Statistics

Problem Statement

John and Brus are interested in a new game called "Hexagon Flower". The rules are simple. You are given a flower formed by seven hexagons arranged as follows:



The objective of the game is to place a number in each hexagon of the flower such that all of the following conditions are satisfied:

• Each number is an integer between 1 and n*2, inclusive.
• Each number is distinct.
• For every pair of adjacent hexagons, if the numbers placed in them are a and b, then a%n != b%n.

Given n, return the total number of distinct solutions. Two solutions are considered the same if you can rotate one to form the other.

For example, if n = 4 then:



The top three placements are not valid. The other three placements are valid, but the first two among them are considered equal since one can be rotated to become the other.

Definition

Class:

TheHexagonsDivOne

Method:

count

Parameters:

int

Returns:

long

Method signature:

long count(int n)

(be sure your method is public)

Constraints

• n will be between 1 and 150, inclusive.

Examples

1. 3

   Returns: 0

   There are not enough numbers to fill the flower with.

2. 4

   Returns: 256

3. 8

   Returns: 3458560

4. 20

   Returns: 11193888000

5. 1

   Returns: 0

6. 2

   Returns: 0

7. 3

   Returns: 0

8. 5

   Returns: 12800

9. 6

   Returns: 142080

10. 7

    Returns: 842240

11. 9

    Returns: 11160576

12. 10

    Returns: 30374400

13. 11

    Returns: 72821760

14. 12

    Returns: 158273280

15. 13

    Returns: 318123520

16. 14

    Returns: 599895296

17. 15

    Returns: 1072780800

18. 16

    Returns: 1834327040

19. 17

    Returns: 3018373120

20. 18

    Returns: 4804346880

21. 19

    Returns: 7428028416

22. 21

    Returns: 16489105920

23. 22

    Returns: 23799381760

24. 23

    Returns: 33726640640

25. 24

    Returns: 47008743936

26. 25

    Returns: 64541312000

27. 26

    Returns: 87401766400

28. 27

    Returns: 116875699200

29. 28

    Returns: 154485676800

30. 29

    Returns: 202022585856

31. 30

    Returns: 261579628800

32. 31

    Returns: 335589076480

33. 32

    Returns: 426861885440

34. 33

    Returns: 538630287360

35. 34

    Returns: 674593458176

36. 35

    Returns: 838966374400

37. 36

    Returns: 1036531964160

38. 37

    Returns: 1272696660480

39. 38

    Returns: 1553549464320

40. 39

    Returns: 1885924624896

41. 40

    Returns: 2277468044800

42. 41

    Returns: 2736707517440

43. 42

    Returns: 3273126904320

44. 43

    Returns: 3897244359680

45. 44

    Returns: 4620694710016

46. 45

    Returns: 5456316096000

47. 46

    Returns: 6418240984320

48. 47

    Returns: 7521991656960

49. 48

    Returns: 8784580285440

50. 49

    Returns: 10224613697536

51. 50

    Returns: 11862402944000

52. 51

    Returns: 13720077772800

53. 52

    Returns: 15821706118400

54. 53

    Returns: 18193418713600

55. 54

    Returns: 20863538931456

56. 55

    Returns: 23862717964800

57. 56

    Returns: 27224075450880

58. 57

    Returns: 30983345648640

59. 58

    Returns: 35179029276160

60. 59

    Returns: 39852551115776

61. 60

    Returns: 45048423494400

62. 61

    Returns: 50814415746560

63. 62

    Returns: 57201729767680

64. 63

    Returns: 64265181765120

65. 64

    Returns: 72063390314496

66. 65

    Returns: 80658970828800

67. 66

    Returns: 90118736547840

68. 67

    Returns: 100513906155520

69. 68

    Returns: 111920318132480

70. 69

    Returns: 124418651951616

71. 70

    Returns: 138094656224000

72. 71

    Returns: 153039383902720

73. 72

    Returns: 169349434652160

74. 73

    Returns: 187127204490240

75. 74

    Returns: 206481142811136

76. 75

    Returns: 227526016896000

77. 76

    Returns: 250383184019200

78. 77

    Returns: 275180871257600

79. 78

    Returns: 302054463110400

80. 79

    Returns: 331146797037056

81. 80

    Returns: 362608467020800

82. 81

    Returns: 396598135265280

83. 82

    Returns: 433282852131840

84. 83

    Returns: 472838384424960

85. 84

    Returns: 515449552133376

86. 85

    Returns: 561310573734400

87. 86

    Returns: 610625420168960

88. 87

    Returns: 663608177594880

89. 88

    Returns: 720483419025920

90. 89

    Returns: 781486584964096

91. 90

    Returns: 846864373132800

92. 91

    Returns: 916875137418240

93. 92

    Returns: 991789296126720

94. 93

    Returns: 1071889749665280

95. 94

    Returns: 1157472307753216

96. 95

    Returns: 1248846126272000

97. 96

    Returns: 1346334153861120

98. 97

    Returns: 1450273588367360

99. 98

    Returns: 1561016343255040

100. 99

     Returns: 1678929524084736

101. 100

     Returns: 1804395915168000

102. 101

     Returns: 1937814476505600

103. 102

     Returns: 2079600851116800

104. 103

     Returns: 2230187882867200

105. 104

     Returns: 2390026144902656

106. 105

     Returns: 2559584478796800

107. 106

     Returns: 2739350544519680

108. 107

     Returns: 2929831381335040

109. 108

     Returns: 3131553979733760

110. 109

     Returns: 3345065864510976

111. 110

     Returns: 3570935689094400

112. 111

     Returns: 3809753841231360

113. 112

     Returns: 4062133060142080

114. 113

     Returns: 4328709065246720

115. 114

     Returns: 4610141196573696

116. 115

     Returns: 4907113066956800

117. 116

     Returns: 5220333226128640

118. 117

     Returns: 5550535836817920

119. 118

     Returns: 5898481362958080

120. 119

     Returns: 6264957270114816

121. 120

     Returns: 6650778738240000

122. 121

     Returns: 7056789386859520

123. 122

     Returns: 7483862012802560

124. 123

     Returns: 7932899340579840

125. 124

     Returns: 8404834785518336

126. 125

     Returns: 8900633229760000

127. 126

     Returns: 9421291811232000

128. 127

     Returns: 9967840725696000

129. 128

     Returns: 10541344041984000

130. 129

     Returns: 11142900530528256

131. 130

     Returns: 11773644505292800

132. 131

     Returns: 12434746679214080

133. 132

     Returns: 13127415033258240

134. 133

     Returns: 13852895699202560

135. 134

     Returns: 14612473856248576

136. 135

     Returns: 15407474641574400

137. 136

     Returns: 16239264074933760

138. 137

     Returns: 17109249997409280

139. 138

     Returns: 18018883024427520

140. 139

     Returns: 18969657513143296

141. 140

     Returns: 19963112544300800

142. 141

     Returns: 21000832918679040

143. 142

     Returns: 22084450168229120

144. 143

     Returns: 23215643582010880

145. 144

     Returns: 24396141247036416

146. 145

     Returns: 25627721104128000

147. 146

     Returns: 26912212018897920

148. 147

     Returns: 28251494867957760

149. 148

     Returns: 29647503640464640

150. 149

     Returns: 31102226555111936

151. 150

     Returns: 32617707192672000