 1 1 NUM ejpam-4901 60 955 , , PUNCT ejpam-4901 60 956 1 1 NUM ejpam-4901 60 957 ) ) PUNCT ejpam-4901 60 958 , , PUNCT ejpam-4901 60 959 ( ( PUNCT ejpam-4901 60 960 2 2 NUM ejpam-4901 60 961 , , PUNCT ejpam-4901 60 962 4 4 NUM ejpam-4901 60 963 ) ) PUNCT ejpam-4901 60 964 , , PUNCT ejpam-4901 60 965 ( ( PUNCT ejpam-4901 60 966 3 3 NUM ejpam-4901 60 967 , , PUNCT ejpam-4901 60 968 2 2 NUM ejpam-4901 60 969 ) ) PUNCT ejpam-4901 60 970 } } PUNCT ejpam-4901 60 971 { { PUNCT ejpam-4901 60 972 ( ( PUNCT ejpam-4901 60 973 1 1 NUM ejpam-4901 60 974 , , PUNCT ejpam-4901 60 975 2 2 NUM ejpam-4901 60 976 ) ) PUNCT ejpam-4901 60 977 , , PUNCT ejpam-4901 60 978 ( ( PUNCT ejpam-4901 60 979 2 2 NUM ejpam-4901 60 980 , , PUNCT ejpam-4901 60 981 4 4 NUM ejpam-4901 60 982 ) ) PUNCT ejpam-4901 60 983 , , PUNCT ejpam-4901 60 984 ( ( PUNCT ejpam-4901 60 985 3 3 NUM ejpam-4901 60 986 , , PUNCT ejpam-4901 60 987 3 3 NUM ejpam-4901 60 988 ) ) PUNCT ejpam-4901 60 989 } } PUNCT ejpam-4901 60 990 { { PUNCT ejpam-4901 60 991 ( ( PUNCT ejpam-4901 60 992 1 1 NUM ejpam-4901 60 993 , , PUNCT ejpam-4901 60 994 3 3 NUM ejpam-4901 60 995 ) ) PUNCT ejpam-4901 60 996 , , PUNCT ejpam-4901 60 997 ( ( PUNCT ejpam-4901 60 998 2 2 NUM ejpam-4901 60 999 , , PUNCT ejpam-4901 60 1000 4 4 NUM ejpam-4901 60 1001 ) ) PUNCT ejpam-4901 60 1002 , , PUNCT ejpam-4901 60 1003 ( ( PUNCT ejpam-4901 60 1004 3 3 NUM ejpam-4901 60 1005 , , PUNCT ejpam-4901 60 1006 1 1 NUM ejpam-4901 60 1007 ) ) PUNCT ejpam-4901 60 1008 } } PUNCT ejpam-4901 60 1009 { { PUNCT ejpam-4901 60 1010 ( ( PUNCT ejpam-4901 60 1011 1 1 NUM ejpam-4901 60 1012 , , PUNCT ejpam-4901 60 1013 4 4 NUM ejpam-4901 60 1014 ) ) PUNCT ejpam-4901 60 1015 , , PUNCT ejpam-4901 60 1016 ( ( PUNCT ejpam-4901 60 1017 2 2 NUM ejpam-4901 60 1018 , , PUNCT ejpam-4901 60 1019 3 3 NUM ejpam-4901 60 1020 ) ) PUNCT ejpam-4901 60 1021 , , PUNCT ejpam-4901 60 1022 ( ( PUNCT ejpam-4901 60 1023 3 3 NUM ejpam-4901 60 1024 , , PUNCT ejpam-4901 60 1025 1 1 NUM ejpam-4901 60 1026 ) ) PUNCT ejpam-4901 60 1027 } } PUNCT ejpam-4901 60 1028 { { PUNCT ejpam-4901 60 1029 ( ( PUNCT ejpam-4901 60 1030 1 1 NUM ejpam-4901 60 1031 , , PUNCT ejpam-4901 60 1032 1 1 NUM ejpam-4901 60 1033 ) ) PUNCT ejpam-4901 60 1034 , , PUNCT ejpam-4901 60 1035 ( ( PUNCT ejpam-4901 60 1036 2 2 NUM ejpam-4901 60 1037 , , PUNCT ejpam-4901 60 1038 4 4 NUM ejpam-4901 60 1039 ) ) PUNCT ejpam-4901 60 1040 , , PUNCT ejpam-4901 60 1041 ( ( PUNCT ejpam-4901 60 1042 3 3 NUM ejpam-4901 60 1043 , , PUNCT ejpam-4901 60 1044 3 3 NUM ejpam-4901 60 1045 ) ) PUNCT ejpam-4901 60 1046 } } PUNCT ejpam-4901 60 1047 { { PUNCT ejpam-4901 60 1048 ( ( PUNCT ejpam-4901 60 1049 1 1 NUM ejpam-4901 60 1050 , , PUNCT ejpam-4901 60 1051 2 2 NUM ejpam-4901 60 1052 ) ) PUNCT ejpam-4901 60 1053 , , PUNCT ejpam-4901 60 1054 ( ( PUNCT ejpam-4901 60 1055 2 2 NUM ejpam-4901 60 1056 , , PUNCT ejpam-4901 60 1057 4 4 NUM ejpam-4901 60 1058 ) ) PUNCT ejpam-4901 60 1059 , , PUNCT ejpam-4901 60 1060 ( ( PUNCT ejpam-4901 60 1061 3 3 NUM ejpam-4901 60 1062 , , PUNCT ejpam-4901 60 1063 4 4 NUM ejpam-4901 60 1064 ) ) PUNCT ejpam-4901 60 1065 } } PUNCT ejpam-4901 60 1066 { { PUNCT ejpam-4901 60 1067 ( ( PUNCT ejpam-4901 60 1068 1 1 NUM ejpam-4901 60 1069 , , PUNCT ejpam-4901 60 1070 3 3 NUM ejpam-4901 60 1071 ) ) PUNCT ejpam-4901 60 1072 , , PUNCT ejpam-4901 60 1073 ( ( PUNCT ejpam-4901 60 1074 2 2 NUM ejpam-4901 60 1075 , , PUNCT ejpam-4901 60 1076 4 4 NUM ejpam-4901 60 1077 ) ) PUNCT ejpam-4901 60 1078 , , PUNCT ejpam-4901 60 1079 ( ( PUNCT ejpam-4901 60 1080 3 3 NUM ejpam-4901 60 1081 , , PUNCT ejpam-4901 60 1082 2 2 NUM ejpam-4901 60 1083 ) ) PUNCT ejpam-4901 60 1084 } } PUNCT ejpam-4901 60 1085 { { PUNCT ejpam-4901 60 1086 ( ( PUNCT ejpam-4901 60 1087 1 1 NUM ejpam-4901 60 1088 , , PUNCT ejpam-4901 60 1089 4 4 NUM ejpam-4901 60 1090 ) ) PUNCT ejpam-4901 60 1091 , , PUNCT ejpam-4901 60 1092 ( ( PUNCT ejpam-4901 60 1093 2 2 NUM ejpam-4901 60 1094 , , PUNCT ejpam-4901 60 1095 3 3 NUM ejpam-4901 60 1096 ) ) PUNCT ejpam-4901 60 1097 , , PUNCT ejpam-4901 60 1098 ( ( PUNCT ejpam-4901 60 1099 3 3 NUM ejpam-4901 60 1100 , , PUNCT ejpam-4901 60 1101 2 2 NUM ejpam-4901 60 1102 ) ) PUNCT ejpam-4901 60 1103 } } PUNCT ejpam-4901 60 1104 thus thus ADV ejpam-4901 60 1105 , , PUNCT ejpam-4901 60 1106 the the DET ejpam-4901 60 1107 total total ADJ ejpam-4901 60 1108 number number NOUN ejpam-4901 60 1109 of of ADP ejpam-4901 60 1110 restricted restrict VERB ejpam-4901 60 1111 one one NUM ejpam-4901 60 1112 - - PUNCT ejpam-4901 60 1113 to to ADP ejpam-4901 60 1114 - - PUNCT ejpam-4901 60 1115 one one NUM ejpam-4901 60 1116 function function NOUN ejpam-4901 60 1117 is be AUX ejpam-4901 60 1118 73 73 NUM ejpam-4901 60 1119 . . PUNCT ejpam-4901 61 1 using use VERB ejpam-4901 61 2 proposition proposition NOUN ejpam-4901 61 3 1 1 NUM ejpam-4901 61 4 , , PUNCT ejpam-4901 61 5 with with ADP ejpam-4901 61 6 m m PROPN ejpam-4901 61 7 = = SYM ejpam-4901 61 8 3 3 NUM ejpam-4901 61 9 and and CCONJ ejpam-4901 61 10 n n NOUN ejpam-4901 61 11 = = SYM ejpam-4901 61 12 4 4 NUM ejpam-4901 61 13 , , PUNCT ejpam-4901 61 14 we we PRON ejpam-4901 61 15 have have VERB ejpam-4901 61 16 |î3| |î3| ADJ ejpam-4901 61 17 = = SYM ejpam-4901 61 18 3∑ 3∑ NUM ejpam-4901 61 19 i=0 i=0 PROPN ejpam-4901 61 20 ( ( PUNCT ejpam-4901 61 21 3 3 NUM ejpam-4901 61 22 i i NOUN ejpam-4901 61 23 ) ) PUNCT ejpam-4901 61 24 ( ( PUNCT ejpam-4901 61 25 4)i 4)i X ejpam-4901 61 26 = = PUNCT ejpam-4901 61 27 ( ( PUNCT ejpam-4901 61 28 3 3 NUM ejpam-4901 61 29 0 0 NUM ejpam-4901 61 30 ) ) PUNCT ejpam-4901 61 31 ( ( PUNCT ejpam-4901 61 32 4)0 4)0 NUM ejpam-4901 61 33 + + CCONJ ejpam-4901 61 34 ( ( PUNCT ejpam-4901 61 35 3 3 NUM ejpam-4901 61 36 1 1 NUM ejpam-4901 61 37 ) ) PUNCT ejpam-4901 61 38 ( ( PUNCT ejpam-4901 61 39 4)1 4)1 NOUN ejpam-4901 61 40 + + CCONJ ejpam-4901 61 41 ( ( PUNCT ejpam-4901 61 42 3 3 NUM ejpam-4901 61 43 2 2 NUM ejpam-4901 61 44 ) ) PUNCT ejpam-4901 61 45 ( ( PUNCT ejpam-4901 62 1 4)2 4)2 X ejpam-4901 62 2 + + CCONJ ejpam-4901 62 3 ( ( PUNCT ejpam-4901 62 4 3 3 NUM ejpam-4901 62 5 3 3 NUM ejpam-4901 62 6 ) ) PUNCT ejpam-4901 62 7 ( ( PUNCT ejpam-4901 62 8 4)3 4)3 NOUN ejpam-4901 62 9 = = SYM ejpam-4901 62 10 1 1 NUM ejpam-4901 62 11 + + NUM ejpam-4901 62 12 3(4 3(4 NUM ejpam-4901 62 13 ) ) PUNCT ejpam-4901 63 1 + + CCONJ ejpam-4901 64 1 3(4)(3 3(4)(3 NUM ejpam-4901 64 2 ) ) PUNCT ejpam-4901 64 3 + + NUM ejpam-4901 64 4 1(4)(3)(2 1(4)(3)(2 NUM ejpam-4901 64 5 ) ) PUNCT ejpam-4901 64 6 = = SYM ejpam-4901 64 7 73 73 NUM ejpam-4901 64 8 . . PUNCT ejpam-4901 65 1 the the DET ejpam-4901 65 2 next next ADJ ejpam-4901 65 3 proposition proposition NOUN ejpam-4901 65 4 counts count VERB ejpam-4901 65 5 the the DET ejpam-4901 65 6 number number NOUN ejpam-4901 65 7 of of ADP ejpam-4901 65 8 restricted restrict VERB ejpam-4901 65 9 one one NUM ejpam-4901 65 10 - - PUNCT ejpam-4901 65 11 to to ADP ejpam-4901 65 12 - - PUNCT ejpam-4901 65 13 one one NUM ejpam-4901 65 14 functions function NOUN ejpam-4901 65 15 f f NOUN ejpam-4901 65 16 with with ADP ejpam-4901 65 17 the the DET ejpam-4901 65 18 condition condition NOUN ejpam-4901 65 19 that that SCONJ ejpam-4901 65 20 f(a f(a NOUN ejpam-4901 65 21 ) ) PUNCT ejpam-4901 65 22 ≤ ≤ NOUN ejpam-4901 66 1 a,∀a a,∀a PUNCT ejpam-4901 66 2 ∈ ∈ PROPN ejpam-4901 66 3 s. s. PROPN ejpam-4901 66 4 proposition proposition NOUN ejpam-4901 66 5 2 2 X ejpam-4901 66 6 . . PUNCT ejpam-4901 67 1 let let VERB ejpam-4901 67 2 f f PROPN ejpam-4901 67 3 |s |s PROPN ejpam-4901 67 4 : : PUNCT ejpam-4901 67 5 nm nm ADV ejpam-4901 67 6 −→ −→ NOUN ejpam-4901 67 7 nn nn INTJ ejpam-4901 67 8 such such ADJ ejpam-4901 67 9 that that SCONJ ejpam-4901 67 10 m m VERB ejpam-4901 67 11 ≤ ≤ ADJ ejpam-4901 67 12 n n ADP ejpam-4901 67 13 and and CCONJ ejpam-4901 67 14 f(a f(a NOUN ejpam-4901 67 15 ) ) PUNCT ejpam-4901 67 16 ≤ ≤ NOUN ejpam-4901 68 1 a,∀a a,∀a PUNCT ejpam-4901 68 2 ∈ ∈ PROPN ejpam-4901 68 3 s. s. PROPN ejpam-4901 68 4 if if SCONJ ejpam-4901 68 5 ŷ(i ŷ(i PROPN ejpam-4901 68 6 , , PUNCT ejpam-4901 68 7 m m NOUN ejpam-4901 68 8 ) ) PUNCT ejpam-4901 68 9 = = SYM ejpam-4901 69 1 ∣∣⋃{f ∣∣⋃{f PROPN ejpam-4901 69 2 |si |si X ejpam-4901 69 3 : : PUNCT ejpam-4901 69 4 f f X ejpam-4901 69 5 is be AUX ejpam-4901 69 6 one one NUM ejpam-4901 69 7 to to ADP ejpam-4901 69 8 one one NUM ejpam-4901 69 9 and and CCONJ ejpam-4901 69 10 |si| |si| PROPN ejpam-4901 69 11 = = SYM ejpam-4901 70 1 i i PROPN ejpam-4901 70 2 } } PUNCT ejpam-4901 70 3 ∣∣,then ∣∣,then ADV ejpam-4901 70 4 |ŷ |ŷ X ejpam-4901 70 5 ( ( PUNCT ejpam-4901 70 6 i i NOUN ejpam-4901 70 7 , , PUNCT ejpam-4901 70 8 m)| m)| NOUN ejpam-4901 70 9 = = SYM ejpam-4901 70 10 ∑ ∑ PUNCT ejpam-4901 70 11 1≤j1 1≤j1 NUM ejpam-4901 70 12 < < X ejpam-4901 70 13 j2< j2< NOUN ejpam-4901 70 14 ... ... PUNCT ejpam-4901 70 15 > X ejpam-4901 102 33 m m PROPN ejpam-4901 102 34 and and CCONJ ejpam-4901 102 35 ŷ ŷ NUM ejpam-4901 102 36 ( ( PUNCT ejpam-4901 102 37 i i PRON ejpam-4901 102 38 , , PUNCT ejpam-4901 102 39 m m PROPN ejpam-4901 102 40 ) ) PUNCT ejpam-4901 102 41 = = SYM ejpam-4901 102 42 0 0 PUNCT ejpam-4901 102 43 when when SCONJ ejpam-4901 102 44 i i PRON ejpam-4901 102 45 > > X ejpam-4901 102 46 0 0 X ejpam-4901 102 47 . . PUNCT ejpam-4901 102 48 proof proof NOUN ejpam-4901 102 49 . . PUNCT ejpam-4901 103 1 we we PRON ejpam-4901 103 2 know know VERB ejpam-4901 103 3 that that PRON ejpam-4901 103 4 ŷ ŷ NUM ejpam-4901 103 5 ( ( PUNCT ejpam-4901 103 6 i i PRON ejpam-4901 103 7 , , PUNCT ejpam-4901 103 8 m+1 m+1 NUM ejpam-4901 103 9 ) ) PUNCT ejpam-4901 103 10 counts count VERB ejpam-4901 103 11 the the DET ejpam-4901 103 12 number number NOUN ejpam-4901 103 13 of of ADP ejpam-4901 103 14 restricted restrict VERB ejpam-4901 103 15 one one NUM ejpam-4901 103 16 - - PUNCT ejpam-4901 103 17 to to ADP ejpam-4901 103 18 - - PUNCT ejpam-4901 103 19 one one NUM ejpam-4901 103 20 functions function NOUN ejpam-4901 104 1 f f X ejpam-4901 105 1 |si |si X ejpam-4901 105 2 overall overall ADJ ejpam-4901 105 3 si si PROPN ejpam-4901 105 4 ⊆ ⊆ NUM ejpam-4901 105 5 nm+1 nm+1 NUM ejpam-4901 105 6 . . NOUN ejpam-4901 105 7 forming form VERB ejpam-4901 105 8 such such ADJ ejpam-4901 105 9 restricted restrict VERB ejpam-4901 105 10 one one NUM ejpam-4901 105 11 - - PUNCT ejpam-4901 105 12 to to ADP ejpam-4901 105 13 - - PUNCT ejpam-4901 105 14 one one NUM ejpam-4901 105 15 functions function NOUN ejpam-4901 105 16 can can AUX ejpam-4901 105 17 also also ADV ejpam-4901 105 18 be be AUX ejpam-4901 105 19 done do VERB ejpam-4901 105 20 by by ADP ejpam-4901 105 21 considering consider VERB ejpam-4901 105 22 the the DET ejpam-4901 105 23 following follow VERB ejpam-4901 105 24 disjoint disjoint NOUN ejpam-4901 105 25 cases case NOUN ejpam-4901 105 26 : : PUNCT ejpam-4901 105 27 case case NOUN ejpam-4901 105 28 1 1 NUM ejpam-4901 105 29 . . PUNCT ejpam-4901 105 30 forming form VERB ejpam-4901 105 31 those those DET ejpam-4901 105 32 functions function NOUN ejpam-4901 105 33 f f X ejpam-4901 105 34 |si |si X ejpam-4901 105 35 overall overall ADJ ejpam-4901 105 36 si si PROPN ejpam-4901 105 37 ⊆ ⊆ NUM ejpam-4901 105 38 nm+1 nm+1 PROPN ejpam-4901 105 39 such such ADJ ejpam-4901 105 40 that that DET ejpam-4901 105 41 m+ m+ NUM ejpam-4901 105 42 1 1 NUM ejpam-4901 105 43 /∈ /∈ PUNCT ejpam-4901 106 1 si si INTJ ejpam-4901 106 2 . . PROPN ejpam-4901 106 3 then then ADV ejpam-4901 106 4 the the DET ejpam-4901 106 5 number number NOUN ejpam-4901 106 6 of of ADP ejpam-4901 106 7 such such ADJ ejpam-4901 106 8 restricted restrict VERB ejpam-4901 106 9 one one NUM ejpam-4901 106 10 - - PUNCT ejpam-4901 106 11 to to ADP ejpam-4901 106 12 - - PUNCT ejpam-4901 106 13 one one NUM ejpam-4901 106 14 functions function NOUN ejpam-4901 106 15 is be AUX ejpam-4901 106 16 equal equal ADJ ejpam-4901 106 17 to to ADP ejpam-4901 106 18 the the DET ejpam-4901 106 19 number number NOUN ejpam-4901 106 20 of of ADP ejpam-4901 106 21 restricted restricted ADJ ejpam-4901 106 22 oneto oneto NOUN ejpam-4901 106 23 - - PUNCT ejpam-4901 106 24 one one NUM ejpam-4901 106 25 functions function NOUN ejpam-4901 106 26 f f X ejpam-4901 106 27 |si |si X ejpam-4901 106 28 overall overall ADJ ejpam-4901 106 29 si si PROPN ejpam-4901 106 30 ⊆ ⊆ NUM ejpam-4901 106 31 nm+1 nm+1 NUM ejpam-4901 106 32 . . PUNCT ejpam-4901 106 33 by by ADP ejpam-4901 106 34 definition definition NOUN ejpam-4901 106 35 , , PUNCT ejpam-4901 106 36 there there PRON ejpam-4901 106 37 are be VERB ejpam-4901 106 38 ŷ ŷ NUM ejpam-4901 106 39 ( ( PUNCT ejpam-4901 106 40 i i PRON ejpam-4901 106 41 , , PUNCT ejpam-4901 106 42 m m PROPN ejpam-4901 106 43 ) ) PUNCT ejpam-4901 106 44 such such ADJ ejpam-4901 106 45 functions function NOUN ejpam-4901 106 46 . . PUNCT ejpam-4901 107 1 case case NOUN ejpam-4901 107 2 2 2 NUM ejpam-4901 107 3 . . PUNCT ejpam-4901 107 4 forming form VERB ejpam-4901 107 5 those those DET ejpam-4901 107 6 functions function NOUN ejpam-4901 107 7 f f X ejpam-4901 108 1 |si |si X ejpam-4901 108 2 overall overall ADJ ejpam-4901 108 3 si si PROPN ejpam-4901 108 4 ⊆ ⊆ NUM ejpam-4901 108 5 nm+1 nm+1 NUM ejpam-4901 108 6 such such ADJ ejpam-4901 108 7 that that SCONJ ejpam-4901 108 8 m m VERB ejpam-4901 108 9 + + ADV ejpam-4901 108 10 1 1 NUM ejpam-4901 108 11 /∈ /∈ SYM ejpam-4901 108 12 si si INTJ ejpam-4901 108 13 . . PUNCT ejpam-4901 109 1 this this DET ejpam-4901 109 2 event event NOUN ejpam-4901 109 3 can can AUX ejpam-4901 109 4 be be AUX ejpam-4901 109 5 decomposed decompose VERB ejpam-4901 109 6 into into ADP ejpam-4901 109 7 the the DET ejpam-4901 109 8 following follow VERB ejpam-4901 109 9 sequence sequence NOUN ejpam-4901 109 10 of of ADP ejpam-4901 109 11 events event NOUN ejpam-4901 109 12 : : PUNCT ejpam-4901 109 13 e1 e1 NOUN ejpam-4901 109 14 : : PUNCT ejpam-4901 109 15 event event NOUN ejpam-4901 109 16 of of ADP ejpam-4901 109 17 forming form VERB ejpam-4901 109 18 those those DET ejpam-4901 109 19 restricted restrict VERB ejpam-4901 109 20 one one NUM ejpam-4901 109 21 - - PUNCT ejpam-4901 109 22 to to ADP ejpam-4901 109 23 - - PUNCT ejpam-4901 109 24 one one NUM ejpam-4901 109 25 functions function NOUN ejpam-4901 109 26 f f PROPN ejpam-4901 109 27 |si−1 |si−1 PROPN ejpam-4901 109 28 overall overall ADJ ejpam-4901 109 29 si−1 si−1 PROPN ejpam-4901 109 30 ⊆ ⊆ NUM ejpam-4901 109 31 nm nm NOUN ejpam-4901 109 32 . . PUNCT ejpam-4901 110 1 e2 e2 PROPN ejpam-4901 110 2 : : PUNCT ejpam-4901 110 3 event event NOUN ejpam-4901 110 4 of of ADP ejpam-4901 110 5 inserting insert VERB ejpam-4901 110 6 m+ m+ NOUN ejpam-4901 110 7 1 1 NUM ejpam-4901 110 8 to to ADP ejpam-4901 110 9 si−1 si−1 VERB ejpam-4901 110 10 so so SCONJ ejpam-4901 110 11 that that SCONJ ejpam-4901 110 12 every every DET ejpam-4901 110 13 si si PROPN ejpam-4901 110 14 = = PROPN ejpam-4901 110 15 si−1 si−1 PROPN ejpam-4901 110 16 ∪ ∪ X ejpam-4901 110 17 { { PUNCT ejpam-4901 110 18 m+ m+ NOUN ejpam-4901 110 19 1 1 NUM ejpam-4901 110 20 } } PUNCT ejpam-4901 110 21 contains contain VERB ejpam-4901 110 22 m+ m+ NUM ejpam-4901 110 23 1 1 NUM ejpam-4901 110 24 and and CCONJ ejpam-4901 110 25 then then ADV ejpam-4901 110 26 mapping mapping NOUN ejpam-4901 110 27 m+ m+ NUM ejpam-4901 110 28 1 1 NUM ejpam-4901 110 29 to to ADP ejpam-4901 110 30 nm+1 nm+1 PROPN ejpam-4901 110 31 so so SCONJ ejpam-4901 110 32 that that SCONJ ejpam-4901 110 33 one one NUM ejpam-4901 110 34 - - PUNCT ejpam-4901 110 35 to to ADP ejpam-4901 110 36 - - PUNCT ejpam-4901 110 37 oneness oneness NOUN ejpam-4901 110 38 of of ADP ejpam-4901 110 39 f f PROPN ejpam-4901 110 40 will will AUX ejpam-4901 110 41 be be AUX ejpam-4901 110 42 preserved preserve VERB ejpam-4901 110 43 . . PUNCT ejpam-4901 111 1 note note VERB ejpam-4901 111 2 that that DET ejpam-4901 111 3 |e1| |e1| NOUN ejpam-4901 111 4 = = SYM ejpam-4901 111 5 ŷ ŷ NUM ejpam-4901 111 6 ( ( PUNCT ejpam-4901 111 7 i− i− PROPN ejpam-4901 111 8 1,m 1,m PROPN ejpam-4901 111 9 ) ) PUNCT ejpam-4901 111 10 and and CCONJ ejpam-4901 111 11 |e2| |e2| ADJ ejpam-4901 111 12 = = SYM ejpam-4901 111 13 m+ m+ NUM ejpam-4901 111 14 1− 1− NUM ejpam-4901 111 15 ( ( PUNCT ejpam-4901 111 16 i− i− PROPN ejpam-4901 111 17 1 1 NUM ejpam-4901 111 18 ) ) PUNCT ejpam-4901 111 19 . . PUNCT ejpam-4901 112 1 by by ADP ejpam-4901 112 2 multiplication multiplication NOUN ejpam-4901 112 3 principle principle NOUN ejpam-4901 112 4 , , PUNCT ejpam-4901 112 5 the the DET ejpam-4901 112 6 number number NOUN ejpam-4901 112 7 of of ADP ejpam-4901 112 8 such such ADJ ejpam-4901 112 9 restricted restrict VERB ejpam-4901 112 10 one one NUM ejpam-4901 112 11 - - PUNCT ejpam-4901 112 12 to to ADP ejpam-4901 112 13 - - PUNCT ejpam-4901 112 14 one one NUM ejpam-4901 112 15 functions function NOUN ejpam-4901 112 16 f f NOUN ejpam-4901 112 17 |si |si ADP ejpam-4901 112 18 = = SYM ejpam-4901 112 19 f f X ejpam-4901 112 20 |si−1∪{m+1 |si−1∪{m+1 PROPN ejpam-4901 112 21 } } PUNCT ejpam-4901 112 22 overall overall ADJ ejpam-4901 112 23 si si PROPN ejpam-4901 112 24 ⊆ ⊆ NUM ejpam-4901 112 25 nm+1 nm+1 PROPN ejpam-4901 112 26 is be AUX ejpam-4901 112 27 equal equal ADJ ejpam-4901 112 28 to to ADP ejpam-4901 112 29 |e1||e2| |e1||e2| PROPN ejpam-4901 112 30 = = SYM ejpam-4901 112 31 ŷ ŷ X ejpam-4901 112 32 ( ( PUNCT ejpam-4901 112 33 i− i− PROPN ejpam-4901 112 34 1,m)(m+ 1,m)(m+ NUM ejpam-4901 112 35 2− 2− NUM ejpam-4901 112 36 i i NOUN ejpam-4901 112 37 ) ) PUNCT ejpam-4901 112 38 . . PUNCT ejpam-4901 113 1 since since SCONJ ejpam-4901 113 2 any any PRON ejpam-4901 113 3 of of ADP ejpam-4901 113 4 these these DET ejpam-4901 113 5 cases case NOUN ejpam-4901 113 6 gives give VERB ejpam-4901 113 7 the the DET ejpam-4901 113 8 desired desire VERB ejpam-4901 113 9 restricted restrict VERB ejpam-4901 113 10 one one NUM ejpam-4901 113 11 - - PUNCT ejpam-4901 113 12 to to ADP ejpam-4901 113 13 - - PUNCT ejpam-4901 113 14 one one NUM ejpam-4901 113 15 functions function NOUN ejpam-4901 113 16 , , PUNCT ejpam-4901 113 17 by by ADP ejpam-4901 113 18 addition addition NOUN ejpam-4901 113 19 principle principle NOUN ejpam-4901 113 20 , , PUNCT ejpam-4901 113 21 ŷ ŷ NUM ejpam-4901 113 22 ( ( PUNCT ejpam-4901 113 23 i i PRON ejpam-4901 113 24 , , PUNCT ejpam-4901 113 25 m+ m+ NOUN ejpam-4901 113 26 1 1 NUM ejpam-4901 113 27 ) ) PUNCT ejpam-4901 113 28 = = SYM ejpam-4901 113 29 ŷ ŷ NUM ejpam-4901 113 30 ( ( PUNCT ejpam-4901 113 31 i i PROPN ejpam-4901 113 32 , , PUNCT ejpam-4901 113 33 m m PROPN ejpam-4901 113 34 ) ) PUNCT ejpam-4901 114 1 + + CCONJ ejpam-4901 114 2 ( ( PUNCT ejpam-4901 114 3 m+ m+ NUM ejpam-4901 114 4 2− 2− NUM ejpam-4901 114 5 i)ŷ i)ŷ PROPN ejpam-4901 114 6 ( ( PUNCT ejpam-4901 114 7 i− i− PROPN ejpam-4901 114 8 1,m 1,m PROPN ejpam-4901 114 9 ) ) PUNCT ejpam-4901 114 10 . . PUNCT ejpam-4901 115 1 example example NOUN ejpam-4901 116 1 3 3 NUM ejpam-4901 116 2 . . X ejpam-4901 116 3 from from ADP ejpam-4901 116 4 example example NOUN ejpam-4901 116 5 2 2 NUM ejpam-4901 116 6 , , PUNCT ejpam-4901 116 7 ŷ ŷ NUM ejpam-4901 116 8 ( ( PUNCT ejpam-4901 116 9 2 2 NUM ejpam-4901 116 10 , , PUNCT ejpam-4901 116 11 3 3 NUM ejpam-4901 116 12 ) ) PUNCT ejpam-4901 116 13 = = SYM ejpam-4901 116 14 7 7 NUM ejpam-4901 116 15 and and CCONJ ejpam-4901 116 16 using use VERB ejpam-4901 116 17 proposition proposition NOUN ejpam-4901 116 18 3 3 NUM ejpam-4901 116 19 , , PUNCT ejpam-4901 116 20 ŷ ŷ NUM ejpam-4901 116 21 ( ( PUNCT ejpam-4901 116 22 1 1 NUM ejpam-4901 116 23 , , PUNCT ejpam-4901 116 24 3 3 NUM ejpam-4901 116 25 ) ) PUNCT ejpam-4901 116 26 = = SYM ejpam-4901 117 1 3∑ 3∑ NUM ejpam-4901 117 2 ji=1 ji=1 ADV ejpam-4901 117 3 ji ji NOUN ejpam-4901 118 1 = = NOUN ejpam-4901 118 2 1 1 NUM ejpam-4901 118 3 + + NUM ejpam-4901 118 4 2 2 NUM ejpam-4901 118 5 + + SYM ejpam-4901 118 6 3 3 NUM ejpam-4901 118 7 = = SYM ejpam-4901 118 8 6 6 NUM ejpam-4901 118 9 . . PUNCT ejpam-4901 119 1 then then ADV ejpam-4901 119 2 , , PUNCT ejpam-4901 119 3 by by ADP ejpam-4901 119 4 applying apply VERB ejpam-4901 119 5 proposition proposition NOUN ejpam-4901 119 6 3 3 NUM ejpam-4901 119 7 , , PUNCT ejpam-4901 119 8 with with ADP ejpam-4901 119 9 i i NOUN ejpam-4901 119 10 = = SYM ejpam-4901 119 11 2,m 2,m NOUN ejpam-4901 119 12 = = SYM ejpam-4901 119 13 3 3 NUM ejpam-4901 119 14 , , PUNCT ejpam-4901 119 15 we we PRON ejpam-4901 119 16 have have VERB ejpam-4901 119 17 ŷ ŷ NUM ejpam-4901 119 18 ( ( PUNCT ejpam-4901 119 19 2 2 NUM ejpam-4901 119 20 , , PUNCT ejpam-4901 119 21 4 4 NUM ejpam-4901 119 22 ) ) PUNCT ejpam-4901 119 23 = = SYM ejpam-4901 120 1 ŷ ŷ NUM ejpam-4901 120 2 ( ( PUNCT ejpam-4901 120 3 2 2 NUM ejpam-4901 120 4 , , PUNCT ejpam-4901 120 5 3 3 NUM ejpam-4901 120 6 ) ) PUNCT ejpam-4901 120 7 + + CCONJ ejpam-4901 120 8 ( ( PUNCT ejpam-4901 120 9 3 3 NUM ejpam-4901 120 10 + + NUM ejpam-4901 120 11 2− 2− NUM ejpam-4901 120 12 2)ŷ 2)ŷ NUM ejpam-4901 120 13 ( ( PUNCT ejpam-4901 120 14 1 1 NUM ejpam-4901 120 15 , , PUNCT ejpam-4901 120 16 3 3 NUM ejpam-4901 120 17 ) ) PUNCT ejpam-4901 120 18 . . PUNCT ejpam-4901 121 1 = = PUNCT ejpam-4901 121 2 7 7 NUM ejpam-4901 121 3 + + NUM ejpam-4901 121 4 3(6 3(6 NUM ejpam-4901 121 5 ) ) PUNCT ejpam-4901 121 6 = = SYM ejpam-4901 121 7 25 25 NUM ejpam-4901 121 8 . . PUNCT ejpam-4901 122 1 using use VERB ejpam-4901 122 2 proposition proposition NOUN ejpam-4901 122 3 2 2 NUM ejpam-4901 122 4 , , PUNCT ejpam-4901 122 5 we we PRON ejpam-4901 122 6 have have VERB ejpam-4901 122 7 ŷ ŷ NUM ejpam-4901 122 8 ( ( PUNCT ejpam-4901 122 9 2 2 NUM ejpam-4901 122 10 , , PUNCT ejpam-4901 122 11 4 4 NUM ejpam-4901 122 12 ) ) PUNCT ejpam-4901 122 13 = = SYM ejpam-4901 123 1 ∑ ∑ PUNCT ejpam-4901 123 2 1≤j1≤j2≤3 1≤j1≤j2≤3 NOUN ejpam-4901 123 3 j1(j2 j1(j2 NOUN ejpam-4901 123 4 − − NOUN ejpam-4901 123 5 1 1 NUM ejpam-4901 123 6 ) ) PUNCT ejpam-4901 123 7 ) ) PUNCT ejpam-4901 124 1 = = PUNCT ejpam-4901 125 1 1(2− 1(2− PRON ejpam-4901 125 2 1 1 NUM ejpam-4901 125 3 ) ) PUNCT ejpam-4901 125 4 + + CCONJ ejpam-4901 125 5 1(3− 1(3− NUM ejpam-4901 125 6 1 1 NUM ejpam-4901 125 7 ) ) PUNCT ejpam-4901 125 8 + + CCONJ ejpam-4901 125 9 1(4− 1(4− NUM ejpam-4901 125 10 1 1 NUM ejpam-4901 125 11 ) ) PUNCT ejpam-4901 125 12 + + CCONJ ejpam-4901 126 1 2(3− 2(3− NUM ejpam-4901 126 2 1 1 NUM ejpam-4901 126 3 ) ) PUNCT ejpam-4901 126 4 + + CCONJ ejpam-4901 126 5 2(4− 2(4− NUM ejpam-4901 126 6 1 1 NUM ejpam-4901 126 7 ) ) PUNCT ejpam-4901 126 8 + + CCONJ ejpam-4901 126 9 3(4− 3(4− NUM ejpam-4901 126 10 1 1 NUM ejpam-4901 126 11 ) ) PUNCT ejpam-4901 126 12 = = SYM ejpam-4901 126 13 25 25 NUM ejpam-4901 126 14 . . PUNCT ejpam-4901 126 15 m. m. NOUN ejpam-4901 126 16 j. j. PROPN ejpam-4901 126 17 latayada latayada PROPN ejpam-4901 126 18 / / SYM ejpam-4901 126 19 eur eur PROPN ejpam-4901 126 20 . . PUNCT ejpam-4901 127 1 j. j. PROPN ejpam-4901 127 2 pure pure PROPN ejpam-4901 127 3 appl appl PROPN ejpam-4901 127 4 . . PROPN ejpam-4901 127 5 math math PROPN ejpam-4901 127 6 , , PUNCT ejpam-4901 127 7 16 16 NUM ejpam-4901 127 8 ( ( PUNCT ejpam-4901 127 9 4 4 NUM ejpam-4901 127 10 ) ) PUNCT ejpam-4901 127 11 ( ( PUNCT ejpam-4901 127 12 2023 2023 NUM ejpam-4901 127 13 ) ) PUNCT ejpam-4901 127 14 , , PUNCT ejpam-4901 127 15 2751 2751 NUM ejpam-4901 127 16 - - SYM ejpam-4901 127 17 2762 2762 NUM ejpam-4901 127 18 2757 2757 NUM ejpam-4901 127 19 note note VERB ejpam-4901 127 20 that that PRON ejpam-4901 127 21 ŷ ŷ NUM ejpam-4901 127 22 ( ( PUNCT ejpam-4901 127 23 0 0 NUM ejpam-4901 127 24 , , PUNCT ejpam-4901 127 25 1 1 NUM ejpam-4901 127 26 ) ) PUNCT ejpam-4901 127 27 = = SYM ejpam-4901 128 1 ŷ ŷ NUM ejpam-4901 128 2 ( ( PUNCT ejpam-4901 128 3 0 0 NUM ejpam-4901 128 4 , , PUNCT ejpam-4901 128 5 1 1 NUM ejpam-4901 128 6 ) ) PUNCT ejpam-4901 128 7 + + CCONJ ejpam-4901 128 8 ( ( PUNCT ejpam-4901 128 9 0 0 NUM ejpam-4901 128 10 + + NUM ejpam-4901 128 11 2− 2− NUM ejpam-4901 128 12 0)ŷ 0)ŷ NUM ejpam-4901 128 13 ( ( PUNCT ejpam-4901 128 14 −1 −1 NOUN ejpam-4901 128 15 , , PUNCT ejpam-4901 128 16 0 0 NUM ejpam-4901 128 17 ) ) PUNCT ejpam-4901 128 18 = = SYM ejpam-4901 129 1 1 1 NUM ejpam-4901 129 2 ŷ ŷ NUM ejpam-4901 129 3 ( ( PUNCT ejpam-4901 129 4 1 1 NUM ejpam-4901 129 5 , , PUNCT ejpam-4901 129 6 1 1 NUM ejpam-4901 129 7 ) ) PUNCT ejpam-4901 129 8 = = SYM ejpam-4901 129 9 ŷ ŷ NUM ejpam-4901 129 10 ( ( PUNCT ejpam-4901 129 11 1 1 NUM ejpam-4901 129 12 , , PUNCT ejpam-4901 129 13 0 0 NUM ejpam-4901 129 14 ) ) PUNCT ejpam-4901 129 15 + + CCONJ ejpam-4901 129 16 ( ( PUNCT ejpam-4901 129 17 0 0 NUM ejpam-4901 129 18 + + NUM ejpam-4901 129 19 2− 2− NUM ejpam-4901 129 20 1)ŷ 1)ŷ NUM ejpam-4901 129 21 ( ( PUNCT ejpam-4901 129 22 0 0 NUM ejpam-4901 129 23 , , PUNCT ejpam-4901 129 24 0 0 NUM ejpam-4901 129 25 ) ) PUNCT ejpam-4901 129 26 = = SYM ejpam-4901 129 27 1 1 NUM ejpam-4901 129 28 ŷ ŷ NUM ejpam-4901 129 29 ( ( PUNCT ejpam-4901 129 30 1 1 NUM ejpam-4901 129 31 , , PUNCT ejpam-4901 129 32 2 2 NUM ejpam-4901 129 33 ) ) PUNCT ejpam-4901 129 34 = = SYM ejpam-4901 129 35 ŷ ŷ NUM ejpam-4901 129 36 ( ( PUNCT ejpam-4901 129 37 0 0 NUM ejpam-4901 129 38 , , PUNCT ejpam-4901 129 39 1 1 NUM ejpam-4901 129 40 ) ) PUNCT ejpam-4901 129 41 + + CCONJ ejpam-4901 129 42 ( ( PUNCT ejpam-4901 129 43 1 1 NUM ejpam-4901 129 44 + + NUM ejpam-4901 129 45 2− 2− NUM ejpam-4901 129 46 0)ŷ 0)ŷ NUM ejpam-4901 129 47 ( ( PUNCT ejpam-4901 129 48 −1 −1 NOUN ejpam-4901 129 49 , , PUNCT ejpam-4901 129 50 1 1 NUM ejpam-4901 129 51 ) ) PUNCT ejpam-4901 129 52 = = SYM ejpam-4901 129 53 1 1 NUM ejpam-4901 129 54 ŷ ŷ NUM ejpam-4901 129 55 ( ( PUNCT ejpam-4901 129 56 1 1 NUM ejpam-4901 129 57 , , PUNCT ejpam-4901 129 58 2 2 NUM ejpam-4901 129 59 ) ) PUNCT ejpam-4901 129 60 = = SYM ejpam-4901 129 61 ŷ ŷ NUM ejpam-4901 129 62 ( ( PUNCT ejpam-4901 129 63 0 0 NUM ejpam-4901 129 64 , , PUNCT ejpam-4901 129 65 1 1 NUM ejpam-4901 129 66 ) ) PUNCT ejpam-4901 129 67 + + CCONJ ejpam-4901 129 68 ( ( PUNCT ejpam-4901 129 69 1 1 NUM ejpam-4901 129 70 + + NUM ejpam-4901 129 71 2− 2− NUM ejpam-4901 129 72 0)ŷ 0)ŷ NUM ejpam-4901 129 73 ( ( PUNCT ejpam-4901 129 74 −1 −1 NOUN ejpam-4901 129 75 , , PUNCT ejpam-4901 129 76 1 1 NUM ejpam-4901 129 77 ) ) PUNCT ejpam-4901 129 78 = = SYM ejpam-4901 129 79 1 1 X ejpam-4901 129 80 . . PUNCT ejpam-4901 130 1 the the DET ejpam-4901 130 2 following follow VERB ejpam-4901 130 3 table table NOUN ejpam-4901 130 4 of of ADP ejpam-4901 130 5 values value NOUN ejpam-4901 130 6 for for ADP ejpam-4901 130 7 ŷ ŷ NUM ejpam-4901 130 8 ( ( PUNCT ejpam-4901 130 9 i i PROPN ejpam-4901 130 10 , , PUNCT ejpam-4901 130 11 m m VERB ejpam-4901 130 12 ) ) PUNCT ejpam-4901 130 13 can can AUX ejpam-4901 130 14 be be AUX ejpam-4901 130 15 constructed construct VERB ejpam-4901 130 16 using use VERB ejpam-4901 130 17 proposition proposition NOUN ejpam-4901 130 18 3 3 NUM ejpam-4901 130 19 . . PUNCT ejpam-4901 130 20 @ @ ADP ejpam-4901 130 21 @ @ ADP ejpam-4901 130 22 @m @m PROPN ejpam-4901 131 1 i i NOUN ejpam-4901 131 2 0 0 NUM ejpam-4901 131 3 1 1 NUM ejpam-4901 131 4 2 2 NUM ejpam-4901 131 5 3 3 NUM ejpam-4901 131 6 4 4 NUM ejpam-4901 131 7 5 5 NUM ejpam-4901 131 8 6 6 NUM ejpam-4901 131 9 0 0 NUM ejpam-4901 131 10 1 1 NUM ejpam-4901 131 11 1 1 NUM ejpam-4901 131 12 1 1 NUM ejpam-4901 131 13 1 1 NUM ejpam-4901 131 14 2 2 NUM ejpam-4901 131 15 1 1 NUM ejpam-4901 131 16 3 3 NUM ejpam-4901 131 17 1 1 NUM ejpam-4901 131 18 3 3 NUM ejpam-4901 131 19 1 1 NUM ejpam-4901 131 20 6 6 NUM ejpam-4901 131 21 7 7 NUM ejpam-4901 131 22 1 1 NUM ejpam-4901 131 23 4 4 NUM ejpam-4901 131 24 1 1 NUM ejpam-4901 131 25 10 10 NUM ejpam-4901 131 26 25 25 NUM ejpam-4901 131 27 15 15 NUM ejpam-4901 131 28 1 1 NUM ejpam-4901 131 29 5 5 NUM ejpam-4901 131 30 1 1 NUM ejpam-4901 131 31 15 15 NUM ejpam-4901 131 32 65 65 NUM ejpam-4901 131 33 90 90 NUM ejpam-4901 131 34 31 31 NUM ejpam-4901 131 35 1 1 NUM ejpam-4901 131 36 6 6 NUM ejpam-4901 131 37 1 1 NUM ejpam-4901 131 38 21 21 NUM ejpam-4901 131 39 140 140 NUM ejpam-4901 131 40 350 350 NUM ejpam-4901 131 41 301 301 NUM ejpam-4901 131 42 63 63 NUM ejpam-4901 131 43 1 1 NUM ejpam-4901 131 44 table table NOUN ejpam-4901 131 45 2 2 NUM ejpam-4901 131 46 : : PUNCT ejpam-4901 131 47 values value NOUN ejpam-4901 131 48 of of ADP ejpam-4901 131 49 ŷ ŷ NUM ejpam-4901 131 50 ( ( PUNCT ejpam-4901 131 51 i i PROPN ejpam-4901 131 52 , , PUNCT ejpam-4901 131 53 m m PROPN ejpam-4901 131 54 ) ) PUNCT ejpam-4901 131 55 for for ADP ejpam-4901 131 56 0 0 NUM ejpam-4901 131 57 ≤ ≤ NUM ejpam-4901 131 58 i i PRON ejpam-4901 131 59 ≤ ≤ NOUN ejpam-4901 131 60 6 6 NUM ejpam-4901 131 61 , , PUNCT ejpam-4901 131 62 0 0 NUM ejpam-4901 131 63 ≤ ≤ NUM ejpam-4901 131 64 m m VERB ejpam-4901 131 65 ≤ ≤ NUM ejpam-4901 131 66 6 6 NUM ejpam-4901 131 67 remark remark NOUN ejpam-4901 131 68 1 1 NUM ejpam-4901 131 69 . . PUNCT ejpam-4901 132 1 we we PRON ejpam-4901 132 2 know know VERB ejpam-4901 132 3 from from ADP ejpam-4901 132 4 proposition proposition NOUN ejpam-4901 132 5 1 1 NUM ejpam-4901 132 6 , , PUNCT ejpam-4901 132 7 that that SCONJ ejpam-4901 132 8 the the DET ejpam-4901 132 9 total total ADJ ejpam-4901 132 10 number number NOUN ejpam-4901 132 11 of of ADP ejpam-4901 132 12 restricted restrict VERB ejpam-4901 132 13 one one NUM ejpam-4901 132 14 - - PUNCT ejpam-4901 132 15 to to ADP ejpam-4901 132 16 - - PUNCT ejpam-4901 132 17 one one NUM ejpam-4901 132 18 functions function NOUN ejpam-4901 132 19 f f X ejpam-4901 132 20 |si |si X ejpam-4901 132 21 : : PUNCT ejpam-4901 132 22 nm nm ADV ejpam-4901 132 23 −→ −→ PROPN ejpam-4901 132 24 nn nn PROPN ejpam-4901 132 25 , , PUNCT ejpam-4901 132 26 ∀s ∀s PROPN ejpam-4901 132 27 ⊆ ⊆ NUM ejpam-4901 132 28 nm nm NOUN ejpam-4901 132 29 is be AUX ejpam-4901 132 30 |îm| |îm| PROPN ejpam-4901 132 31 = = SYM ejpam-4901 132 32 m∑ m∑ VERB ejpam-4901 132 33 i=0 i=0 PROPN ejpam-4901 132 34 ( ( PUNCT ejpam-4901 132 35 m m VERB ejpam-4901 132 36 i i NOUN ejpam-4901 132 37 ) ) PUNCT ejpam-4901 133 1 ( ( PUNCT ejpam-4901 133 2 n)i n)i X ejpam-4901 133 3 ( ( PUNCT ejpam-4901 133 4 1 1 NUM ejpam-4901 133 5 ) ) PUNCT ejpam-4901 133 6 and and CCONJ ejpam-4901 133 7 , , PUNCT ejpam-4901 133 8 from from ADP ejpam-4901 133 9 proposition proposition NOUN ejpam-4901 133 10 2 2 NUM ejpam-4901 133 11 , , PUNCT ejpam-4901 133 12 the the DET ejpam-4901 133 13 number number NOUN ejpam-4901 133 14 of of ADP ejpam-4901 133 15 restricted restrict VERB ejpam-4901 133 16 one one NUM ejpam-4901 133 17 - - PUNCT ejpam-4901 133 18 to to ADP ejpam-4901 133 19 - - PUNCT ejpam-4901 133 20 one one NUM ejpam-4901 133 21 functions function NOUN ejpam-4901 133 22 f f X ejpam-4901 133 23 |si |si X ejpam-4901 133 24 : : PUNCT ejpam-4901 133 25 nm nm ADV ejpam-4901 133 26 −→ −→ PROPN ejpam-4901 133 27 nn nn PROPN ejpam-4901 133 28 , , PUNCT ejpam-4901 133 29 ∀si ∀si PROPN ejpam-4901 133 30 ⊆ ⊆ NUM ejpam-4901 133 31 nm nm NOUN ejpam-4901 133 32 , , PUNCT ejpam-4901 133 33 |si| |si| PROPN ejpam-4901 133 34 = = PUNCT ejpam-4901 134 1 i i PRON ejpam-4901 134 2 such such ADJ ejpam-4901 134 3 that that DET ejpam-4901 134 4 f(a f(a NOUN ejpam-4901 134 5 ) ) PUNCT ejpam-4901 134 6 ≤ ≤ NOUN ejpam-4901 135 1 a,∀a a,∀a VERB ejpam-4901 135 2 ∈ ∈ NOUN ejpam-4901 135 3 nm nm ADV ejpam-4901 135 4 is be AUX ejpam-4901 135 5 ŷ ŷ NUM ejpam-4901 135 6 ( ( PUNCT ejpam-4901 135 7 i i PRON ejpam-4901 135 8 , , PUNCT ejpam-4901 135 9 m m PROPN ejpam-4901 135 10 ) ) PUNCT ejpam-4901 135 11 = = PUNCT ejpam-4901 136 1 ∑ ∑ PUNCT ejpam-4901 136 2 1≤j1 1≤j1 NUM ejpam-4901 136 3 < < X ejpam-4901 136 4 j2< j2< NOUN ejpam-4901 136 5 ... ... PUNCT ejpam-4901 136 6