The PrimeLatz conjecture

(a tribute to Lothar Collatz)

Start from any integer N.

If N is even, divide N by 2.

If N is odd, add to N the next 3 prime numbers > N.

Iterate.

Conjecture: all N’s will enter in a loop, sooner or later.

__________

The prime numbers < 1000 are:

Let’s start with 1:

1 is odd; we add to 1 the next 3 primes (2,3,5) and get 11

11 is odd; we get 11+(13+17+19)=60

60 is even; we get 30

30 is even; we get 15

15 is odd; we get 15+(17+19+23)=74

74 is even; we get 37

37 is odd; we get 37+(41+43+47)=168

168 is even; we get 84

84 is even; we get 42

42 is even; we get 21

21 is odd; we get 21+(23+29+31)=104

104 is even; we get 52

52 is even; we get 26

26 is even; we get 13

13 is odd; we get 13+(17+19+23)=72

72 is even; we get 36

36 is even; we get 18

18 is even; we get 9

9 is odd; we get 9+(11+13+17)=50

50 is even; we get 25

25 is odd; we get 25+(29+31+37)=122

122 is even; we get 61

61 is odd; we get 61+(67+71+73)=272

272 is even; we get 136

136 is even; we get 68

68 is even; we get 34

34 is even; we get 17

17 is odd; we get 17+(19+23+29)=88

88 is even; we get 44

44 is even; we get 22

22 is even; we get 11... entering thus in a loop.

Best,

É.

(Please have a try with 83...)

__________

A couple of hours after this was posted, had Hans Havermann computed the future of a lot of integers, noting that they were all ending in the loop above (starting here with the smallest integer, 9):

[Hans Havermann]

Confining myself to iterative chains where all members are less than 100 million, I find no loops other than your:

{9,50,25,122,61,272,136,68,34,17,88,44,22,11,60,30,15,74,37,168,84,42,21,104,52,26,13,72,36,18}.

Jean-Marc Falcoz was quick to send this too (in French):

[Jean-Marc Falcoz]:

Ci-dessous, voici les 10 000 premiers termes : {1,30} signifie que 1 rentre dans une boucle après la 30e itération.

Parmi ces 10 000 termes, le maximum est 6578, qui boucle après 6333 itérations.

Je joins le graphe.

b-file by Jean-Marc Falcoz (first 10 000 terms of the PrimeLatz conjecture and number of iterations needed to enter the above loop):

{1, 30}

{2, 31}

{3, 30}

{4, 32}

{5, 30}

{6, 31}

{7, 35}

{8, 33}

{9, 29}

{10, 31}

{11, 29}

{12, 32}

{13, 29}

{14, 36}

{15, 29}

{16, 34}

{17, 29}

{18, 29}

{19, 43}

{20, 32}

{21, 29}

{22, 29}

{23, 31}

{24, 33}

{25, 29}

{26, 29}

{27, 50}

{28, 37}

{29, 58}

{30, 29}

{31, 47}

{32, 35}

{33, 41}

{34, 29}

{35, 98}

{36, 29}

{37, 29}

{38, 44}

{39, 95}

{40, 33}

{41, 35}

{42, 29}

{43, 50}

{44, 29}

{45, 44}

{46, 32}

{47, 60}

{48, 34}

{49, 68}

{50, 29}

{51, 41}

{52, 29}

{53, 32}

{54, 51}

{55, 57}

{56, 38}

{57, 31}

{58, 59}

{59, 54}

{60, 29}

{61, 29}

{62, 48}

{63, 35}

{64, 36}

{65, 59}

{66, 42}

{67, 48}

{68, 29}

{69, 56}

{70, 99}

{71, 40}

{72, 29}

{73, 53}

{74, 29}

{75, 59}

{76, 45}

{77, 39}

{78, 96}

{79, 44}

{80, 34}

{81, 50}

{82, 36}

{83, 1870}

{84, 29}

{85, 93}

{86, 51}

{87, 41}

{88, 29}

{89, 96}

{90, 45}

{91, 72}

{92, 33}

{93, 90}

{94, 61}

{95, 81}

{96, 35}

{97, 45}

{98, 69}

{99, 78}

{100, 30}

{101, 48}

{102, 42}

{103, 55}

{104, 29}

{105, 45}

{106, 33}

{107, 35}

{108, 52}

{109, 33}

{110, 58}

{111, 66}

{112, 39}

{113, 75}

{114, 32}

{115, 56}

{116, 60}

{117, 40}

{118, 55}

{119, 69}

{120, 30}

{121, 55}

{122, 29}

{123, 37}

{124, 49}

{125, 63}

{126, 36}

{127, 72}

{128, 37}

{129, 52}

{130, 60}

{131, 66}

{132, 43}

{133, 47}

{134, 49}

{135, 103}

{136, 29}

{137, 33}

{138, 57}

{139, 63}

{140, 100}

{141, 1931}

{142, 41}

{143, 63}

{144, 30}

{145, 46}

{146, 54}

{147, 1904}

{148, 30}

{149, 60}

{150, 60}

{151, 1901}

{152, 46}

{153, 38}

{154, 40}

{155, 57}

{156, 97}

{157, 39}

{158, 45}

{159, 60}

{160, 35}

{161, 1874}

{162, 51}

{163, 57}

{164, 37}

{165, 36}

{166, 1871}

{167, 51}

{168, 29}

{169, 109}

{170, 94}

{171, 33}

{172, 52}

{173, 91}

{174, 42}

{175, 48}

{176, 30}

{177, 76}

{178, 97}

{179, 94}

{180, 46}

{181, 88}

{182, 73}

{183, 100}

{184, 34}

{185, 1868}

{186, 91}

{187, 39}

{188, 62}

{189, 40}

{190, 82}

{191, 97}

{192, 36}

{193, 34}

{194, 46}

{195, 94}

{196, 70}

{197, 88}

{198, 79}

{199, 77}

{200, 31}

{201, 92}

{202, 49}

{203, 56}

{204, 43}

{205, 76}

{206, 56}

{207, 46}

{208, 30}

{209, 970}

{210, 46}

{211, 250}

{212, 34}

{213, 39}

{214, 36}

{215, 74}

{216, 53}

{217, 43}

{218, 34}

{219, 96}

{220, 59}

{221, 68}

{222, 67}

{223, 36}

{224, 40}

{225, 65}

{226, 76}

{227, 64}

{228, 33}

{229, 70}

{230, 57}

{231, 59}

{232, 61}

{233, 67}

{234, 41}

{235, 82}

{236, 56}

{237, 59}

{238, 70}

{239, 119}

{240, 31}

{241, 64}

{242, 56}

{243, 67}

{244, 30}

{245, 76}

{246, 38}

{247, 116}

{248, 50}

{249, 57}

{250, 64}

{251, 64}

{252, 37}

{253, 61}

{254, 73}

{255, 54}

{256, 38}

{257, 67}

{258, 53}

{259, 35}

{260, 61}

{261, 51}

{262, 67}

{263, 107}

{264, 44}

{265, 64}

{266, 48}

{267, 70}

{268, 50}

{269, 94}

{270, 104}

{271, 67}

{272, 29}

{273, 43}

{274, 34}

{275, 48}

{276, 58}

{277, 1971}

{278, 64}

{279, 45}

{280, 101}

{281, 1965}

{282, 1932}

{283, 1965}

{284, 42}

{285, 1932}

{286, 64}

{287, 73}

{288, 31}

{289, 64}

{290, 47}

{291, 1962}

{292, 55}

{293, 42}

{294, 1905}

{295, 64}

{296, 31}

{297, 104}

{298, 61}

{299, 1929}

{300, 61}

{301, 44}

{302, 1902}

{303, 1893}

{304, 47}

{305, 59}

{306, 39}

{307, 101}

{308, 41}

{309, 56}

{310, 58}

{311, 64}

{312, 98}

{313, 67}

{314, 40}

{315, 43}

{316, 46}

{317, 52}

{318, 61}

{319, 1899}

{320, 36}

{321, 55}

{322, 1875}

{323, 1899}

{324, 52}

{325, 40}

{326, 58}

{327, 116}

{328, 38}

{329, 33}

{330, 37}

{331, 58}

{332, 1872}

{333, 49}

{334, 52}

{335, 37}

{336, 30}

{337, 176}

{338, 110}

{339, 37}

{340, 95}

{341, 55}

{342, 34}

{343, 46}

{344, 53}

{345, 89}

{346, 92}

{347, 34}

{348, 43}

{349, 80}

{350, 49}

{351, 107}

{352, 31}

{353, 49}

{354, 77}

{355, 107}

{356, 98}

{357, 77}

{358, 95}

{359, 53}

{360, 47}

{361, 1872}

{362, 89}

{363, 46}

{364, 74}

{365, 92}

{366, 101}

{367, 1881}

{368, 35}

{369, 66}

{370, 1869}

{371, 89}

{372, 92}

{373, 89}

{374, 40}

{375, 159}

{376, 63}

{377, 101}

{378, 41}

{379, 243}

{380, 83}

{381, 86}

{382, 98}

{383, 1866}

{384, 37}

{385, 38}

{386, 35}

{387, 240}

{388, 47}

{389, 56}

{390, 95}

{391, 117}

{392, 71}

{393, 35}

{394, 89}

{395, 237}

{396, 80}

{397, 98}

{398, 78}

{399, 53}

{400, 32}

{401, 92}

{402, 93}

{403, 99}

{404, 50}

{405, 111}

{406, 57}

{407, 50}

{408, 44}

{409, 50}

{410, 77}

{411, 284}

{412, 57}

{413, 96}

{414, 47}

{415, 86}

{416, 31}

{417, 254}

{418, 971}

{419, 43}

{420, 47}

{421, 93}

{422, 251}

{423, 103}

{424, 35}

{425, 57}

{426, 40}

{427, 78}

{428, 37}

{429, 77}

{430, 75}

{431, 90}

{432, 54}

{433, 74}

{434, 44}

{435, 968}

{436, 35}

{437, 72}

{438, 97}

{439, 75}

{440, 60}

{441, 71}

{442, 69}

{443, 2111}

{444, 68}

{445, 248}

{446, 37}

{447, 72}

{448, 41}

{449, 94}

{450, 66}

{451, 74}

{452, 77}

{453, 245}

{454, 65}

{455, 94}

{456, 34}

{457, 63}

{458, 71}

{459, 91}

{460, 58}

{461, 89}

{462, 60}

{463, 63}

{464, 62}

{465, 38}

{466, 68}

{467, 89}

{468, 42}

{469, 103}

{470, 83}

{471, 68}

{472, 57}

{473, 129}

{474, 60}

{475, 83}

{476, 71}

{477, 115}

{478, 120}

{479, 92}

{480, 32}

{481, 86}

{482, 65}

{483, 80}

{484, 57}

{485, 123}

{486, 68}

{487, 86}

{488, 31}

{489, 89}

{490, 77}

{491, 73}

{492, 39}

{493, 80}

{494, 117}

{495, 83}

{496, 51}

{497, 68}

{498, 58}

{499, 77}

{500, 65}

{501, 77}

{502, 65}

{503, 71}

{504, 38}

{505, 2023}

{506, 62}

{507, 65}

{508, 74}

{509, 114}

{510, 55}

{511, 71}

{512, 39}

{513, 51}

{514, 68}

{515, 62}

{516, 54}

{517, 2014}

{518, 36}

{519, 111}

{520, 62}

{521, 59}

{522, 52}

{523, 71}

{524, 68}

{525, 59}

{526, 108}

{527, 1987}

{528, 45}

{529, 50}

{530, 65}

{531, 33}

{532, 49}

{533, 56}

{534, 71}

{535, 2005}

{536, 51}

{537, 41}

{538, 95}

{539, 47}

{540, 105}

{541, 62}

{542, 68}

{543, 1984}

{544, 30}

{545, 2002}

{546, 44}

{547, 1999}

{548, 35}

{549, 92}

{550, 49}

{551, 105}

{552, 59}

{553, 1999}

{554, 1972}

{555, 1972}

{556, 65}

{557, 41}

{558, 46}

{559, 1996}

{560, 102}

{561, 1969}

{562, 1966}

{563, 1936}

{564, 1933}

{565, 38}

{566, 1966}

{567, 1969}

{568, 43}

{569, 35}

{570, 1933}

{571, 1966}

{572, 65}

{573, 1912}

{574, 74}

{575, 92}

{576, 32}

{577, 66}

{578, 65}

{579, 110}

{580, 48}

{581, 68}

{582, 1963}

{583, 89}

{584, 56}

{585, 68}

{586, 43}

{587, 1969}

{588, 1906}

{589, 63}

{590, 65}

{591, 65}

{592, 32}

{593, 65}

{594, 105}

{595, 1966}

{596, 62}

{597, 1963}

{598, 1930}

{599, 71}

{600, 62}

{601, 1960}

{602, 45}

{603, 63}

{604, 1903}

{605, 68}

{606, 1894}

{607, 105}

{608, 48}

{609, 1930}

{610, 60}

{611, 1930}

{612, 40}

{613, 62}

{614, 102}

{615, 1927}

{616, 42}

{617, 1891}

{618, 57}

{619, 174}

{620, 59}

{621, 56}

{622, 65}

{623, 1912}

{624, 99}

{625, 54}

{626, 68}

{627, 1888}

{628, 41}

{629, 65}

{630, 44}

{631, 52}

{632, 47}

{633, 1906}

{634, 53}

{635, 51}

{636, 62}

{637, 59}

{638, 1900}

{639, 168}

{640, 37}

{641, 1903}

{642, 56}

{643, 46}

{644, 1876}

{645, 45}

{646, 1900}

{647, 65}

{648, 53}

{649, 65}

{650, 41}

{651, 42}

{652, 59}

{653, 240}

{654, 117}

{655, 62}

{656, 39}

{657, 207}

{658, 34}

{659, 198}

{660, 38}

{661, 129}

{662, 59}

{663, 180}

{664, 1873}

{665, 216}

{666, 50}

{667, 1897}

{668, 53}

{669, 1897}

{670, 38}

{671, 114}

{672, 31}

{673, 126}

{674, 177}

{675, 1894}

{676, 111}

{677, 57}

{678, 38}

{679, 126}

{680, 96}

{681, 123}

{682, 56}

{683, 47}

{684, 35}

{685, 98}

{686, 47}

{687, 90}

{688, 54}

{689, 120}

{690, 90}

{691, 111}

{692, 93}

{693, 174}

{694, 35}

{695, 53}

{696, 44}

{697, 87}

{698, 81}

{699, 1936}

{700, 50}

{701, 81}

{702, 108}

{703, 92}

{704, 32}

{705, 108}

{706, 50}

{707, 1933}

{708, 78}

{709, 1876}

{710, 108}

{711, 111}

{712, 99}

{713, 111}

{714, 78}

{715, 105}

{716, 96}

{717, 93}

{718, 54}

{719, 111}

{720, 48}

{721, 96}

{722, 1873}

{723, 108}

{724, 90}

{725, 111}

{726, 47}

{727, 105}

{728, 75}

{729, 39}

{730, 93}

{731, 108}

{732, 102}

{733, 99}

{734, 1882}

{735, 93}

{736, 36}

{737, 102}

{738, 67}

{739, 51}

{740, 1870}

{741, 44}

{742, 90}

{743, 90}

{744, 93}

{745, 48}

{746, 90}

{747, 105}

{748, 41}

{749, 111}

{750, 160}

{751, 1879}

{752, 64}

{753, 87}

{754, 102}

{755, 172}

{756, 42}

{757, 57}

{758, 244}

{759, 42}

{760, 84}

{761, 129}

{762, 87}

{763, 157}

{764, 99}

{765, 54}

{766, 1867}

{767, 244}

{768, 38}

{769, 1870}

{770, 39}

{771, 121}

{772, 36}

{773, 154}

{774, 241}

{775, 84}

{776, 48}

{777, 106}

{778, 57}

{779, 999}

{780, 96}

{781, 121}

{782, 118}

{783, 102}

{784, 72}

{785, 1864}

{786, 36}

{787, 238}

{788, 90}

{789, 100}

{790, 238}

{791, 96}

{792, 81}

{793, 996}

{794, 99}

{795, 47}

{796, 79}

{797, 102}

{798, 54}

{799, 115}

{800, 33}

{801, 235}

{802, 93}

{803, 44}

{804, 94}

{805, 57}

{806, 100}

{807, 61}

{808, 51}

{809, 48}

{810, 112}

{811, 41}

{812, 58}

{813, 96}

{814, 51}

{815, 213}

{816, 45}

{817, 288}

{818, 51}

{819, 73}

{820, 78}

{821, 93}

{822, 285}

{823, 378}

{824, 58}

{825, 90}

{826, 97}

{827, 109}

{828, 48}

{829, 67}

{830, 87}

{831, 60}

{832, 32}

{833, 67}

{834, 255}

{835, 107}

{836, 972}

{837, 106}

{838, 44}

{839, 44}

{840, 48}

{841, 282}

{842, 94}

{843, 84}

{844, 252}

{845, 57}

{846, 104}

{847, 82}

{848, 36}

{849, 285}

{850, 58}

{851, 498}

{852, 41}

{853, 81}

{854, 79}

{855, 495}

{856, 38}

{857, 58}

{858, 78}

{859, 972}

{860, 76}

{861, 106}

{862, 91}

{863, 101}

{864, 55}

{865, 76}

{866, 75}

{867, 78}

{868, 45}

{869, 114}

{870, 969}

{871, 79}

{872, 36}

{873, 88}

{874, 73}

{875, 100}

{876, 98}

{877, 75}

{878, 76}

{879, 97}

{880, 61}

{881, 82}

{882, 72}

{883, 966}

{884, 70}

{885, 330}

{886, 2112}

{887, 249}

{888, 69}

{889, 91}

{890, 249}

{891, 73}

{892, 38}

{893, 81}

{894, 73}

{895, 69}

{896, 42}

{897, 963}

{898, 95}

{899, 249}

{900, 67}

{901, 98}

{902, 75}

{903, 98}

{904, 78}

{905, 2109}

{906, 246}

{907, 70}

{908, 66}

{909, 246}

{910, 95}

{911, 64}

{912, 35}

{913, 131}

{914, 64}

{915, 92}

{916, 72}

{917, 243}

{918, 92}

{919, 572}

{920, 59}

{921, 72}

{922, 90}

{923, 237}

{924, 61}

{925, 89}

{926, 64}

{927, 49}

{928, 63}

{929, 92}

{930, 39}

{931, 125}

{932, 69}

{933, 86}

{934, 90}

{935, 87}

{936, 43}

{937, 98}

{938, 104}

{939, 122}

{940, 84}

{941, 75}

{942, 69}

{943, 67}

{944, 58}

{945, 119}

{946, 130}

{947, 80}

{948, 61}

{949, 36}

{950, 84}

{951, 113}

{952, 72}

{953, 116}

{954, 116}

{955, 38}

{956, 121}

{957, 61}

{958, 93}

{959, 84}

{960, 33}

{961, 116}

{962, 87}

{963, 101}

{964, 66}

{965, 127}

{966, 81}

{967, 113}

{968, 58}

{969, 113}

{970, 124}

{971, 87}

{972, 69}

{973, 124}

{974, 87}

{975, 110}

{976, 32}

{977, 65}

{978, 90}

{979, 84}

{980, 78}

{981, 121}

{982, 74}

{983, 89}

{984, 40}

{985, 81}

{986, 81}

{987, 62}

{988, 118}

{989, 2033}

{990, 84}

{991, 87}

{992, 52}

{993, 84}

{994, 69}

{995, 86}

{996, 59}

{997, 79}

{998, 78}

{999, 2027}

{1000, 66}

{1001, 71}

{1002, 78}

{1003, 81}

{1004, 66}

{1005, 95}

{1006, 72}

{1007, 66}

{1008, 39}

{1009, 160}

{1010, 2024}

{1011, 78}

{1012, 63}

{1013, 121}

{1014, 66}

{1015, 108}

{1016, 75}

{1017, 75}

{1018, 115}

{1019, 55}

{1020, 56}

{1021, 118}

{1022, 72}

{1023, 62}

{1024, 40}

{1025, 58}

{1026, 52}

{1027, 165}

{1028, 69}

{1029, 2021}

{1030, 63}

{1031, 115}

{1032, 55}

{1033, 2018}

{1034, 2015}

{1035, 282}

{1036, 37}

{1037, 56}

{1038, 112}

{1039, 63}

{1040, 63}

{1041, 60}

{1042, 60}

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{1044, 53}

{1045, 87}

{1046, 72}

{1047, 112}

{1048, 69}

{1049, 49}

{1050, 60}

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{1052, 109}

{1053, 57}

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{1055, 37}

{1056, 46}

{1057, 81}

{1058, 51}

{1059, 72}

{1060, 66}

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{1062, 34}

{1063, 69}

{1064, 50}

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{1066, 57}

{1067, 77}

{1068, 72}

{1069, 60}

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{1071, 57}

{1072, 52}

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{1074, 42}

{1075, 1680}

{1076, 96}

{1077, 51}

{1078, 48}

{1079, 74}

{1080, 106}

{1081, 34}

{1082, 63}

{1083, 83}

{1084, 69}

{1085, 57}

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{1087, 48}

{1088, 31}

{1089, 54}

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{1091, 39}

{1092, 45}

{1093, 157}

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{1095, 51}

{1096, 36}

{1097, 56}

{1098, 93}

{1099, 48}

{1100, 50}

{1101, 48}

{1102, 106}

{1103, 151}

{1104, 60}

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{1106, 2000}

{1107, 45}

{1108, 1973}

{1109, 117}

{1110, 1973}

{1111, 106}

{1112, 66}

{1113, 148}

{1114, 42}

{1115, 2000}

{1116, 47}

{1117, 42}

{1118, 1997}

{1119, 90}

{1120, 103}

{1121, 1997}

{1122, 1970}

{1123, 69}

{1124, 1967}

{1125, 111}

{1126, 1937}

{1127, 1937}

{1128, 1934}

{1129, 73}

{1130, 39}

{1131, 1994}

{1132, 1967}

{1133, 96}

{1134, 1970}

{1135, 2350}

{1136, 44}

{1137, 81}

{1138, 36}

{1139, 66}

{1140, 1934}

{1141, 36}

{1142, 1967}

{1143, 133}

{1144, 66}

{1145, 106}

{1146, 1913}

{1147, 99}

{1148, 75}

{1149, 70}

{1150, 93}

{1151, 78}

{1152, 33}

{1153, 103}

{1154, 67}

{1155, 106}

{1156, 66}

{1157, 60}

{1158, 111}

{1159, 106}

{1160, 49}

{1161, 1994}

{1162, 69}

{1163, 72}

{1164, 1964}

{1165, 1910}

{1166, 90}

{1167, 100}

{1168, 57}

{1169, 1991}

{1170, 69}

{1171, 67}

{1172, 44}

{1173, 121}

{1174, 1970}

{1175, 36}

{1176, 1907}

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{1178, 64}

{1179, 108}

{1180, 66}

{1181, 87}

{1182, 66}

{1183, 64}

{1184, 33}

{1185, 105}

{1186, 66}

{1187, 115}

{1188, 106}

{1189, 1946}

{1190, 1967}

{1191, 61}

{1192, 63}

{1193, 67}

{1194, 1964}

{1195, 79}

{1196, 1931}

{1197, 75}

{1198, 72}

{1199, 1943}

{1200, 63}

{1201, 1964}

{1202, 1961}

{1203, 109}

{1204, 46}

{1205, 238}

{1206, 64}

{1207, 72}

{1208, 1904}

{1209, 1943}

{1210, 69}

{1211, 52}

{1212, 1895}

{1213, 217}

{1214, 106}

{1215, 69}

{1216, 49}

{1217, 151}

{1218, 1931}

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{1220, 61}

{1221, 66}

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{1223, 1931}

{1224, 41}

{1225, 148}

{1226, 63}

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{1232, 43}

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{1251, 181}

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{1278, 169}

{1279, 2157}

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{1284, 57}

{1285, 166}

{1286, 47}

{1287, 72}

{1288, 1877}

{1289, 2136}

{1290, 46}

{1291, 69}

{1292, 1901}

{1293, 2124}

{1294, 66}

{1295, 202}

{1296, 54}

{1297, 46}

{1298, 66}

{1299, 199}

{1300, 42}

{1301, 44}

{1302, 43}

{1303, 217}

{1304, 60}

{1305, 45}

{1306, 241}

{1307, 211}

{1308, 118}

{1309, 57}

{1310, 63}

{1311, 63}

{1312, 40}

{1313, 42}

{1314, 208}

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{1316, 35}

{1317, 38}

{1318, 199}

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{1321, 35}

{1322, 130}

{1323, 238}

{1324, 60}

{1325, 205}

{1326, 181}

{1327, 208}

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{1330, 217}

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{1332, 51}

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{1336, 54}

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{1340, 39}

{1341, 45}

{1342, 115}

{1343, 106}

{1344, 32}

{1345, 202}

{1346, 127}

{1347, 127}

{1348, 178}

{1349, 214}

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{1352, 112}

{1353, 54}

{1354, 58}

{1355, 60}

{1356, 39}

{1357, 205}

{1358, 127}

{1359, 193}

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{1366, 48}

{1367, 94}

{1368, 36}

{1369, 133}

{1370, 99}

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{1372, 48}

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{1375, 217}

{1376, 55}

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{1379, 48}

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{1383, 57}

{1384, 94}

{1385, 112}

{1386, 175}

{1387, 163}

{1388, 36}

{1389, 85}

{1390, 54}

{1391, 214}

{1392, 45}

{1393, 96}

{1394, 88}

{1395, 118}

{1396, 82}

{1397, 112}

{1398, 1937}

{1399, 133}

{1400, 51}

{1401, 109}

{1402, 82}

{1403, 1883}

{1404, 109}

{1405, 82}

{1406, 93}

{1407, 109}

{1408, 33}

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{1411, 172}

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{1413, 85}

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{1422, 112}

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{1437, 87}

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{1446, 109}

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{1451, 64}

{1452, 48}

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{1464, 103}

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{1473, 106}

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{1489, 115}

{1490, 49}

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{1494, 106}

{1495, 49}

{1496, 42}

{1497, 112}

{1498, 112}

{1499, 248}

{1500, 161}

{1501, 91}

{1502, 1880}

{1503, 524}

{1504, 65}

{1505, 208}

{1506, 88}

{1507, 46}

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{1509, 109}

{1510, 173}

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{1512, 43}

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{1514, 58}

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{1519, 1877}

{1520, 85}

{1521, 170}

{1522, 130}

{1523, 145}

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{1526, 158}

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{1530, 55}

{1531, 40}

{1532, 1868}

{1533, 515}

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{1535, 130}

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{1540, 40}

{1541, 515}

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{1574, 239}

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{1578, 101}

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{1583, 152}

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{1585, 104}

{1586, 997}

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{1592, 80}

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{1595, 37}

{1596, 55}

{1597, 149}

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{1600, 34}

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{1602, 236}

{1603, 98}

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{1606, 45}

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{1624, 59}

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{1641, 39}

{1642, 94}

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{1888, 59}

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{1893, 808}

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{1896, 62}

{1897, 811}

{1898, 37}

{1899, 68}

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{1901, 90}

{1902, 114}

{1903, 525}

{1904, 73}

{1905, 65}

{1906, 117}

{1907, 114}

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{1910, 39}

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{1912, 122}

{1913, 87}

{1914, 62}

{1915, 85}

{1916, 94}

{1917, 105}

{1918, 85}

{1919, 78}

{1920, 34}

{1921, 111}

{1922, 117}

{1923, 117}

{1924, 88}

{1925, 108}

{1926, 102}

{1927, 39}

{1928, 67}

{1929, 451}

{1930, 128}

{1931, 124}

{1932, 82}

{1933, 75}

{1934, 114}

{1935, 36}

{1936, 59}

{1937, 82}

{1938, 114}

{1939, 99}

{1940, 125}

{1941, 121}

{1942, 88}

{1943, 69}

{1944, 70}

{1945, 72}

{1946, 125}

{1947, 79}

{1948, 88}

{1949, 111}

{1950, 111}

{1951, 2061}

{1952, 33}

{1953, 96}

{1954, 66}

{1955, 76}

{1956, 91}

{1957, 66}

{1958, 85}

{1959, 94}

{1960, 79}

{1961, 85}

{1962, 122}

{1963, 108}

{1964, 75}

{1965, 122}

{1966, 90}

{1967, 85}

{1968, 41}

{1969, 59}

{1970, 82}

{1971, 79}

{1972, 82}

{1973, 93}

{1974, 63}

{1975, 82}

{1976, 119}

{1977, 56}

{1978, 2034}

{1979, 76}

{1980, 85}

{1981, 2055}

{1982, 88}

{1983, 90}

{1984, 53}

{1985, 76}

{1986, 85}

{1987, 83}

{1988, 70}

{1989, 73}

{1990, 87}

{1991, 79}

{1992, 60}

{1993, 2031}

{1994, 80}

{1995, 76}

{1996, 79}

{1997, 76}

{1998, 2028}

{1999, 149}

{2000, 67}

{2001, 70}

{2002, 72}

{2003, 2043}

{2004, 79}

{2005, 85}

{2006, 82}

{2007, 84}

{2008, 67}

{2009, 43}

{2010, 96}

{2011, 72}

{2012, 73}

{2013, 118}

{2014, 67}

{2015, 82}

{2016, 40}

{2017, 70}

{2018, 161}

{2019, 77}

{2020, 2025}

{2021, 69}

{2022, 79}

{2023, 93}

{2024, 64}

{2025, 112}

{2026, 122}

{2027, 47}

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{2030, 109}

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{2032, 76}

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{2035, 172}

{2036, 116}

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{2039, 73}

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{2042, 119}

{2043, 106}

{2044, 73}

{2045, 66}

{2046, 63}

{2047, 2025}

{2048, 41}

{2049, 1880}

{2050, 59}

{2051, 2022}

{2052, 53}

{2053, 169}

{2054, 166}

{2055, 125}

{2056, 70}

{2057, 103}

{2058, 2022}

{2059, 2019}

{2060, 64}

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{5091, 180}

{5092, 174}

{5093, 57}

{5094, 1921}

{5095, 109}

{5096, 62}

{5097, 1891}

{5098, 80}

{5099, 69}

{5100, 54}

{5101, 1888}

{5102, 1918}

{5103, 1966}

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{5105, 66}

{5106, 171}

{5107, 66}

{5108, 1909}

{5109, 171}

{5110, 1885}

{5111, 63}

{5112, 171}

{5113, 107}

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{5115, 1915}

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{5118, 77}

{5119, 82}

{5120, 40}

{5121, 97}

{5122, 168}

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{5124, 52}

{5125, 77}

{5126, 91}

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{5133, 104}

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{5135, 86}

{5136, 59}

{5137, 342}

{5138, 54}

{5139, 1915}

{5140, 168}

{5141, 1882}

{5142, 2156}

{5143, 333}

{5144, 49}

{5145, 67}

{5146, 1906}

{5147, 94}

{5148, 74}

{5149, 51}

{5150, 101}

{5151, 339}

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{5153, 64}

{5154, 88}

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{5158, 53}

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{5161, 74}

{5162, 165}

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{5166, 51}

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{5171, 59}

{5172, 2126}

{5173, 91}

{5174, 222}

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{5176, 68}

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{5179, 138}

{5180, 204}

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{5182, 74}

{5183, 2153}

{5184, 56}

{5185, 79}

{5186, 50}

{5187, 162}

{5188, 48}

{5189, 82}

{5190, 219}

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{5193, 89}

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{5195, 76}

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{5198, 129}

{5199, 73}

{5200, 44}

{5201, 129}

{5202, 246}

{5203, 83}

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{5205, 71}

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{5209, 2129}

{5210, 198}

{5211, 80}

{5212, 219}

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{5214, 126}

{5215, 2129}

{5216, 62}

{5217, 126}

{5218, 68}

{5219, 77}

{5220, 47}

{5221, 216}

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{5224, 243}

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{5226, 195}

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{5230, 43}

{5231, 50}

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{5234, 46}

{5235, 278}

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{5238, 1718}

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{5246, 44}

{5247, 234}

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{5279, 189}

{5280, 41}

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{5299, 231}

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{5301, 59}

{5302, 1709}

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{5304, 183}

{5305, 437}

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{5307, 162}

{5308, 210}

{5309, 56}

{5310, 207}

{5311, 1721}

{5312, 1876}

{5313, 204}

{5314, 219}

{5315, 1706}

{5316, 50}

{5317, 204}

{5318, 159}

{5319, 2053}

{5320, 219}

{5321, 53}

{5322, 1903}

{5323, 1712}

{5324, 132}

{5325, 216}

{5326, 113}

{5327, 276}

{5328, 53}

{5329, 201}

{5330, 201}

{5331, 50}

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{5333, 1915}

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{5339, 213}

{5340, 198}

{5341, 104}

{5342, 210}

{5343, 240}

{5344, 56}

{5345, 105}

{5346, 44}

{5347, 110}

{5348, 198}

{5349, 77}

{5350, 1694}

{5351, 240}

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{5355, 101}

{5356, 102}

{5357, 225}

{5358, 92}

{5359, 207}

{5360, 41}

{5361, 1691}

{5362, 234}

{5363, 219}

{5364, 47}

{5365, 135}

{5366, 37}

{5367, 74}

{5368, 117}

{5369, 89}

{5370, 231}

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{5372, 108}

{5373, 819}

{5374, 132}

{5375, 132}

{5376, 34}

{5377, 228}

{5378, 237}

{5379, 98}

{5380, 204}

{5381, 216}

{5382, 71}

{5383, 1903}

{5384, 129}

{5385, 95}

{5386, 216}

{5387, 303}

{5388, 129}

{5389, 1903}

{5390, 213}

{5391, 92}

{5392, 180}

{5393, 216}

{5394, 234}

{5395, 68}

{5396, 216}

{5397, 1900}

{5398, 234}

{5399, 216}

{5400, 1897}

{5401, 153}

{5402, 63}

{5403, 213}

{5404, 1897}

{5405, 213}

{5406, 210}

{5407, 231}

{5408, 114}

{5409, 213}

{5410, 210}

{5411, 234}

{5412, 56}

{5413, 65}

{5414, 228}

{5415, 231}

{5416, 60}

{5417, 207}

{5418, 207}

{5419, 132}

{5420, 62}

{5421, 201}

{5422, 198}

{5423, 213}

{5424, 41}

{5425, 225}

{5426, 204}

{5427, 132}

{5428, 207}

{5429, 195}

{5430, 47}

{5431, 198}

{5432, 129}

{5433, 210}

{5434, 129}

{5435, 201}

{5436, 195}

{5437, 207}

{5438, 195}

{5439, 198}

{5440, 99}

{5441, 210}

{5442, 44}

{5443, 195}

{5444, 105}

{5445, 165}

{5446, 201}

{5447, 44}

{5448, 126}

{5449, 111}

{5450, 213}

{5451, 207}

{5452, 1894}

{5453, 228}

{5454, 53}

{5455, 177}

{5456, 59}

{5457, 177}

{5458, 204}

{5459, 62}

{5460, 192}

{5461, 41}

{5462, 198}

{5463, 210}

{5464, 50}

{5465, 210}

{5466, 53}

{5467, 156}

{5468, 96}

{5469, 108}

{5470, 225}

{5471, 174}

{5472, 38}

{5473, 207}

{5474, 105}

{5475, 201}

{5476, 135}

{5477, 132}

{5478, 204}

{5479, 255}

{5480, 101}

{5481, 117}

{5482, 102}

{5483, 168}

{5484, 1891}

{5485, 129}

{5486, 189}

{5487, 195}

{5488, 50}

{5489, 222}

{5490, 102}

{5491, 201}

{5492, 114}

{5493, 129}

{5494, 129}

{5495, 141}

{5496, 93}

{5497, 1894}

{5498, 255}

{5499, 126}

{5500, 219}

{5501, 126}

{5502, 1891}

{5503, 534}

{5504, 57}

{5505, 99}

{5506, 186}

{5507, 99}

{5508, 126}

{5509, 243}

{5510, 180}

{5511, 531}

{5512, 123}

{5513, 96}

{5514, 123}

{5515, 141}

{5516, 50}

{5517, 120}

{5518, 107}

{5519, 240}

{5520, 93}

{5521, 117}

{5522, 132}

{5523, 252}

{5524, 1888}

{5525, 93}

{5526, 168}

{5527, 68}

{5528, 114}

{5529, 123}

{5530, 3453}

{5531, 519}

{5532, 59}

{5533, 3462}

{5534, 114}

{5535, 90}

{5536, 96}

{5537, 62}

{5538, 510}

{5539, 234}

{5540, 114}

{5541, 3459}

{5542, 219}

{5543, 183}

{5544, 177}

{5545, 120}

{5546, 104}

{5547, 129}

{5548, 165}

{5549, 3450}

{5550, 126}

{5551, 59}

{5552, 38}

{5553, 303}

{5554, 104}

{5555, 516}

{5556, 87}

{5557, 231}

{5558, 180}

{5559, 126}

{5560, 56}

{5561, 513}

{5562, 111}

{5563, 507}

{5564, 216}

{5565, 101}

{5566, 123}

{5567, 3441}

{5568, 47}

{5569, 300}

{5570, 297}

{5571, 111}

{5572, 98}

{5573, 1942}

{5574, 141}

{5575, 225}

{5576, 90}

{5577, 101}

{5578, 177}

{5579, 108}

{5580, 120}

{5581, 294}

{5582, 138}

{5583, 117}

{5584, 84}

{5585, 270}

{5586, 120}

{5587, 96}

{5588, 114}

{5589, 174}

{5590, 285}

{5591, 2005}

{5592, 1939}

{5593, 98}

{5594, 96}

{5595, 168}

{5596, 135}

{5597, 117}

{5598, 282}

{5599, 270}

{5600, 53}

{5601, 120}

{5602, 114}

{5603, 267}

{5604, 111}

{5605, 2002}

{5606, 111}

{5607, 165}

{5608, 84}

{5609, 114}

{5610, 93}

{5611, 279}

{5612, 1885}

{5613, 99}

{5614, 56}

{5615, 1996}

{5616, 111}

{5617, 93}

{5618, 162}

{5619, 264}

{5620, 84}

{5621, 99}

{5622, 213}

{5623, 261}

{5624, 95}

{5625, 114}

{5626, 117}

{5627, 1999}

{5628, 111}

{5629, 96}

{5630, 90}

{5631, 96}

{5632, 35}

{5633, 114}

{5634, 1990}

{5635, 123}

{5636, 117}

{5637, 59}

{5638, 111}

{5639, 93}

{5640, 111}

{5641, 56}

{5642, 144}

{5643, 1993}

{5644, 174}

{5645, 162}

{5646, 108}

{5647, 90}

{5648, 53}

{5649, 159}

{5650, 210}

{5651, 114}

{5652, 87}

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{5654, 246}

{5655, 111}

{5656, 1936}

{5657, 144}

{5658, 132}

{5659, 93}

{5660, 108}

{5661, 111}

{5662, 1882}

{5663, 201}

{5664, 81}

{5665, 1981}

{5666, 108}

{5667, 141}

{5668, 105}

{5669, 207}

{5670, 243}

{5671, 129}

{5672, 1879}

{5673, 237}

{5674, 108}

{5675, 90}

{5676, 198}

{5677, 138}

{5678, 132}

{5679, 132}

{5680, 111}

{5681, 144}

{5682, 105}

{5683, 240}

{5684, 126}

{5685, 87}

{5686, 129}

{5687, 204}

{5688, 114}

{5689, 201}

{5690, 171}

{5691, 174}

{5692, 84}

{5693, 231}

{5694, 105}

{5695, 129}

{5696, 102}

{5697, 114}

{5698, 195}

{5699, 171}

{5700, 123}

{5701, 114}

{5702, 1936}

{5703, 174}

{5704, 114}

{5705, 129}

{5706, 126}

{5707, 168}

{5708, 102}

{5709, 192}

{5710, 108}

{5711, 177}

{5712, 81}

{5713, 2053}

{5714, 120}

{5715, 174}

{5716, 92}

{5717, 171}

{5718, 165}

{5719, 171}

{5720, 108}

{5721, 111}

{5722, 117}

{5723, 99}

{5724, 1933}

{5725, 123}

{5726, 105}

{5727, 2050}

{5728, 99}

{5729, 138}

{5730, 99}

{5731, 120}

{5732, 2813}

{5733, 2050}

{5734, 213}

{5735, 168}

{5736, 96}

{5737, 2047}

{5738, 117}

{5739, 165}

{5740, 135}

{5741, 120}

{5742, 117}

{5743, 162}

{5744, 57}

{5745, 99}

{5746, 102}

{5747, 1882}

{5748, 89}

{5749, 135}

{5750, 1930}

{5751, 1879}

{5752, 114}

{5753, 117}

{5754, 2813}

{5755, 2822}

{5756, 1924}

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{5758, 162}

{5759, 141}

{5760, 51}

{5761, 216}

{5762, 114}

{5763, 102}

{5764, 96}

{5765, 210}

{5766, 114}

{5767, 114}

{5768, 99}

{5769, 1927}

{5770, 2810}

{5771, 117}

{5772, 132}

{5773, 162}

{5774, 86}

{5775, 120}

{5776, 1876}

{5777, 2819}

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{5779, 99}

{5780, 111}

{5781, 114}

{5782, 117}

{5783, 159}

{5784, 111}

{5785, 111}

{5786, 2807}

{5787, 204}

{5788, 105}

{5789, 111}

{5790, 1921}

{5791, 129}

{5792, 93}

{5793, 201}

{5794, 129}

{5795, 69}

{5796, 108}

{5797, 108}

{5798, 83}

{5799, 135}

{5800, 114}

{5801, 2804}

{5802, 1918}

{5803, 126}

{5804, 66}

{5805, 132}

{5806, 66}

{5807, 120}

{5808, 50}

{5809, 2804}

{5810, 102}

{5811, 123}

{5812, 105}

{5813, 126}

{5814, 80}

{5815, 1915}

{5816, 108}

{5817, 117}

{5818, 120}

{5819, 126}

{5820, 69}

{5821, 120}

{5822, 114}

{5823, 126}

{5824, 78}

{5825, 123}

{5826, 114}

{5827, 120}

{5828, 63}

{5829, 99}

{5830, 77}

{5831, 114}

{5832, 42}

{5833, 123}

{5834, 63}

{5835, 2792}

{5836, 111}

{5837, 117}

{5838, 123}

{5839, 114}

{5840, 96}

{5841, 120}

{5842, 114}

{5843, 1891}

{5844, 108}

{5845, 780}

{5846, 117}

{5847, 111}

{5848, 111}

{5849, 74}

{5850, 1888}

{5851, 108}

{5852, 105}

{5853, 71}

{5854, 42}

{5855, 108}

{5856, 105}

{5857, 174}

{5858, 108}

{5859, 105}

{5860, 105}

{5861, 123}

{5862, 144}

{5863, 2648}

{5864, 102}

{5865, 114}

{5866, 66}

{5867, 79}

{5868, 60}

{5869, 120}

{5870, 111}

{5871, 114}

{5872, 1885}

{5873, 45}

{5874, 76}

{5875, 150}

{5876, 73}

{5877, 123}

{5878, 550}

{5879, 144}

{5880, 96}

{5881, 1075}

{5882, 111}

{5883, 147}

{5884, 105}

{5885, 60}

{5886, 53}

{5887, 117}

{5888, 39}

{5889, 105}

{5890, 141}

{5891, 63}

{5892, 108}

{5893, 73}

{5894, 108}

{5895, 150}

{5896, 105}

{5897, 261}

{5898, 102}

{5899, 249}

{5900, 102}

{5901, 1072}

{5902, 57}

{5903, 102}

{5904, 70}

{5905, 1684}

{5906, 547}

{5907, 108}

{5908, 50}

{5909, 138}

{5910, 105}

{5911, 99}

{5912, 54}

{5913, 246}

{5914, 102}

{5915, 102}

{5916, 102}

{5917, 81}

{5918, 102}

{5919, 1060}

{5920, 1873}

{5921, 544}

{5922, 102}

{5923, 99}

{5924, 105}

{5925, 96}

{5926, 99}

{5927, 1057}

{5928, 47}

{5929, 78}

{5930, 99}

{5931, 99}

{5932, 99}

{5933, 1678}

{5934, 538}

{5935, 99}

{5936, 93}

{5937, 117}

{5938, 63}

{5939, 132}

{5940, 102}

{5941, 99}

{5942, 1909}

{5943, 123}

{5944, 93}

{5945, 123}

{5946, 117}

{5947, 150}

{5948, 96}

{5949, 1663}

{5950, 1054}

{5951, 96}

{5952, 96}

{5953, 535}

{5954, 99}

{5955, 843}

{5956, 117}

{5957, 123}

{5958, 111}

{5959, 63}

{5960, 51}

{5961, 47}

{5962, 253}

{5963, 105}

{5964, 99}

{5965, 129}

{5966, 120}

{5967, 147}

{5968, 93}

{5969, 60}

{5970, 60}

{5971, 1657}, {5972, 1900}

{5973, 117}

{5974, 63}

{5975, 132}

{5976, 108}

{5977, 117}

{5978, 166}

{5979, 102}

{5980, 51}

{5981, 57}

{5982, 532}

{5983, 120}

{5984, 44}

{5985, 126}

{5986, 57}

{5987, 114}

{5988, 114}

{5989, 1900}

{5990, 547}

{5991, 1906}

{5992, 114}

{5993, 1051}

{5994, 96}

{5995, 108}

{5996, 250}

{5997, 117}

{5998, 57}

{5999, 60}

{6000, 163}

{6001, 529}

{6002, 54}

{6003, 544}

{6004, 93}

{6005, 351}

{6006, 51}

{6007, 84}

{6008, 1882}

{6009, 1897}

{6010, 1048}

{6011, 114}

{6012, 526}

{6013, 348}

{6014, 114}

{6015, 54}

{6016, 67}

{6017, 114}

{6018, 54}

{6019, 108}

{6020, 210}

{6021, 81}

{6022, 532}

{6023, 181}

{6024, 90}

{6025, 1624}

{6026, 1897}

{6027, 51}

{6028, 48}

{6029, 1045}

{6030, 111}

{6031, 51}

{6032, 105}

{6033, 178}

{6034, 48}

{6035, 222}

{6036, 111}

{6037, 532}

{6038, 108}

{6039, 1042}

{6040, 175}

{6041, 1897}

{6042, 213}

{6043, 225}

{6044, 844}

{6045, 529}

{6046, 1894}

{6047, 108}

{6048, 45}

{6049, 240}

{6050, 1882}

{6051, 213}

{6052, 1033}

{6053, 526}

{6054, 178}

{6055, 184}

{6056, 60}

{6057, 274}

{6058, 207}

{6059, 150}

{6060, 105}

{6061, 210}

{6062, 162}

{6063, 222}

{6064, 247}

{6065, 210}

{6066, 90}

{6067, 178}

{6068, 523}

{6069, 271}

{6070, 207}

{6071, 207}

{6072, 45}

{6073, 184}

{6074, 108}

{6075, 1891}

{6076, 1879}

{6077, 175}

{6078, 204}

{6079, 159}

{6080, 87}

{6081, 204}

{6082, 529}

{6083, 181}

{6084, 172}

{6085, 262}

{6086, 1033}

{6087, 150}

{6088, 132}

{6089, 196}

{6090, 156}

{6091, 178}

{6092, 147}

{6093, 175}

{6094, 105}

{6095, 201}

{6096, 90}

{6097, 844}

{6098, 1873}

{6099, 198}

{6100, 1882}

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{9061, 844}

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{9089, 2968}

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{9091, 199}

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{9095, 196}

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{9098, 2965}

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{9100, 1973}

{9101, 1934}

{9102, 127}

{9103, 144}

{9104, 39}

{9105, 730}

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{9999, 1937}

{10000, 58}

Many thanks to all contributors !

Best,

É.