Representing MAX functions using two-hidden-layer ReLU networks

arXiv cs.LG 08/27/26, 04:00 AM Papers
Summary
This paper explores the theoretical representation of MAX functions using two-hidden-layer ReLU neural networks, providing detailed coefficient lists and identities for exact representations.
arXiv:2608.25221v1 Announce Type: new Abstract: We study exact representations of $\mathrm{MAX}_N(x)=\max{x_1,\ldots,x_N}$ using two-hidden-layer ReLU neural networks. This problem has been studied in recent years in an attempt to characterize the exact number of hidden layers required to represent continuous piecewise linear functions. The best lower bound is 2, while the current upper bound is logarithmic in $N$. It remains completely open if the right answer is a constant number of hidden layers (possibly even 2!) or not. In fact, a recent breakthrough was the representation of $\mathrm{MAX}_5$ as a two-hidden-layer ReLU function obtained in [Bakaev et al., 2026], and the case of $\mathrm{MAX}_N$ was stated as open for $N\geq 6$ in that paper. Using a careful computer assisted search, we obtain two-hidden-layer ReLU representations of $\mathrm{MAX}_5, \mathrm{MAX}_6, \mathrm{MAX}_7$, and $\mathrm{MAX}_8$. We obtain these by considering rational linear combinations of terms of the form $\max\{\sum_{r=1}^{s}\max(x_{a_r},x_{b_r}),\sum_{r=1}^{s}\max(x_{c_r},x_{d_r})\}$, where $a_r,b_r,c_r,d_r\in\{1,\ldots,N\}$. Each inner maximum of two coordinates can be computed in a first hidden layer, and the outer maximum of the two side-sums can be computed in a second hidden layer. Consequently, every finite linear combination of these terms has a two-hidden-layer ReLU realization. An identity for $\mathrm{MAX}_N$ in this form therefore gives an exact two-hidden-layer ReLU representation of $\mathrm{MAX}_N$. Very recently, two-hidden-layer representations of $\mathrm{MAX}_N$ of the above form were obtained for all $N\leq 10$ in [Ruess et al., 2026]. Our representations are different and were developed independently. While our techniques share most of the high-level ideas presented in [Ruess et al., 2026], there are also some minor differences which may be of interest for future research on this problem.
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# Representing MAX functions using two-hidden-layer ReLU networks
Source: [https://arxiv.org/html/2608.25221](https://arxiv.org/html/2608.25221)
Zhimao Wang††thanks:Department of Applied Mathematics, Johns Hopkins University,zwang539@jh\.edu,basu\.amitabh@jhu\.edu

## Appendix AThe completeMAX7\\operatorname\{MAX\}\_\{7\}coefficient list

Table[A](https://arxiv.org/html/2608.25221#A1)gives the 109 nonzero coefficients and corresponding atom patterns inTheorem[4\.1](https://arxiv.org/html/2608.25221#S4.Thmtheorem1)\.

Table 2:Complete coefficient list for the exactMAX7\\operatorname\{MAX\}\_\{7\}identity\. Each entry isj,cj,Qj=\[left∣right\]j,\\ c\_\{j\},\\ Q\_\{j\}=\\texttt\{\[left $\\mid$ right\]\}\. To denote the entire orbit of equivalence classes under the symmetries we consider, we use abstract letters to denote the patterns\. The coefficient corresponds to the coefficient of the function obtained by summing all atoms obtained when the letters range over all possible values, i\.e\.,𝚊,𝚋,𝚌\{\\tt a,b,c\}etc\. range over\{1,…,7\}\\\{1,\\ldots,7\\\}\.1\.1342\\scriptstyle\\tfrac\{13\}\{42\}aa aa aa \| aa aa aa

2\.31840\\scriptstyle\\tfrac\{31\}\{840\}aa aa aa \| aa aa bc

3\.2920160\\scriptstyle\\tfrac\{29\}\{20160\}aa aa aa \| bc bd cd

4\.−731680\\scriptstyle\-\\tfrac\{73\}\{1680\}aa aa bc \| aa aa bc

5\.2913440\\scriptstyle\\tfrac\{29\}\{13440\}aa aa bc \| bc cd dd

6\.−11344\\scriptstyle\-\\tfrac\{1\}\{1344\}aa aa bc \| bc de df

7\.−296720\\scriptstyle\-\\tfrac\{29\}\{6720\}aa aa bc \| bd cd dd

8\.2913440\\scriptstyle\\tfrac\{29\}\{13440\}aa aa bd \| bc cc dd

9\.−2913440\\scriptstyle\-\\tfrac\{29\}\{13440\}aa aa cd \| bc bc dd

10\.11680\\scriptstyle\\tfrac\{1\}\{1680\}aa bb cc \| bc de df

11\.−1448\\scriptstyle\-\\tfrac\{1\}\{448\}aa bb cc \| cc de df

12\.−2340320\\scriptstyle\-\\tfrac\{23\}\{40320\}aa bb cc \| de df dg

13\.15376\\scriptstyle\\tfrac\{1\}\{5376\}aa bb cc \| de df ef

14\.5330240\\scriptstyle\\tfrac\{53\}\{30240\}aa bb cc \| de df fg

15\.−13360\\scriptstyle\-\\tfrac\{1\}\{3360\}aa bb cc \| de ef ff

16\.−13840\\scriptstyle\-\\tfrac\{1\}\{3840\}aa bb cc \| df ef ef

17\.11792\\scriptstyle\\tfrac\{1\}\{1792\}aa bb cc \| df ef ff

18\.−11680\\scriptstyle\-\\tfrac\{1\}\{1680\}aa bb cd \| ab ce cf

19\.11680\\scriptstyle\\tfrac\{1\}\{1680\}aa bb cd \| ab cf de

20\.1224\\scriptstyle\\tfrac\{1\}\{224\}aa bb cd \| bb ce cf

21\.−1336\\scriptstyle\-\\tfrac\{1\}\{336\}aa bb cd \| bb cf de

22\.1330240\\scriptstyle\\tfrac\{13\}\{30240\}aa bb cd \| cd ef eg

23\.12016\\scriptstyle\\tfrac\{1\}\{2016\}aa bb cd \| ce cf cg

24\.−134032\\scriptstyle\-\\tfrac\{13\}\{4032\}aa bb cd \| ce cf fg

25\.75760\\scriptstyle\\tfrac\{7\}\{5760\}aa bb cd \| ce ef eg

26\.1360480\\scriptstyle\\tfrac\{13\}\{60480\}aa bb cd \| dd ef eg

27\.1360480\\scriptstyle\\tfrac\{13\}\{60480\}aa bb dd \| cd ef eg

28\.−4120160\\scriptstyle\-\\tfrac\{41\}\{20160\}aa bb de \| cd cf fg

29\.176720\\scriptstyle\\tfrac\{17\}\{6720\}aa bb de \| ce df ff

30\.−11344\\scriptstyle\-\\tfrac\{1\}\{1344\}aa bb de \| ce ef ff

31\.−1480\\scriptstyle\-\\tfrac\{1\}\{480\}aa bb de \| cf ef ff

32\.13360\\scriptstyle\\tfrac\{1\}\{3360\}aa bb ef \| cd cd df

33\.−13360\\scriptstyle\-\\tfrac\{1\}\{3360\}aa bb ef \| cd cd ef

34\.1113440\\scriptstyle\\tfrac\{11\}\{13440\}aa bb ef \| cd cd ff

35\.−16720\\scriptstyle\-\\tfrac\{1\}\{6720\}aa bb ef \| cd cf de

36\.−16720\\scriptstyle\-\\tfrac\{1\}\{6720\}aa bb ef \| cd cf df

37\.12240\\scriptstyle\\tfrac\{1\}\{2240\}aa bb ef \| cd de df

38\.−32240\\scriptstyle\-\\tfrac\{3\}\{2240\}aa bb ef \| cd de ff

39\.32240\\scriptstyle\\tfrac\{3\}\{2240\}aa bb ef \| cd df df

40\.−16720\\scriptstyle\-\\tfrac\{1\}\{6720\}aa bb ef \| cd df ef

41\.1960\\scriptstyle\\tfrac\{1\}\{960\}aa bb ef \| ce de ff

42\.−1960\\scriptstyle\-\\tfrac\{1\}\{960\}aa bb ef \| ce df df

43\.−12240\\scriptstyle\-\\tfrac\{1\}\{2240\}aa bb ef \| cf df df

44\.97120960\\scriptstyle\\tfrac\{97\}\{120960\}aa bc bc \| de df dg

45\.−11120\\scriptstyle\-\\tfrac\{1\}\{1120\}aa bc bc \| de df fg

46\.1760480\\scriptstyle\\tfrac\{17\}\{60480\}aa bc bd \| be bf bg

47\.1320160\\scriptstyle\\tfrac\{13\}\{20160\}aa bc bd \| be bf fg

48\.−3110080\\scriptstyle\-\\tfrac\{31\}\{10080\}aa bc bd \| be ef eg

49\.−1320160\\scriptstyle\-\\tfrac\{13\}\{20160\}aa bc bd \| bf bg de

50\.72880\\scriptstyle\\tfrac\{7\}\{2880\}aa bc bd \| bg de df

51\.−237560\\scriptstyle\-\\tfrac\{23\}\{7560\}aa bc bd \| de df dg

52\.−1320160\\scriptstyle\-\\tfrac\{13\}\{20160\}aa bc be \| cd ef eg

53\.16720\\scriptstyle\\tfrac\{1\}\{6720\}aa bc cd \| be bf fg

54\.2920160\\scriptstyle\\tfrac\{29\}\{20160\}aa bc cd \| be ef eg

55\.116720\\scriptstyle\\tfrac\{11\}\{6720\}aa bc cd \| be ef fg

56\.1320160\\scriptstyle\\tfrac\{13\}\{20160\}aa bc cd \| bf ce fg

57\.72880\\scriptstyle\\tfrac\{7\}\{2880\}aa bc de \| bd bf fg

58\.1672\\scriptstyle\\tfrac\{1\}\{672\}aa bc de \| bd df dg

59\.−72880\\scriptstyle\-\\tfrac\{7\}\{2880\}aa bc de \| bf cd fg

60\.13360\\scriptstyle\\tfrac\{1\}\{3360\}aa bc de \| cc ef ff

61\.1310080\\scriptstyle\\tfrac\{13\}\{10080\}aa bc ef \| bd be eg

62\.13360\\scriptstyle\\tfrac\{1\}\{3360\}aa bc ef \| cc de df

63\.−1840\\scriptstyle\-\\tfrac\{1\}\{840\}aa bc ef \| cc de ff

64\.−11680\\scriptstyle\-\\tfrac\{1\}\{1680\}aa bc ef \| cc df df

65\.−1560\\scriptstyle\-\\tfrac\{1\}\{560\}aa bc fg \| be bf cd

66\.1560\\scriptstyle\\tfrac\{1\}\{560\}aa bc fg \| be cd ef

67\.−1840\\scriptstyle\-\\tfrac\{1\}\{840\}aa be cd \| cf de ff

68\.11120\\scriptstyle\\tfrac\{1\}\{1120\}aa be cd \| df ef ff

69\.31120\\scriptstyle\\tfrac\{3\}\{1120\}aa cd ef \| be df ff

70\.−1672\\scriptstyle\-\\tfrac\{1\}\{672\}aa cd ef \| bf de ef

71\.1672\\scriptstyle\\tfrac\{1\}\{672\}aa ce df \| be bf df

72\.13360\\scriptstyle\\tfrac\{1\}\{3360\}aa ce df \| be de ff

73\.1560\\scriptstyle\\tfrac\{1\}\{560\}aa ce df \| bf bf de

74\.11680\\scriptstyle\\tfrac\{1\}\{1680\}aa ce df \| bf de ef

75\.−1420\\scriptstyle\-\\tfrac\{1\}\{420\}aa ce df \| bf de ff

76\.11120\\scriptstyle\\tfrac\{1\}\{1120\}aa ce df \| bf df ef

77\.−11120\\scriptstyle\-\\tfrac\{1\}\{1120\}aa cf de \| bd be bf

78\.−1840\\scriptstyle\-\\tfrac\{1\}\{840\}aa cf de \| bd ef ef

79\.−11680\\scriptstyle\-\\tfrac\{1\}\{1680\}aa cf de \| be bf cd

80\.1840\\scriptstyle\\tfrac\{1\}\{840\}aa cf de \| be cd ff

81\.11680\\scriptstyle\\tfrac\{1\}\{1680\}aa cf de \| be cf df

82\.−11120\\scriptstyle\-\\tfrac\{1\}\{1120\}aa cf de \| bf df ef

83\.12520\\scriptstyle\\tfrac\{1\}\{2520\}aa de fg \| bc bd bf

84\.−1360480\\scriptstyle\-\\tfrac\{13\}\{60480\}aa ef eg \| bc bd cd

85\.1320160\\scriptstyle\\tfrac\{13\}\{20160\}aa ef eg \| bc cd dd

86\.−1320160\\scriptstyle\-\\tfrac\{13\}\{20160\}aa ef fg \| bc bd gg

87\.−1320160\\scriptstyle\-\\tfrac\{13\}\{20160\}aa ef gg \| bc bd fg

88\.1320160\\scriptstyle\\tfrac\{13\}\{20160\}aa eg fg \| bc bd ef

89\.−4760480\\scriptstyle\-\\tfrac\{47\}\{60480\}ab ab cd \| ce cf cg

90\.2320160\\scriptstyle\\tfrac\{23\}\{20160\}ab ab cd \| ce cf fg

91\.−140320\\scriptstyle\-\\tfrac\{1\}\{40320\}ab ab cd \| ce ef eg

92\.−14032\\scriptstyle\-\\tfrac\{1\}\{4032\}ab ab de \| cd cf fg

93\.4760480\\scriptstyle\\tfrac\{47\}\{60480\}ab ac ad \| ae ef eg

94\.−12520\\scriptstyle\-\\tfrac\{1\}\{2520\}ab ac ae \| cd ef eg

95\.12520\\scriptstyle\\tfrac\{1\}\{2520\}ab ac ae \| cd ef fg

96\.16048\\scriptstyle\\tfrac\{1\}\{6048\}ab ac bc \| de df fg

97\.12520\\scriptstyle\\tfrac\{1\}\{2520\}ab ac cd \| ae af fg

98\.−12880\\scriptstyle\-\\tfrac\{1\}\{2880\}ab ac cd \| ae ef eg

99\.−12016\\scriptstyle\-\\tfrac\{1\}\{2016\}ab ac cd \| ae ef fg

100\.−15040\\scriptstyle\-\\tfrac\{1\}\{5040\}ab ac de \| ad af fg

101\.−11680\\scriptstyle\-\\tfrac\{1\}\{1680\}ab ac de \| af cd fg

102\.−11440\\scriptstyle\-\\tfrac\{1\}\{1440\}ab ac ef \| ae cd eg

103\.−1320160\\scriptstyle\-\\tfrac\{13\}\{20160\}ab ac ef \| df eg gg

104\.12016\\scriptstyle\\tfrac\{1\}\{2016\}ab ac fg \| ae cd ef

105\.11008\\scriptstyle\\tfrac\{1\}\{1008\}ab ac fg \| af cd de

106\.16720\\scriptstyle\\tfrac\{1\}\{6720\}ab ac fg \| de dg ef

107\.−16720\\scriptstyle\-\\tfrac\{1\}\{6720\}ab ac fg \| de dg eg

108\.−1840\\scriptstyle\-\\tfrac\{1\}\{840\}ab ae bc \| bd ef fg

109\.15040\\scriptstyle\\tfrac\{1\}\{5040\}ab ae cd \| bc ef fg

## Appendix BThe completeMAX8\\operatorname\{MAX\}\_\{8\}coefficient list

Table[B](https://arxiv.org/html/2608.25221#A2)gives the 1,290 nonzero coefficients and corresponding atom patterns in Theorem[5\.1](https://arxiv.org/html/2608.25221#S5.Thmtheorem1)\.

Table 3:Complete coefficient list for the exact four\-summandMAX8\\operatorname\{MAX\}\_\{8\}identity\. Each entry isj,dj,Rj=\[left∣right\]j,\\ d\_\{j\},\\ R\_\{j\}=\\texttt\{\[left $\\mid$ right\]\}\. To denote the entire orbit of equivalence classes under the symmetries we consider, we use abstract letters to denote the patterns\. The coefficient corresponds to the coefficient of the function obtained by summing all atoms obtained when the letters range over all possible values, i\.e\.,𝚊,𝚋,𝚌\{\\tt a,b,c\}etc\. range over\{1,…,8\}\\\{1,\\ldots,8\\\}\.1\.777411280\\scriptstyle\\tfrac\{77741\}\{1280\}aa aa aa aa \| aa aa aa aa

2\.−884312096\\scriptstyle\-\\tfrac\{8843\}\{12096\}aa aa aa aa \| aa aa aa bc

3\.28849241920\\scriptstyle\\tfrac\{28849\}\{241920\}aa aa aa aa \| bc bd cd cd

4\.−28849483840\\scriptstyle\-\\tfrac\{28849\}\{483840\}aa aa aa aa \| bd bd cd cd

5\.−435091362880\\scriptstyle\-\\tfrac\{435091\}\{362880\}aa aa aa bc \| aa aa aa bc

6\.28849362880\\scriptstyle\\tfrac\{28849\}\{362880\}aa aa aa bc \| bc bd cd dd

7\.28849362880\\scriptstyle\\tfrac\{28849\}\{362880\}aa aa aa bc \| bc cd cd dd

8\.28849362880\\scriptstyle\\tfrac\{28849\}\{362880\}aa aa aa bc \| bd cc dd dd

9\.−28849181440\\scriptstyle\-\\tfrac\{28849\}\{181440\}aa aa aa bc \| bd cd cd dd

10\.−28849362880\\scriptstyle\-\\tfrac\{28849\}\{362880\}aa aa aa bc \| bd cd dd dd

11\.−28849362880\\scriptstyle\-\\tfrac\{28849\}\{362880\}aa aa aa cd \| bc bc bc dd

12\.−187604800\\scriptstyle\-\\tfrac\{187\}\{604800\}aa aa bb bb \| cd ce fg fh

13\.971201600\\scriptstyle\\tfrac\{971\}\{201600\}aa aa bc bc \| aa aa de df

14\.120160\\scriptstyle\\tfrac\{1\}\{20160\}aa aa bc bc \| de df dg dh

15\.101604800\\scriptstyle\\tfrac\{101\}\{604800\}aa aa bc bc \| de df dg gh

16\.−4032419200\\scriptstyle\-\\tfrac\{403\}\{2419200\}aa aa bc bc \| de dg ef gh

17\.97180640\\scriptstyle\\tfrac\{971\}\{80640\}aa aa bc bd \| aa aa be bf

18\.−97150400\\scriptstyle\-\\tfrac\{971\}\{50400\}aa aa bc bd \| aa aa bf de

19\.−120160\\scriptstyle\-\\tfrac\{1\}\{20160\}aa aa bc bd \| be bf bg bh

20\.−7345600\\scriptstyle\-\\tfrac\{7\}\{345600\}aa aa bc bd \| be bf fg fh

21\.4512419200\\scriptstyle\\tfrac\{451\}\{2419200\}aa aa bc bd \| be bg ef gh

22\.−4511209600\\scriptstyle\-\\tfrac\{451\}\{1209600\}aa aa bc bd \| bf bg de gh

23\.4512419200\\scriptstyle\\tfrac\{451\}\{2419200\}aa aa bc bd \| bf de fg gh

24\.167483840\\scriptstyle\\tfrac\{167\}\{483840\}aa aa bc bd \| bg bh de df

25\.4512419200\\scriptstyle\\tfrac\{451\}\{2419200\}aa aa bc bd \| bg de df gh

26\.−4511209600\\scriptstyle\-\\tfrac\{451\}\{1209600\}aa aa bc bd \| bg de ef gh

27\.−123040\\scriptstyle\-\\tfrac\{1\}\{23040\}aa aa bc bd \| bh de df dg

28\.4512419200\\scriptstyle\\tfrac\{451\}\{2419200\}aa aa bc be \| bg bh cd ef

29\.−4512419200\\scriptstyle\-\\tfrac\{451\}\{2419200\}aa aa bc be \| bh cd ef eg

30\.4512419200\\scriptstyle\\tfrac\{451\}\{2419200\}aa aa bc be \| bh cd ef fg

31\.4512419200\\scriptstyle\\tfrac\{451\}\{2419200\}aa aa bc be \| cd ef eg gh

32\.−112600\\scriptstyle\-\\tfrac\{1\}\{12600\}aa aa bc bf \| cd ce fg fh

33\.−4512419200\\scriptstyle\-\\tfrac\{451\}\{2419200\}aa aa bc bf \| cd ce fg gh

34\.4512419200\\scriptstyle\\tfrac\{451\}\{2419200\}aa aa bc bf \| cd de fg gh

35\.−110080\\scriptstyle\-\\tfrac\{1\}\{10080\}aa aa bc cc \| de df dg dh

36\.−101302400\\scriptstyle\-\\tfrac\{101\}\{302400\}aa aa bc cc \| de df dg gh

37\.4031209600\\scriptstyle\\tfrac\{403\}\{1209600\}aa aa bc cc \| de dg ef gh

38\.7345600\\scriptstyle\\tfrac\{7\}\{345600\}aa aa bc cd \| bf ce fg fh

39\.−4512419200\\scriptstyle\-\\tfrac\{451\}\{2419200\}aa aa bc cd \| bf de fg gh

40\.1921600\\scriptstyle\\tfrac\{19\}\{21600\}aa aa bc dd \| cd ef eg eh

41\.116800\\scriptstyle\\tfrac\{1\}\{16800\}aa aa bc dd \| cd ef eg gh

42\.−89171814400\\scriptstyle\-\\tfrac\{8917\}\{1814400\}aa aa bc de \| aa aa df dg

43\.89171814400\\scriptstyle\\tfrac\{8917\}\{1814400\}aa aa bc de \| aa aa df fg

44\.89173628800\\scriptstyle\\tfrac\{8917\}\{3628800\}aa aa bc de \| aa aa dg ef

45\.48591036800\\scriptstyle\\tfrac\{4859\}\{1036800\}aa aa bc de \| bc de fg fh

46\.−1921600\\scriptstyle\-\\tfrac\{19\}\{21600\}aa aa bc de \| bc df dg dh

47\.−1180640\\scriptstyle\-\\tfrac\{11\}\{80640\}aa aa bc de \| bc ee fg fh

48\.−11161280\\scriptstyle\-\\tfrac\{11\}\{161280\}aa aa bc de \| cc ee fg fh

49\.−527403200\\scriptstyle\-\\tfrac\{527\}\{403200\}aa aa bc ee \| bc de fg fh

50\.2334560\\scriptstyle\\tfrac\{23\}\{34560\}aa aa bc ee \| cc de fg fh

51\.−4512419200\\scriptstyle\-\\tfrac\{451\}\{2419200\}aa aa bc ef \| bd be eg eh

52\.−4512419200\\scriptstyle\-\\tfrac\{451\}\{2419200\}aa aa bc ef \| be cd eh fg

53\.4512419200\\scriptstyle\\tfrac\{451\}\{2419200\}aa aa bc fg \| be cd ef fh

54\.−1921600\\scriptstyle\-\\tfrac\{19\}\{21600\}aa aa bd cd \| bc ef eg eh

55\.1921600\\scriptstyle\\tfrac\{19\}\{21600\}aa aa bd cd \| cd ef eg eh

56\.7971209600\\scriptstyle\\tfrac\{797\}\{1209600\}aa aa cc de \| bc df dg dh

57\.−12911209600\\scriptstyle\-\\tfrac\{1291\}\{1209600\}aa aa cc ee \| bc de fg fh

58\.1116128\\scriptstyle\\tfrac\{11\}\{16128\}aa aa cd cd \| bd ef eg eh

59\.2391209600\\scriptstyle\\tfrac\{239\}\{1209600\}aa aa cd dd \| bc ef eg eh

60\.−19151200\\scriptstyle\-\\tfrac\{19\}\{151200\}aa aa cd dd \| bc ef eg gh

61\.−18611209600\\scriptstyle\-\\tfrac\{1861\}\{1209600\}aa aa cd dd \| bd ef eg eh

62\.−11890\\scriptstyle\-\\tfrac\{1\}\{1890\}aa aa cd ef \| bc dd eg gh

63\.11890\\scriptstyle\\tfrac\{1\}\{1890\}aa aa cd ef \| bd cd eg gh

64\.125200\\scriptstyle\\tfrac\{1\}\{25200\}aa aa cd gh \| bc be ef eg

65\.−11890\\scriptstyle\-\\tfrac\{1\}\{1890\}aa aa dd ef \| bd cd eg gh

66\.991806400\\scriptstyle\\tfrac\{991\}\{806400\}aa aa de de \| bc bc fg fh

67\.1180640\\scriptstyle\\tfrac\{11\}\{80640\}aa aa de de \| bc cc fg fh

68\.−19371209600\\scriptstyle\-\\tfrac\{1937\}\{1209600\}aa aa de ee \| bc bc fg fh

69\.−89177257600\\scriptstyle\-\\tfrac\{8917\}\{7257600\}aa aa de fg \| aa aa bc bc

70\.−150400\\scriptstyle\-\\tfrac\{1\}\{50400\}aa aa de gh \| bc bf cd fg

71\.−1140320\\scriptstyle\-\\tfrac\{11\}\{40320\}aa aa eg fg \| bc bd fh hh

72\.1140320\\scriptstyle\\tfrac\{11\}\{40320\}aa aa eg fg \| bc bd gh hh

73\.23201600\\scriptstyle\\tfrac\{23\}\{201600\}aa aa eg fh \| bc bd fg hh

74\.2967200\\scriptstyle\\tfrac\{29\}\{67200\}aa aa eg fh \| bc bd fh gh

75\.281151200\\scriptstyle\\tfrac\{281\}\{151200\}aa aa eh fg \| bc bd eg fh

76\.−1913604800\\scriptstyle\-\\tfrac\{1913\}\{604800\}aa aa eh fg \| bc bd fh gh

77\.1312600\\scriptstyle\\tfrac\{13\}\{12600\}aa aa eh fg \| bc bd gh gh

78\.−1140320\\scriptstyle\-\\tfrac\{11\}\{40320\}aa aa fg gh \| bc bd eg hh

79\.−114800\\scriptstyle\-\\tfrac\{11\}\{4800\}aa aa fg hh \| bc bd eg fh

80\.1937604800\\scriptstyle\\tfrac\{1937\}\{604800\}aa aa fg hh \| bc bd eg gh

81\.−1147604800\\scriptstyle\-\\tfrac\{1147\}\{604800\}aa aa fg hh \| bc bd eh gh

82\.−211302400\\scriptstyle\-\\tfrac\{211\}\{302400\}aa aa fh gh \| bc bd ef eg

83\.−3743200\\scriptstyle\-\\tfrac\{37\}\{43200\}aa aa fh gh \| bc bd eg eg

84\.431302400\\scriptstyle\\tfrac\{431\}\{302400\}aa aa fh gh \| bc bd eg eh

85\.2069604800\\scriptstyle\\tfrac\{2069\}\{604800\}aa aa fh gh \| bc bd eg fg

86\.−431302400\\scriptstyle\-\\tfrac\{431\}\{302400\}aa aa fh gh \| bc bd eg fh

87\.13100800\\scriptstyle\\tfrac\{13\}\{100800\}aa aa fh gh \| bc bd eh eh

88\.−73456\\scriptstyle\-\\tfrac\{7\}\{3456\}aa aa gh hh \| bc bd ef fg

89\.−13151200\\scriptstyle\-\\tfrac\{13\}\{151200\}aa ab bb cd \| cd ef eg eh

90\.19241920\\scriptstyle\\tfrac\{19\}\{241920\}aa ab bb cd \| cd ef eg gh

91\.17200\\scriptstyle\\tfrac\{1\}\{7200\}aa ab bb cd \| ce cf cg ch

92\.121600\\scriptstyle\\tfrac\{1\}\{21600\}aa ab bb cd \| dd ef eg eh

93\.−125200\\scriptstyle\-\\tfrac\{1\}\{25200\}aa ab bb cd \| dd ef eg gh

94\.133600\\scriptstyle\\tfrac\{1\}\{33600\}aa ab bb dd \| cd ef eg eh

95\.122400\\scriptstyle\\tfrac\{1\}\{22400\}aa ab bb dd \| cd ef eg gh

96\.16300\\scriptstyle\\tfrac\{1\}\{6300\}aa ab bb fg \| cd ce gh hh

97\.−16300\\scriptstyle\-\\tfrac\{1\}\{6300\}aa ab bb gh \| cd ce fg fh

98\.13150\\scriptstyle\\tfrac\{1\}\{3150\}aa ab bb gh \| cd ce fg hh

99\.−16300\\scriptstyle\-\\tfrac\{1\}\{6300\}aa ab bb gh \| cd ce fh hh

100\.16300\\scriptstyle\\tfrac\{1\}\{6300\}aa ab bb hh \| cd ce fh gh

101\.110080\\scriptstyle\\tfrac\{1\}\{10080\}aa bb bb cd \| ce cf cg ch

102\.512096\\scriptstyle\\tfrac\{5\}\{12096\}aa bb bb cd \| ce cf fg fh

103\.−4511209600\\scriptstyle\-\\tfrac\{451\}\{1209600\}aa bb bb cd \| ce cg ef gh

104\.139604800\\scriptstyle\\tfrac\{139\}\{604800\}aa bb bb cd \| cf cg ch de

105\.4511209600\\scriptstyle\\tfrac\{451\}\{1209600\}aa bb bb cd \| cf cg de gh

106\.−524192\\scriptstyle\-\\tfrac\{5\}\{24192\}aa bb bb cd \| cf de fg fh

107\.−4511209600\\scriptstyle\-\\tfrac\{451\}\{1209600\}aa bb bb cd \| cf de fg gh

108\.−6431209600\\scriptstyle\-\\tfrac\{643\}\{1209600\}aa bb bb cd \| cg ch de df

109\.4511209600\\scriptstyle\\tfrac\{451\}\{1209600\}aa bb bb cd \| cg de ef gh

110\.−125200\\scriptstyle\-\\tfrac\{1\}\{25200\}aa bb bb de \| cd cf fg fh

111\.125200\\scriptstyle\\tfrac\{1\}\{25200\}aa bb bb de \| cd cf fg gh

112\.−125200\\scriptstyle\-\\tfrac\{1\}\{25200\}aa bb bb ef \| cd ce cg gh

113\.−17200\\scriptstyle\-\\tfrac\{1\}\{7200\}aa bb bc cc \| de df dg dh

114\.−1967200\\scriptstyle\-\\tfrac\{19\}\{67200\}aa bb cc dd \| cd ef eg eh

115\.−3531209600\\scriptstyle\-\\tfrac\{353\}\{1209600\}aa bb cc dd \| cd ef eg gh

116\.10936329030400\\scriptstyle\\tfrac\{109363\}\{29030400\}aa bb cc dd \| ef ef gh gh

117\.−144940958060800\\scriptstyle\-\\tfrac\{1449409\}\{58060800\}aa bb cc dd \| ef ef gh hh

118\.57558719353600\\scriptstyle\\tfrac\{575587\}\{19353600\}aa bb cc dd \| ef ff gh hh

119\.−4626123224320\\scriptstyle\-\\tfrac\{46261\}\{23224320\}aa bb cc dd \| eg eh fg fh

120\.22753729030400\\scriptstyle\\tfrac\{227537\}\{29030400\}aa bb cc dd \| eg fg fh hh

121\.73817257600\\scriptstyle\\tfrac\{7381\}\{7257600\}aa bb cc dd \| eg fg gh hh

122\.89597257600\\scriptstyle\\tfrac\{8959\}\{7257600\}aa bb cc dd \| eg fh fh gh

123\.−89177257600\\scriptstyle\-\\tfrac\{8917\}\{7257600\}aa bb cc dd \| eh fg fh gh

124\.23134400\\scriptstyle\\tfrac\{23\}\{134400\}aa bb cc dd \| eh fh gh gh

125\.3733518400\\scriptstyle\\tfrac\{3733\}\{518400\}aa bb cc de \| bc de fg fh

126\.1933600\\scriptstyle\\tfrac\{19\}\{33600\}aa bb cc de \| bc df dg dh

127\.353604800\\scriptstyle\\tfrac\{353\}\{604800\}aa bb cc de \| bc df dg gh

128\.−71134400\\scriptstyle\-\\tfrac\{71\}\{134400\}aa bb cc de \| bc dg dh ef

129\.83241920\\scriptstyle\\tfrac\{83\}\{241920\}aa bb cc de \| bc dg ef gh

130\.112116758060800\\scriptstyle\\tfrac\{1121167\}\{58060800\}aa bb cc de \| de fg fh gh

131\.−214513628800\\scriptstyle\-\\tfrac\{21451\}\{3628800\}aa bb cc de \| de fg gh hh

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263\.11609604800\\scriptstyle\\tfrac\{11609\}\{604800\}aa bb ef gh \| cd ch dg fh

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288\.−209272419200\\scriptstyle\-\\tfrac\{20927\}\{2419200\}aa bb eg fg \| cd cd fh hh

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318\.−571492419200\\scriptstyle\-\\tfrac\{57149\}\{2419200\}aa bb eg fh \| cd cd dh fg

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324\.−35091209600\\scriptstyle\-\\tfrac\{3509\}\{1209600\}aa bb eg fh \| cd ch dh fg

325\.−43259806400\\scriptstyle\-\\tfrac\{43259\}\{806400\}aa bb eg fh \| cd dd fg hh

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328\.−14263604800\\scriptstyle\-\\tfrac\{14263\}\{604800\}aa bb eg fh \| cd dg fg hh

329\.8083806400\\scriptstyle\\tfrac\{8083\}\{806400\}aa bb eg fh \| cd dh fg gh

330\.479272419200\\scriptstyle\\tfrac\{47927\}\{2419200\}aa bb eg fh \| cg df dg hh

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360\.3717280\\scriptstyle\\tfrac\{37\}\{17280\}aa bb eh fg \| ch dg dh fh

361\.−1950400\\scriptstyle\-\\tfrac\{19\}\{50400\}aa bb eh fg \| ch dh fh gh

362\.−112600\\scriptstyle\-\\tfrac\{1\}\{12600\}aa bb fg gh \| ab cd ce hh

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366\.152892419200\\scriptstyle\\tfrac\{15289\}\{2419200\}aa bb fg gh \| cd de ee hh

367\.5359241920\\scriptstyle\\tfrac\{5359\}\{241920\}aa bb fg gh \| ce de de hh

368\.761403200\\scriptstyle\\tfrac\{761\}\{403200\}aa bb fg gh \| ce de df hh

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624\.−1134400\\scriptstyle\-\\tfrac\{1\}\{134400\}aa bd cd cd \| eg fh fh gh

625\.1134400\\scriptstyle\\tfrac\{1\}\{134400\}aa bd cd cd \| eh fg fh gh

626\.1110080\\scriptstyle\\tfrac\{11\}\{10080\}aa bd cd fg \| bc eg eh hh

627\.1151200\\scriptstyle\\tfrac\{1\}\{151200\}aa bd cd fg \| bc eg fh hh

628\.313241920\\scriptstyle\\tfrac\{313\}\{241920\}aa bd cd fg \| bc eh gh hh

629\.−20691209600\\scriptstyle\-\\tfrac\{2069\}\{1209600\}aa bd cd fg \| cd eg eh hh

630\.469172800\\scriptstyle\\tfrac\{469\}\{172800\}aa bd cd fg \| cd eg fh hh

631\.−337151200\\scriptstyle\-\\tfrac\{337\}\{151200\}aa bd cd fg \| cd eg gh hh

632\.14291209600\\scriptstyle\\tfrac\{1429\}\{1209600\}aa bd cd fg \| cd eh gh hh

633\.−1151200\\scriptstyle\-\\tfrac\{1\}\{151200\}aa bd cd gh \| bc ef eh fg

634\.−143200\\scriptstyle\-\\tfrac\{1\}\{43200\}aa bd cd gh \| bc ef fg fh

635\.−1399604800\\scriptstyle\-\\tfrac\{1399\}\{604800\}aa bd cd gh \| bc ef fg hh

636\.20691209600\\scriptstyle\\tfrac\{2069\}\{1209600\}aa bd cd gh \| cd ef eh fh

637\.−469172800\\scriptstyle\-\\tfrac\{469\}\{172800\}aa bd cd gh \| cd ef fg hh

638\.−14291209600\\scriptstyle\-\\tfrac\{1429\}\{1209600\}aa bd cd gh \| cd ef fh fh

639\.11890\\scriptstyle\\tfrac\{1\}\{1890\}aa bd cd gh \| cd eg fg hh

640\.−131209600\\scriptstyle\-\\tfrac\{13\}\{1209600\}aa bd cd gh \| cd eh fh fh

641\.6117280\\scriptstyle\\tfrac\{61\}\{17280\}aa bf ce dg \| df eg gh hh

642\.−23172800\\scriptstyle\-\\tfrac\{23\}\{172800\}aa bf ce dg \| dh eg fg hh

643\.2539403200\\scriptstyle\\tfrac\{2539\}\{403200\}aa bg cf de \| ch dg ef hh

644\.−1453172800\\scriptstyle\-\\tfrac\{1453\}\{172800\}aa bg cf de \| dg ef gh hh

645\.3677241920\\scriptstyle\\tfrac\{3677\}\{241920\}aa bg cf de \| dh eg fg hh

646\.−73986400\\scriptstyle\-\\tfrac\{739\}\{86400\}aa bg cf de \| dh eg fh hh

647\.−30724192\\scriptstyle\-\\tfrac\{307\}\{24192\}aa bg cf de \| eg fg fh hh

648\.−1640\\scriptstyle\-\\tfrac\{1\}\{640\}aa bg cf de \| eg fg gh hh

649\.5930240\\scriptstyle\\tfrac\{59\}\{30240\}aa bg cf de \| eh fg gh hh

650\.−589604800\\scriptstyle\-\\tfrac\{589\}\{604800\}aa bg cf de \| eh fh gh hh

651\.121600\\scriptstyle\\tfrac\{1\}\{21600\}aa cd cd cd \| bd ef eg eh

652\.150400\\scriptstyle\\tfrac\{1\}\{50400\}aa cd cd cd \| bd ef eg gh

653\.1121302400\\scriptstyle\\tfrac\{1121\}\{302400\}aa cd eg fg \| bc bd fh hh

654\.−18760480\\scriptstyle\-\\tfrac\{187\}\{60480\}aa cd eg fg \| bc bd gh hh

655\.−1223302400\\scriptstyle\-\\tfrac\{1223\}\{302400\}aa cd eg fg \| bc dd fh hh

656\.4211209600\\scriptstyle\\tfrac\{421\}\{1209600\}aa cd eg fg \| bc dd gh hh

657\.−127302400\\scriptstyle\-\\tfrac\{127\}\{302400\}aa cd eg fg \| bd bd fh hh

658\.421120960\\scriptstyle\\tfrac\{421\}\{120960\}aa cd eg fg \| bd bd gh hh

659\.−8375600\\scriptstyle\-\\tfrac\{83\}\{75600\}aa cd eg fg \| be df fh hh

660\.1699241920\\scriptstyle\\tfrac\{1699\}\{241920\}aa cd eg fh \| bc bd fg hh

661\.−24780640\\scriptstyle\-\\tfrac\{247\}\{80640\}aa cd eg fh \| bc bd fh gh

662\.−8350400\\scriptstyle\-\\tfrac\{83\}\{50400\}aa cd eg fh \| bc dd fg hh

663\.341100800\\scriptstyle\\tfrac\{341\}\{100800\}aa cd eg fh \| bc dd fh gh

664\.−34871209600\\scriptstyle\-\\tfrac\{3487\}\{1209600\}aa cd eg fh \| bd bd fg hh

665\.−54757600\\scriptstyle\-\\tfrac\{547\}\{57600\}aa cd eg fh \| bd bd fh gh

666\.8111209600\\scriptstyle\\tfrac\{811\}\{1209600\}aa cd eh fg \| bc bd eg fh

667\.−19721600\\scriptstyle\-\\tfrac\{197\}\{21600\}aa cd eh fg \| bc bd fh gh

668\.52980640\\scriptstyle\\tfrac\{529\}\{80640\}aa cd eh fg \| bc bd gh gh

669\.−7989600\\scriptstyle\-\\tfrac\{79\}\{89600\}aa cd eh fg \| bc dd eg fh

670\.5171201600\\scriptstyle\\tfrac\{5171\}\{201600\}aa cd eh fg \| bc dd fh gh

671\.−109371209600\\scriptstyle\-\\tfrac\{10937\}\{1209600\}aa cd eh fg \| bc dd gh gh

672\.4631209600\\scriptstyle\\tfrac\{463\}\{1209600\}aa cd eh fg \| bd bd eg fh

673\.−29403200\\scriptstyle\-\\tfrac\{29\}\{403200\}aa cd eh fg \| bd bd fh gh

674\.20722400\\scriptstyle\\tfrac\{207\}\{22400\}aa cd eh fg \| bd bd gh gh

675\.−20211209600\\scriptstyle\-\\tfrac\{2021\}\{1209600\}aa cd fg gh \| bc bd ef hh

676\.33471209600\\scriptstyle\\tfrac\{3347\}\{1209600\}aa cd fg gh \| bc bd eg hh

677\.−48491209600\\scriptstyle\-\\tfrac\{4849\}\{1209600\}aa cd fg gh \| bc dd ef hh

678\.−8571209600\\scriptstyle\-\\tfrac\{857\}\{1209600\}aa cd fg gh \| bd bd ef hh

679\.−10937800\\scriptstyle\-\\tfrac\{109\}\{37800\}aa cd fg gh \| bd bd eg hh

680\.−30911209600\\scriptstyle\-\\tfrac\{3091\}\{1209600\}aa cd fh gh \| bc bd eg eh

681\.−125200\\scriptstyle\-\\tfrac\{1\}\{25200\}aa cd fh gh \| bc bd eh eh

682\.4712096\\scriptstyle\\tfrac\{47\}\{12096\}aa cd fh gh \| bc dd eg eh

683\.−11260\\scriptstyle\-\\tfrac\{1\}\{1260\}aa cd fh gh \| bd bd eg eh

684\.478400\\scriptstyle\\tfrac\{47\}\{8400\}aa ce df gh \| bf dg eg hh

685\.3851403200\\scriptstyle\\tfrac\{3851\}\{403200\}aa ce df gh \| bf dh eg gh

686\.−1289201600\\scriptstyle\-\\tfrac\{1289\}\{201600\}aa ce dg fg \| bf bh de hh

687\.−31134400\\scriptstyle\-\\tfrac\{31\}\{134400\}aa ce dg fg \| bf de fh hh

688\.−5943200\\scriptstyle\-\\tfrac\{59\}\{43200\}aa ce dg fg \| bf de gh hh

689\.−13115120\\scriptstyle\-\\tfrac\{131\}\{15120\}aa ce dg fg \| bf dh ef hh

690\.53604800\\scriptstyle\\tfrac\{53\}\{604800\}aa ce dg fg \| bf dh eg hh

691\.15971209600\\scriptstyle\\tfrac\{1597\}\{1209600\}aa ce dg fg \| bf dh eh hh

692\.−7144800\\scriptstyle\-\\tfrac\{71\}\{44800\}aa ce dg fh \| bf bg de hh

693\.−193151200\\scriptstyle\-\\tfrac\{193\}\{151200\}aa ce dg fh \| bf bg dh eh

694\.11231209600\\scriptstyle\\tfrac\{1123\}\{1209600\}aa ce dh fg \| bf bg bh de

695\.4673302400\\scriptstyle\\tfrac\{4673\}\{302400\}aa ce dh fg \| bf de gh gh

696\.89380640\\scriptstyle\\tfrac\{893\}\{80640\}aa ce dh fg \| bf dg eg hh

697\.−1447604800\\scriptstyle\-\\tfrac\{1447\}\{604800\}aa ce dh fg \| bf dg eh gh

698\.−919604800\\scriptstyle\-\\tfrac\{919\}\{604800\}aa ce dh fg \| bf dh eg gh

699\.−1916128\\scriptstyle\-\\tfrac\{19\}\{16128\}aa cf de gh \| bf bg eg hh

700\.−16712096\\scriptstyle\-\\tfrac\{167\}\{12096\}aa cf de gh \| bf bh eg gh

701\.−4310080\\scriptstyle\-\\tfrac\{43\}\{10080\}aa cf de gh \| bg bh dh ef

702\.3583241920\\scriptstyle\\tfrac\{3583\}\{241920\}aa cf de gh \| bg bh eh fg

703\.−113456\\scriptstyle\-\\tfrac\{11\}\{3456\}aa cf de gh \| bg bh eh fh

704\.247201600\\scriptstyle\\tfrac\{247\}\{201600\}aa cf de gh \| bg ch dh ef

705\.359100800\\scriptstyle\\tfrac\{359\}\{100800\}aa cf de gh \| bg dg ef hh

706\.−2177172800\\scriptstyle\-\\tfrac\{2177\}\{172800\}aa cf de gh \| bg dh ef hh

707\.28131209600\\scriptstyle\\tfrac\{2813\}\{1209600\}aa cf de gh \| bg dh eh fh

708\.177911209600\\scriptstyle\\tfrac\{17791\}\{1209600\}aa cf de gh \| bg ef fg hh

709\.709172800\\scriptstyle\\tfrac\{709\}\{172800\}aa cf de gh \| bg eg fg hh

710\.−1017560\\scriptstyle\-\\tfrac\{101\}\{7560\}aa cf de gh \| bg eh fg hh

711\.−3775600\\scriptstyle\-\\tfrac\{37\}\{75600\}aa cf de gh \| bg eh fh gh

712\.473091209600\\scriptstyle\\tfrac\{47309\}\{1209600\}aa cf de gh \| bg eh fh hh

713\.80811209600\\scriptstyle\\tfrac\{8081\}\{1209600\}aa cf de gh \| bh bh eg fg

714\.−3223241920\\scriptstyle\-\\tfrac\{3223\}\{241920\}aa cf de gh \| bh dg ef gh

715\.18122400\\scriptstyle\\tfrac\{181\}\{22400\}aa cf de gh \| bh dg eg fh

716\.−613151200\\scriptstyle\-\\tfrac\{613\}\{151200\}aa cf de gh \| bh dh eg fg

717\.−118491209600\\scriptstyle\-\\tfrac\{11849\}\{1209600\}aa cf de gh \| bh eg fg hh

718\.−34871209600\\scriptstyle\-\\tfrac\{3487\}\{1209600\}aa cf de gh \| bh eh fg gh

719\.−17350400\\scriptstyle\-\\tfrac\{173\}\{50400\}aa cf dg eg \| be bf dh hh

720\.1657604800\\scriptstyle\\tfrac\{1657\}\{604800\}aa cf dg eg \| be df fh hh

721\.4491209600\\scriptstyle\\tfrac\{449\}\{1209600\}aa cf dg eg \| bg dh ef hh

722\.−37757600\\scriptstyle\-\\tfrac\{377\}\{57600\}aa cf dg eg \| bh dh ef hh

723\.−28943200\\scriptstyle\-\\tfrac\{289\}\{43200\}aa cf dg eh \| bh dg ef gh

724\.−3901403200\\scriptstyle\-\\tfrac\{3901\}\{403200\}aa cf dh eg \| bg bh de fh

725\.−3223302400\\scriptstyle\-\\tfrac\{3223\}\{302400\}aa cf dh eg \| bg bh df eh

726\.8791302400\\scriptstyle\\tfrac\{8791\}\{302400\}aa cf dh eg \| bg bh dh ef

727\.61986400\\scriptstyle\\tfrac\{619\}\{86400\}aa cf dh eg \| bg de fg hh

728\.−119291209600\\scriptstyle\-\\tfrac\{11929\}\{1209600\}aa cf dh eg \| bg de fh hh

729\.−84611209600\\scriptstyle\-\\tfrac\{8461\}\{1209600\}aa cf dh eg \| bg dg ef hh

730\.−761604800\\scriptstyle\-\\tfrac\{761\}\{604800\}aa cf dh eg \| bg dh eh fh

731\.119511209600\\scriptstyle\\tfrac\{11951\}\{1209600\}aa cf dh eg \| bh de fg gh

732\.19348384\\scriptstyle\\tfrac\{193\}\{48384\}aa cf dh eg \| bh dg ef gh

733\.32921600\\scriptstyle\\tfrac\{329\}\{21600\}aa cf dh eg \| bh dg eg fh

734\.42167200\\scriptstyle\\tfrac\{421\}\{67200\}aa cf dh eg \| bh dg eh fg

735\.137134400\\scriptstyle\\tfrac\{137\}\{134400\}aa cg de fg \| be bf fh hh

736\.53891209600\\scriptstyle\\tfrac\{5389\}\{1209600\}aa cg de fg \| be df fh hh

737\.19600\\scriptstyle\\tfrac\{1\}\{9600\}aa cg de fg \| bf bh eg hh

738\.−937403200\\scriptstyle\-\\tfrac\{937\}\{403200\}aa cg de fg \| bf bh eh hh

739\.1151200\\scriptstyle\\tfrac\{1\}\{151200\}aa cg de fg \| bf ce dh hh

740\.5913440\\scriptstyle\\tfrac\{59\}\{13440\}aa cg de fg \| bf dh ef hh

741\.18400\\scriptstyle\\tfrac\{1\}\{8400\}aa cg de fg \| bf dh eg hh

742\.30371209600\\scriptstyle\\tfrac\{3037\}\{1209600\}aa cg de fg \| bf ef eh hh

743\.−439172800\\scriptstyle\-\\tfrac\{439\}\{172800\}aa cg de fg \| bf ef fh hh

744\.931172800\\scriptstyle\\tfrac\{931\}\{172800\}aa cg de fg \| bf ef gh hh

745\.−19600\\scriptstyle\-\\tfrac\{1\}\{9600\}aa cg de fg \| bf eg fh hh

746\.4945\\scriptstyle\\tfrac\{4\}\{945\}aa cg de fg \| bf eg gh hh

747\.533302400\\scriptstyle\\tfrac\{533\}\{302400\}aa cg de fg \| bf eh fh hh

748\.−17357600\\scriptstyle\-\\tfrac\{173\}\{57600\}aa cg de fg \| bf eh gh hh

749\.−103302400\\scriptstyle\-\\tfrac\{103\}\{302400\}aa cg de fg \| bg ef fh hh

750\.409172800\\scriptstyle\\tfrac\{409\}\{172800\}aa cg de fg \| bh ef fh hh

751\.33431209600\\scriptstyle\\tfrac\{3343\}\{1209600\}aa cg de fh \| bf bg bh eh

752\.−125211209600\\scriptstyle\-\\tfrac\{12521\}\{1209600\}aa cg de fh \| bf bg dh eh

753\.−148386400\\scriptstyle\-\\tfrac\{1483\}\{86400\}aa cg de fh \| bf bg eg hh

754\.80891209600\\scriptstyle\\tfrac\{8089\}\{1209600\}aa cg de fh \| bf bg eh hh

755\.−8717604800\\scriptstyle\-\\tfrac\{8717\}\{604800\}aa cg de fh \| bf bh eg gh

756\.473604800\\scriptstyle\\tfrac\{473\}\{604800\}aa cg de fh \| bf eg gh hh

757\.−461591209600\\scriptstyle\-\\tfrac\{46159\}\{1209600\}aa cg de fh \| bf eh gh gh

758\.1279151200\\scriptstyle\\tfrac\{1279\}\{151200\}aa cg de fh \| bh ef fg gh

759\.3149403200\\scriptstyle\\tfrac\{3149\}\{403200\}aa cg de fh \| bh eg fg fh

760\.−130091209600\\scriptstyle\-\\tfrac\{13009\}\{1209600\}aa cg de fh \| bh eh fg fg

761\.133600\\scriptstyle\\tfrac\{1\}\{33600\}aa cg df eg \| be bf bh hh

762\.6143200\\scriptstyle\\tfrac\{61\}\{43200\}aa cg df eg \| be bf dh hh

763\.−653604800\\scriptstyle\-\\tfrac\{653\}\{604800\}aa cg df eg \| be bf fh hh

764\.8811209600\\scriptstyle\\tfrac\{881\}\{1209600\}aa cg df eg \| be bf gh hh

765\.−66767200\\scriptstyle\-\\tfrac\{667\}\{67200\}aa cg df eg \| be fg fh hh

766\.1213604800\\scriptstyle\\tfrac\{1213\}\{604800\}aa cg df eg \| bf bh ef hh

767\.−161172800\\scriptstyle\-\\tfrac\{161\}\{172800\}aa cg df eg \| bf bh eh hh

768\.−398960\\scriptstyle\-\\tfrac\{39\}\{8960\}aa cg df eg \| bf ef eh hh

769\.−463604800\\scriptstyle\-\\tfrac\{463\}\{604800\}aa cg df eg \| bf ef fh hh

770\.983403200\\scriptstyle\\tfrac\{983\}\{403200\}aa cg df eg \| bf ef gh hh

771\.503241920\\scriptstyle\\tfrac\{503\}\{241920\}aa cg df eg \| bf eh fg hh

772\.−2360480\\scriptstyle\-\\tfrac\{23\}\{60480\}aa cg df eg \| bf eh fh hh

773\.−1061302400\\scriptstyle\-\\tfrac\{1061\}\{302400\}aa cg df eg \| bg ef fh hh

774\.667604800\\scriptstyle\\tfrac\{667\}\{604800\}aa cg df eg \| bg ef gh hh

775\.−11151200\\scriptstyle\-\\tfrac\{11\}\{151200\}aa cg df eg \| bg eh fg hh

776\.379172800\\scriptstyle\\tfrac\{379\}\{172800\}aa cg df eg \| bg eh fh hh

777\.−1916800\\scriptstyle\-\\tfrac\{19\}\{16800\}aa cg df eg \| bh ef gh hh

778\.41201600\\scriptstyle\\tfrac\{41\}\{201600\}aa cg df eg \| bh eh fh hh

779\.−13786400\\scriptstyle\-\\tfrac\{137\}\{86400\}aa cg df eh \| be bf bg hh

780\.3760480\\scriptstyle\\tfrac\{37\}\{60480\}aa cg df eh \| bf bg bh eh

781\.2077403200\\scriptstyle\\tfrac\{2077\}\{403200\}aa cg df eh \| bf bg eg hh

782\.35957600\\scriptstyle\\tfrac\{359\}\{57600\}aa cg df eh \| bg bh bh ef

783\.619120960\\scriptstyle\\tfrac\{619\}\{120960\}aa cg df eh \| bg bh eh fh

784\.2033241920\\scriptstyle\\tfrac\{2033\}\{241920\}aa cg df eh \| bg ef fg hh

785\.−31172800\\scriptstyle\-\\tfrac\{31\}\{172800\}aa cg df eh \| bg eg fg hh

786\.−7743200\\scriptstyle\-\\tfrac\{77\}\{43200\}aa cg df eh \| bg eg fh hh

787\.953302400\\scriptstyle\\tfrac\{953\}\{302400\}aa cg df eh \| bg eh fh gh

788\.719151200\\scriptstyle\\tfrac\{719\}\{151200\}aa cg df eh \| bh bh eg fg

789\.2315120\\scriptstyle\\tfrac\{23\}\{15120\}aa cg df eh \| bh eg fg fh

790\.−17629604800\\scriptstyle\-\\tfrac\{17629\}\{604800\}aa cg df eh \| bh eg fg hh

791\.−34571209600\\scriptstyle\-\\tfrac\{3457\}\{1209600\}aa cg df eh \| bh eh fg gh

792\.−1925200\\scriptstyle\-\\tfrac\{19\}\{25200\}aa cg df eh \| bh eh fh gh

793\.14975600\\scriptstyle\\tfrac\{149\}\{75600\}aa cg dg ef \| be df fh hh

794\.−4726880\\scriptstyle\-\\tfrac\{47\}\{26880\}aa cg dg ef \| be fg fh hh

795\.−79100800\\scriptstyle\-\\tfrac\{79\}\{100800\}aa cg dg ef \| bf bg eh hh

796\.−14531209600\\scriptstyle\-\\tfrac\{1453\}\{1209600\}aa cg dg ef \| bf bh de hh

797\.103302400\\scriptstyle\\tfrac\{103\}\{302400\}aa cg dg ef \| bf bh eg hh

798\.47151200\\scriptstyle\\tfrac\{47\}\{151200\}aa cg dg ef \| bf ch de hh

799\.451403200\\scriptstyle\\tfrac\{451\}\{403200\}aa cg dg ef \| bf de fh hh

800\.−18431209600\\scriptstyle\-\\tfrac\{1843\}\{1209600\}aa cg dg ef \| bf de gh hh

801\.−307604800\\scriptstyle\-\\tfrac\{307\}\{604800\}aa cg dg ef \| bf dh eg hh

802\.−281241920\\scriptstyle\-\\tfrac\{281\}\{241920\}aa cg dg ef \| bf dh eh hh

803\.714400\\scriptstyle\\tfrac\{7\}\{14400\}aa cg dg ef \| bf eg gh hh

804\.16048\\scriptstyle\\tfrac\{1\}\{6048\}aa cg dg ef \| bf eh gh hh

805\.4137800\\scriptstyle\\tfrac\{41\}\{37800\}aa cg dg ef \| bf fg fh hh

806\.−2641604800\\scriptstyle\-\\tfrac\{2641\}\{604800\}aa cg dg ef \| bf fg gh hh

807\.673302400\\scriptstyle\\tfrac\{673\}\{302400\}aa cg dg ef \| bf fh gh hh

808\.−139600\\scriptstyle\-\\tfrac\{13\}\{9600\}aa cg dg ef \| bg eh fg hh

809\.318400\\scriptstyle\\tfrac\{31\}\{8400\}aa cg dg ef \| bg fg fh hh

810\.1160480\\scriptstyle\\tfrac\{11\}\{60480\}aa cg dg ef \| bg fg gh hh

811\.−379172800\\scriptstyle\-\\tfrac\{379\}\{172800\}aa cg dg ef \| bg fh gh hh

812\.97302400\\scriptstyle\\tfrac\{97\}\{302400\}aa cg dg ef \| bh df eh hh

813\.4431209600\\scriptstyle\\tfrac\{443\}\{1209600\}aa cg dg ef \| bh eh fg hh

814\.−743302400\\scriptstyle\-\\tfrac\{743\}\{302400\}aa cg dg ef \| bh fg fh hh

815\.−47604800\\scriptstyle\-\\tfrac\{47\}\{604800\}aa cg dg ef \| bh fh gh hh

816\.−82311209600\\scriptstyle\-\\tfrac\{8231\}\{1209600\}aa cg dh ef \| bf dg eg hh

817\.−23322400\\scriptstyle\-\\tfrac\{233\}\{22400\}aa cg dh ef \| bg df eg hh

818\.−134032\\scriptstyle\-\\tfrac\{13\}\{4032\}aa cg dh ef \| bh bh df eg

819\.−4519403200\\scriptstyle\-\\tfrac\{4519\}\{403200\}aa cg dh ef \| bh df eg gh

820\.−47172800\\scriptstyle\-\\tfrac\{47\}\{172800\}aa cg dh ef \| bh df eh gh

821\.−55376\\scriptstyle\-\\tfrac\{5\}\{5376\}aa cg dh ef \| bh dg eh fg

822\.−277302400\\scriptstyle\-\\tfrac\{277\}\{302400\}aa cg dh ef \| bh dg eh fh

823\.2331209600\\scriptstyle\\tfrac\{233\}\{1209600\}aa cg dh ef \| bh dh eh fg

824\.−40191209600\\scriptstyle\-\\tfrac\{4019\}\{1209600\}aa ch de fg \| bf bg bh eh

825\.7151604800\\scriptstyle\\tfrac\{7151\}\{604800\}aa ch de fg \| bf dh eg gh

826\.−1093604800\\scriptstyle\-\\tfrac\{1093\}\{604800\}aa ch de fg \| bf eh gh gh

827\.−20991209600\\scriptstyle\-\\tfrac\{2099\}\{1209600\}aa ch de fg \| bg cf dh eh

828\.−4051604800\\scriptstyle\-\\tfrac\{4051\}\{604800\}aa ch df eg \| bf bh eg gh

829\.4433403200\\scriptstyle\\tfrac\{4433\}\{403200\}aa ch df eg \| bg bh dh ef

830\.1037172800\\scriptstyle\\tfrac\{1037\}\{172800\}aa ch df eg \| bg bh eh fh

831\.−1307604800\\scriptstyle\-\\tfrac\{1307\}\{604800\}aa ch df eg \| bg ch dh ef

832\.211151200\\scriptstyle\\tfrac\{211\}\{151200\}aa ch df eg \| bg dh ef hh

833\.18591209600\\scriptstyle\\tfrac\{1859\}\{1209600\}aa ch df eg \| bh cg dh ef

834\.−37975600\\scriptstyle\-\\tfrac\{379\}\{75600\}aa ch df eg \| bh eg fh gh

835\.589604800\\scriptstyle\\tfrac\{589\}\{604800\}aa ch dg ef \| be bf bg bh

836\.159071209600\\scriptstyle\\tfrac\{15907\}\{1209600\}aa ch dg ef \| be fg fh gh

837\.−47631209600\\scriptstyle\-\\tfrac\{4763\}\{1209600\}aa ch dg ef \| bf bg dh eh

838\.115376\\scriptstyle\\tfrac\{11\}\{5376\}aa ch dg ef \| bf bh eg gh

839\.−338960\\scriptstyle\-\\tfrac\{33\}\{8960\}aa ch dg ef \| bf dg eh gh

840\.−3679241920\\scriptstyle\-\\tfrac\{3679\}\{241920\}aa ch dg ef \| bf dh eg gh

841\.−6071209600\\scriptstyle\-\\tfrac\{607\}\{1209600\}aa ch dg ef \| bg bh cf de

842\.1093302400\\scriptstyle\\tfrac\{1093\}\{302400\}aa ch dg ef \| bg bh fg fh

843\.−4811209600\\scriptstyle\-\\tfrac\{481\}\{1209600\}aa ch dg ef \| bg cf de hh

844\.−16400\\scriptstyle\-\\tfrac\{1\}\{6400\}aa ch dg ef \| bg dh eh fh

845\.−1037151200\\scriptstyle\-\\tfrac\{1037\}\{151200\}aa ch dg ef \| bg eh fg hh

846\.139302400\\scriptstyle\\tfrac\{139\}\{302400\}aa ch dg ef \| bg eh fh gh

847\.70186400\\scriptstyle\\tfrac\{701\}\{86400\}aa ch dg ef \| bh dg eh fg

848\.−714400\\scriptstyle\-\\tfrac\{7\}\{14400\}aa ch dg ef \| bh dh eh fg

849\.5350400\\scriptstyle\\tfrac\{53\}\{50400\}aa ch dg ef \| bh eh fh gh

850\.−1120960\\scriptstyle\-\\tfrac\{1\}\{120960\}aa de df dg \| bb bc cc dh

851\.−1120960\\scriptstyle\-\\tfrac\{1\}\{120960\}aa de df dg \| bc bc bc dh

852\.−1003201600\\scriptstyle\-\\tfrac\{1003\}\{201600\}aa de fg gh \| bc cf ef hh

853\.869302400\\scriptstyle\\tfrac\{869\}\{302400\}aa de fg gh \| bc cf eg hh

854\.643604800\\scriptstyle\\tfrac\{643\}\{604800\}aa de fg gh \| bc cf eh hh

855\.18548384\\scriptstyle\\tfrac\{185\}\{48384\}aa de fg gh \| bf ce cf hh

856\.−18119200\\scriptstyle\-\\tfrac\{181\}\{19200\}aa de fg gh \| bf ce cg hh

857\.1193604800\\scriptstyle\\tfrac\{1193\}\{604800\}aa de fg gh \| bf ce df hh

858\.11744800\\scriptstyle\\tfrac\{117\}\{44800\}aa de fg gh \| bf cf ef hh

859\.9471209600\\scriptstyle\\tfrac\{947\}\{1209600\}aa de fg gh \| bf cf eg hh

860\.−2910800\\scriptstyle\-\\tfrac\{29\}\{10800\}aa de fg gh \| bf cf eh hh

861\.−1219302400\\scriptstyle\-\\tfrac\{1219\}\{302400\}aa de fg gh \| bg cf ef hh

862\.377302400\\scriptstyle\\tfrac\{377\}\{302400\}aa de fg gh \| bg cf eg hh

863\.4859604800\\scriptstyle\\tfrac\{4859\}\{604800\}aa de fg gh \| bg cf eh hh

864\.11375600\\scriptstyle\\tfrac\{113\}\{75600\}aa de fg hh \| bc cf eg gh

865\.−1511604800\\scriptstyle\-\\tfrac\{1511\}\{604800\}aa de fg hh \| bg cf dh eg

866\.−4337604800\\scriptstyle\-\\tfrac\{4337\}\{604800\}aa de fg hh \| bg cf eg fh

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1113\.−137800\\scriptstyle\-\\tfrac\{1\}\{37800\}aa eg fg fh \| bd cd de hh

1114\.−17241920\\scriptstyle\-\\tfrac\{17\}\{241920\}aa eg fg gh \| bc bc df hh

1115\.127302400\\scriptstyle\\tfrac\{127\}\{302400\}aa eg fg gh \| bc bc dg hh

1116\.−13604800\\scriptstyle\-\\tfrac\{13\}\{604800\}aa eg fg gh \| bc bd cd hh

1117\.167200\\scriptstyle\\tfrac\{1\}\{67200\}aa eg fg gh \| bd cd cd hh

1118\.−19604800\\scriptstyle\-\\tfrac\{19\}\{604800\}aa eg fg gh \| bd cd cf hh

1119\.786400\\scriptstyle\\tfrac\{7\}\{86400\}aa eg fg gh \| bd cd cg hh

1120\.125200\\scriptstyle\\tfrac\{1\}\{25200\}aa eg fg gh \| bd cd df hh

1121\.−11201600\\scriptstyle\-\\tfrac\{11\}\{201600\}aa eg fg gh \| bd cd dg hh

1122\.−37604800\\scriptstyle\-\\tfrac\{37\}\{604800\}aa eg fg gh \| bf cd df hh

1123\.−133600\\scriptstyle\-\\tfrac\{1\}\{33600\}aa eg fg gh \| bf cf de hh

1124\.−1302400\\scriptstyle\-\\tfrac\{1\}\{302400\}aa eg fg gh \| bf cf df hh

1125\.137800\\scriptstyle\\tfrac\{1\}\{37800\}aa eg fg hh \| bc bd cd fh

1126\.−118900\\scriptstyle\-\\tfrac\{1\}\{18900\}aa eg fg hh \| bc bd cd gh

1127\.−19115200\\scriptstyle\-\\tfrac\{19\}\{115200\}aa eg fh gh \| bc bc df dh

1128\.−891209600\\scriptstyle\-\\tfrac\{89\}\{1209600\}aa eg fh gh \| bc bc dh fg

1129\.−118900\\scriptstyle\-\\tfrac\{1\}\{18900\}aa eg fh gh \| bc bd cd fh

1130\.229403200\\scriptstyle\\tfrac\{229\}\{403200\}aa eg fh gh \| bc cd df dh

1131\.−2271209600\\scriptstyle\-\\tfrac\{227\}\{1209600\}aa eg fh gh \| bd bh cd cf

1132\.−1360480\\scriptstyle\-\\tfrac\{13\}\{60480\}aa eg fh gh \| bd cd cf dh

1133\.−59302400\\scriptstyle\-\\tfrac\{59\}\{302400\}aa eg fh gh \| bd cd ch df

1134\.16300\\scriptstyle\\tfrac\{1\}\{6300\}aa eg fh gh \| bd cd ch fg

1135\.−13600\\scriptstyle\-\\tfrac\{1\}\{3600\}aa eg fh gh \| be cd df fh

1136\.18400\\scriptstyle\\tfrac\{1\}\{8400\}aa eg fh gh \| bf cd dh ef

1137\.16300\\scriptstyle\\tfrac\{1\}\{6300\}aa eg fh gh \| bh cf df ef

1138\.137800\\scriptstyle\\tfrac\{1\}\{37800\}aa eh fg gh \| bc bd cd ef

1139\.112600\\scriptstyle\\tfrac\{1\}\{12600\}aa eh fg gh \| bd bf cd ce

1140\.17120960\\scriptstyle\\tfrac\{17\}\{120960\}aa eh fg gh \| bd cd de df

1141\.−114400\\scriptstyle\-\\tfrac\{1\}\{14400\}aa eh fh gh \| bc bc df dg

1142\.−73302400\\scriptstyle\-\\tfrac\{73\}\{302400\}aa eh fh gh \| bc bc dg dh

1143\.1181440\\scriptstyle\\tfrac\{1\}\{181440\}aa eh fh gh \| bc bd cd fg

1144\.−11151200\\scriptstyle\-\\tfrac\{11\}\{151200\}aa eh fh gh \| bc cd dg dh

1145\.−125200\\scriptstyle\-\\tfrac\{1\}\{25200\}aa eh fh gh \| bd bg cd cf

1146\.−143200\\scriptstyle\-\\tfrac\{1\}\{43200\}aa eh fh gh \| bd cd cd fg

1147\.1151200\\scriptstyle\\tfrac\{1\}\{151200\}aa eh fh gh \| bd cd cg ef

1148\.121600\\scriptstyle\\tfrac\{1\}\{21600\}aa eh fh gh \| bd cd ch dg

1149\.1604800\\scriptstyle\\tfrac\{1\}\{604800\}aa eh fh gh \| bd cd df dg

1150\.143200\\scriptstyle\\tfrac\{1\}\{43200\}aa eh fh gh \| bd cd dg ef

1151\.−13241920\\scriptstyle\-\\tfrac\{13\}\{241920\}ab ab ab dd \| cd ef eg gh

1152\.−1604800\\scriptstyle\-\\tfrac\{1\}\{604800\}ab ab bc cc \| de df dg dh

1153\.125200\\scriptstyle\\tfrac\{1\}\{25200\}ab ab bc cc \| de dg ef gh

1154\.160480\\scriptstyle\\tfrac\{1\}\{60480\}ab ab bc de \| cc df dg dh

1155\.−131209600\\scriptstyle\-\\tfrac\{13\}\{1209600\}ab ab cc de \| bc df dg dh

1156\.17302400\\scriptstyle\\tfrac\{17\}\{302400\}ab ab cd cd \| eg fg gh hh

1157\.−11302400\\scriptstyle\-\\tfrac\{11\}\{302400\}ab ab cd cd \| eh fh gh gh

1158\.−19450\\scriptstyle\-\\tfrac\{1\}\{9450\}ab ab cd ce \| ab cf cg gh

1159\.−13780\\scriptstyle\-\\tfrac\{1\}\{3780\}ab ab cd ce \| ab cg ch ef

1160\.−112600\\scriptstyle\-\\tfrac\{1\}\{12600\}ab ab cd cf \| ab de fg fh

1161\.2386400\\scriptstyle\\tfrac\{23\}\{86400\}ab ab cd fg \| de ee gh hh

1162\.−1911209600\\scriptstyle\-\\tfrac\{191\}\{1209600\}ab ab cd gh \| de ee fg fh

1163\.1671209600\\scriptstyle\\tfrac\{167\}\{1209600\}ab ab cd gh \| de ee fg hh

1164\.344800\\scriptstyle\\tfrac\{3\}\{44800\}ab ab cd gh \| de ee fh fh

1165\.−1737800\\scriptstyle\-\\tfrac\{17\}\{37800\}ab ab dd ef \| ab cd eg gh

1166\.15400\\scriptstyle\\tfrac\{1\}\{5400\}ab ab dd ef \| ab cd eh fg

1167\.11890\\scriptstyle\\tfrac\{1\}\{1890\}ab ab dd ef \| bb cd eg gh

1168\.532419200\\scriptstyle\\tfrac\{53\}\{2419200\}ab ab dd fg \| cd eg eh hh

1169\.11134400\\scriptstyle\\tfrac\{11\}\{134400\}ab ab dd fg \| cd eg fh hh

1170\.−11268800\\scriptstyle\-\\tfrac\{11\}\{268800\}ab ab dd gh \| cd ef eh fg

1171\.−1131209600\\scriptstyle\-\\tfrac\{113\}\{1209600\}ab ab de fg \| cf eg gh hh

1172\.143200\\scriptstyle\\tfrac\{1\}\{43200\}ab ab de gh \| cd ce fg fh

1173\.−19450\\scriptstyle\-\\tfrac\{1\}\{9450\}ab ab de gh \| cd ce fh fh

1174\.175600\\scriptstyle\\tfrac\{1\}\{75600\}ab ab de gh \| cd ee fg hh

1175\.17151200\\scriptstyle\\tfrac\{17\}\{151200\}ab ab de gh \| cd ee fh fh

1176\.−111200\\scriptstyle\-\\tfrac\{1\}\{11200\}ab ab de gh \| ce ce fh fh

1177\.17172800\\scriptstyle\\tfrac\{17\}\{172800\}ab ab df eg \| cg ch ef hh

1178\.−17172800\\scriptstyle\-\\tfrac\{17\}\{172800\}ab ab df eg \| cg ef gh hh

1179\.47201600\\scriptstyle\\tfrac\{47\}\{201600\}ab ab df eg \| cg eh fg hh

1180\.180640\\scriptstyle\\tfrac\{1\}\{80640\}ab ab df eg \| cg eh fh hh

1181\.1302400\\scriptstyle\\tfrac\{1\}\{302400\}ab ab dg ef \| cf cg ch hh

1182\.−120160\\scriptstyle\-\\tfrac\{1\}\{20160\}ab ab dg ef \| cf cg eh hh

1183\.121600\\scriptstyle\\tfrac\{1\}\{21600\}ab ab dg ef \| cf cg gh hh

1184\.−13151200\\scriptstyle\-\\tfrac\{13\}\{151200\}ab ab dg ef \| cf eg gh hh

1185\.−1302400\\scriptstyle\-\\tfrac\{1\}\{302400\}ab ab dg ef \| cg ch fh hh

1186\.137800\\scriptstyle\\tfrac\{1\}\{37800\}ab ab dg ef \| cg eh fg hh

1187\.143200\\scriptstyle\\tfrac\{1\}\{43200\}ab ab dg ef \| cg fg fh hh

1188\.−118900\\scriptstyle\-\\tfrac\{1\}\{18900\}ab ab dg ef \| cg fg gh hh

1189\.16720\\scriptstyle\\tfrac\{1\}\{6720\}ab ab dg ef \| cg fh gh hh

1190\.−17172800\\scriptstyle\-\\tfrac\{17\}\{172800\}ab ab dg ef \| ch fg gh hh

1191\.43604800\\scriptstyle\\tfrac\{43\}\{604800\}ab ab dg ef \| ch fh gh hh

1192\.−17172800\\scriptstyle\-\\tfrac\{17\}\{172800\}ab ab ef gh \| cd ch dg fh

1193\.1031209600\\scriptstyle\\tfrac\{103\}\{1209600\}ab ab ef gh \| cd dg dh fh

1194\.−112600\\scriptstyle\-\\tfrac\{1\}\{12600\}ab ab ef gh \| cd dg eh fh

1195\.110800\\scriptstyle\\tfrac\{1\}\{10800\}ab ab ef gh \| cd dg fg hh

1196\.15040\\scriptstyle\\tfrac\{1\}\{5040\}ab ab ef gh \| cd dg fh hh

1197\.−112600\\scriptstyle\-\\tfrac\{1\}\{12600\}ab ab ef gh \| cd dh fg gh

1198\.160480\\scriptstyle\\tfrac\{1\}\{60480\}ab ab ef gh \| cg df dg hh

1199\.−1991209600\\scriptstyle\-\\tfrac\{199\}\{1209600\}ab ab ef gh \| cg df dh dh

1200\.175600\\scriptstyle\\tfrac\{1\}\{75600\}ab ab ef gh \| cg df dh eh

1201\.−175600\\scriptstyle\-\\tfrac\{1\}\{75600\}ab ab ef gh \| cg df eg hh

1202\.1511209600\\scriptstyle\\tfrac\{151\}\{1209600\}ab ab ef gh \| cg dg fg hh

1203\.−2291209600\\scriptstyle\-\\tfrac\{229\}\{1209600\}ab ab ef gh \| cg dg fh hh

1204\.31151200\\scriptstyle\\tfrac\{31\}\{151200\}ab ab ef gh \| cg dh dh fh

1205\.2631209600\\scriptstyle\\tfrac\{263\}\{1209600\}ab ab ef gh \| ch df dg gh

1206\.175600\\scriptstyle\\tfrac\{1\}\{75600\}ab ab ef gh \| ch df eg gh

1207\.−37403200\\scriptstyle\-\\tfrac\{37\}\{403200\}ab ab ef gh \| ch dg dg fh

1208\.−18400\\scriptstyle\-\\tfrac\{1\}\{8400\}ab ab ef gh \| ch dg dh fh

1209\.−115120\\scriptstyle\-\\tfrac\{1\}\{15120\}ab ab ef gh \| ch dg eh fg

1210\.−175600\\scriptstyle\-\\tfrac\{1\}\{75600\}ab ab ef gh \| ch dg eh fh

1211\.−175600\\scriptstyle\-\\tfrac\{1\}\{75600\}ab ab ef gh \| ch dg fg fh

1212\.130240\\scriptstyle\\tfrac\{1\}\{30240\}ab ab ef gh \| ch dh eg fg

1213\.291209600\\scriptstyle\\tfrac\{29\}\{1209600\}ab ab ef gh \| ch dh fg gh

1214\.150400\\scriptstyle\\tfrac\{1\}\{50400\}ab ab eg fg \| cd ch df hh

1215\.−133600\\scriptstyle\-\\tfrac\{1\}\{33600\}ab ab eg fg \| cd df dh hh

1216\.112600\\scriptstyle\\tfrac\{1\}\{12600\}ab ab eg fg \| cd df eh hh

1217\.116800\\scriptstyle\\tfrac\{1\}\{16800\}ab ab eg fg \| cd dg dh hh

1218\.−112600\\scriptstyle\-\\tfrac\{1\}\{12600\}ab ab eg fg \| cd dg fh hh

1219\.150400\\scriptstyle\\tfrac\{1\}\{50400\}ab ab eg fg \| cd dg gh hh

1220\.−116800\\scriptstyle\-\\tfrac\{1\}\{16800\}ab ab eg fg \| cd dh gh hh

1221\.−150400\\scriptstyle\-\\tfrac\{1\}\{50400\}ab ab eg fg \| cf df dh hh

1222\.−120160\\scriptstyle\-\\tfrac\{1\}\{20160\}ab ab eg fg \| cf df fh hh

1223\.114400\\scriptstyle\\tfrac\{1\}\{14400\}ab ab eg fg \| cf df gh hh

1224\.−1791209600\\scriptstyle\-\\tfrac\{179\}\{1209600\}ab ab eg fg \| ch df dh hh

1225\.1791209600\\scriptstyle\\tfrac\{179\}\{1209600\}ab ab eg fg \| ch df fh hh

1226\.1791209600\\scriptstyle\\tfrac\{179\}\{1209600\}ab ab eg fg \| ch dg dh hh

1227\.−19241920\\scriptstyle\-\\tfrac\{19\}\{241920\}ab ab eg fg \| ch dg gh hh

1228\.1175600\\scriptstyle\\tfrac\{11\}\{75600\}ab ab eg fg \| ch dh fh hh

1229\.−1791209600\\scriptstyle\-\\tfrac\{179\}\{1209600\}ab ab eg fg \| ch dh gh hh

1230\.−120160\\scriptstyle\-\\tfrac\{1\}\{20160\}ab ab eg fh \| cd cg df hh

1231\.13120960\\scriptstyle\\tfrac\{13\}\{120960\}ab ab eg fh \| cd df dg hh

1232\.15400\\scriptstyle\\tfrac\{1\}\{5400\}ab ab eg fh \| cd dg fg hh

1233\.−121600\\scriptstyle\-\\tfrac\{1\}\{21600\}ab ab eg fh \| cd dh fg gh

1234\.−17200\\scriptstyle\-\\tfrac\{1\}\{7200\}ab ab eg fh \| cg df dg hh

1235\.−137800\\scriptstyle\-\\tfrac\{1\}\{37800\}ab ab eg fh \| cg df dh eh

1236\.137800\\scriptstyle\\tfrac\{1\}\{37800\}ab ab eg fh \| cg df fg hh

1237\.11151200\\scriptstyle\\tfrac\{11\}\{151200\}ab ab eg fh \| cg df gh hh

1238\.112600\\scriptstyle\\tfrac\{1\}\{12600\}ab ab eg fh \| ch df dg eh

1239\.11151200\\scriptstyle\\tfrac\{11\}\{151200\}ab ab eg fh \| ch dg fh gh

1240\.19450\\scriptstyle\\tfrac\{1\}\{9450\}ab ab eg fh \| ch dh fg fg

1241\.−43604800\\scriptstyle\-\\tfrac\{43\}\{604800\}ab ab eh fg \| cd df dg dh

1242\.175600\\scriptstyle\\tfrac\{1\}\{75600\}ab ab eh fg \| cd dg dh ef

1243\.−11151200\\scriptstyle\-\\tfrac\{11\}\{151200\}ab ab eh fg \| cd dh fh gh

1244\.13151200\\scriptstyle\\tfrac\{13\}\{151200\}ab ab eh fg \| cg dh dh fh

1245\.−112600\\scriptstyle\-\\tfrac\{1\}\{12600\}ab ab fg gh \| ab cd ce hh

1246\.1403200\\scriptstyle\\tfrac\{1\}\{403200\}ab ab fg gh \| cd ce de hh

1247\.1403200\\scriptstyle\\tfrac\{1\}\{403200\}ab ab fg gh \| ce de de hh

1248\.−112600\\scriptstyle\-\\tfrac\{1\}\{12600\}ab ab fg gh \| ce de df hh

1249\.114400\\scriptstyle\\tfrac\{1\}\{14400\}ab ab fg gh \| ce de dg hh

1250\.−1403200\\scriptstyle\-\\tfrac\{1\}\{403200\}ab ab fg gh \| ce de ef hh

1251\.−1172800\\scriptstyle\-\\tfrac\{1\}\{172800\}ab ab fg gh \| cf df ef hh

1252\.−112600\\scriptstyle\-\\tfrac\{1\}\{12600\}ab ab fg hh \| ab cd ce gh

1253\.112600\\scriptstyle\\tfrac\{1\}\{12600\}ab ab fh gh \| ab cd ce fg

1254\.112600\\scriptstyle\\tfrac\{1\}\{12600\}ab ab fh gh \| cd de eg eh

1255\.−150400\\scriptstyle\-\\tfrac\{1\}\{50400\}ab ab fh gh \| cd de eh eh

1256\.−114400\\scriptstyle\-\\tfrac\{1\}\{14400\}ab ab fh gh \| ce de dh eg

1257\.1403200\\scriptstyle\\tfrac\{1\}\{403200\}ab ab fh gh \| ce de ef eg

1258\.−160480\\scriptstyle\-\\tfrac\{1\}\{60480\}ab ac ad fg \| ef eg eh hh

1259\.160480\\scriptstyle\\tfrac\{1\}\{60480\}ab ac ad fg \| ef eg gh hh

1260\.−23302400\\scriptstyle\-\\tfrac\{23\}\{302400\}ab ac ad fg \| ef gh gh hh

1261\.1100800\\scriptstyle\\tfrac\{1\}\{100800\}ab ac ad fg \| eg eg eh hh

1262\.175600\\scriptstyle\\tfrac\{1\}\{75600\}ab ac ad fg \| eg eg fh hh

1263\.−121600\\scriptstyle\-\\tfrac\{1\}\{21600\}ab ac ad fg \| eg eg gh hh

1264\.−160480\\scriptstyle\-\\tfrac\{1\}\{60480\}ab ac ad fg \| eg eh eh hh

1265\.−116800\\scriptstyle\-\\tfrac\{1\}\{16800\}ab ac ad fg \| eg eh fg hh

1266\.125200\\scriptstyle\\tfrac\{1\}\{25200\}ab ac ad fg \| eg eh gh hh

1267\.116800\\scriptstyle\\tfrac\{1\}\{16800\}ab ac ad fg \| eg fg fh hh

1268\.23302400\\scriptstyle\\tfrac\{23\}\{302400\}ab ac ad fg \| eg fh gh hh

1269\.−116800\\scriptstyle\-\\tfrac\{1\}\{16800\}ab ac bb cc \| de dg ef gh

1270\.175600\\scriptstyle\\tfrac\{1\}\{75600\}ab ac bc fg \| de dh eg hh

1271\.−175600\\scriptstyle\-\\tfrac\{1\}\{75600\}ab ac bc fg \| de eg eh hh

1272\.−175600\\scriptstyle\-\\tfrac\{1\}\{75600\}ab ac bc fg \| dh eg eh hh

1273\.125200\\scriptstyle\\tfrac\{1\}\{25200\}ab ac cd fg \| ef eg eh hh

1274\.−110080\\scriptstyle\-\\tfrac\{1\}\{10080\}ab ac cd fg \| ef eg gh hh

1275\.150400\\scriptstyle\\tfrac\{1\}\{50400\}ab ac cd fg \| ef gh gh hh

1276\.−17560\\scriptstyle\-\\tfrac\{1\}\{7560\}ab ac cd fg \| eg eg eh hh

1277\.11151200\\scriptstyle\\tfrac\{11\}\{151200\}ab ac cd fg \| eg eg gh hh

1278\.−23151200\\scriptstyle\-\\tfrac\{23\}\{151200\}ab ac cd fg \| eg eh eh hh

1279\.−150400\\scriptstyle\-\\tfrac\{1\}\{50400\}ab ac cd fg \| eg eh fg hh

1280\.16300\\scriptstyle\\tfrac\{1\}\{6300\}ab ac cd fg \| eg eh fh hh

1281\.130240\\scriptstyle\\tfrac\{1\}\{30240\}ab ac cd fg \| eg eh gh hh

1282\.19151200\\scriptstyle\\tfrac\{19\}\{151200\}ab ac cd fg \| eg eh hh hh

1283\.112600\\scriptstyle\\tfrac\{1\}\{12600\}ab ac cd fg \| eg fg fh hh

1284\.−18400\\scriptstyle\-\\tfrac\{1\}\{8400\}ab ac cd fg \| eg fh gh hh

1285\.−116800\\scriptstyle\-\\tfrac\{1\}\{16800\}ab ac cd fg \| eg fh hh hh

1286\.112600\\scriptstyle\\tfrac\{1\}\{12600\}ab ac cd fg \| eh eh gh hh

1287\.−112600\\scriptstyle\-\\tfrac\{1\}\{12600\}ab ac cd fg \| eh fh gh hh

1288\.16300\\scriptstyle\\tfrac\{1\}\{6300\}ab ac de fh \| ef fg gg hh

1289\.−112600\\scriptstyle\-\\tfrac\{1\}\{12600\}ab ac df ef \| dh eg gg hh

1290\.−16300\\scriptstyle\-\\tfrac\{1\}\{6300\}ab ac dg ef \| eg fg fh hh
Representing MAX functions using two-hidden-layer ReLU networks

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