Statistics

Problem Statement for "FoxPaintingBalls"

Problem Statement

A Ball Triangle is a set of identical balls placed in a triangular shape. A Ball Triangle has N rows, numbered 1 to N from top to bottom. For all i, 1 <= i <= N, the i-th row contains i balls. For example, the following image shows a Ball Triangle with N=3.




Fox Jiro has infinitely many Ball Triangles. He can paint a Ball Triangle according to the following conditions:

  • Each of the balls has to be painted either red, green, or blue.
  • No two adjacent balls may share the same color.

The following image shows one valid coloring of a Ball Triangle for N=3.




Jiro wants to paint as many Ball Triangles as he can. As long as he follows the rules above, he may color the Ball Triangles in any way he likes. Some of the colored Ball Triangles may look exactly the same, but they don't have to. The only other constraint is the total amount of paint available to Jiro: In all the triangles together, he can paint at most R balls red, G balls green, and B balls blue.


You are given the longs R, G, and B. You are also given the int N. Return the maximum possible number of Ball Triangles Jiro can paint.

Definition

Class:
FoxPaintingBalls
Method:
theMax
Parameters:
long, long, long, int
Returns:
long
Method signature:
long theMax(long R, long G, long B, int N)
(be sure your method is public)

Constraints

  • R, G and B will each be between 0 and 1,000,000,000,000,000,000 (10^18), inclusive.
  • N will be between 1 and 1,000,000,000, inclusive.

Examples

  1. 2

    2

    2

    3

    Returns: 1

    Jiro can paint one Ball Triangle in the same way as in the image in the statement.

  2. 1

    2

    3

    3

    Returns: 0

    This time Jiro can paint no Ball Triangles.

  3. 8

    6

    6

    4

    Returns: 2

  4. 7

    6

    7

    4

    Returns: 2

  5. 100

    100

    100

    4

    Returns: 30

  6. 1

    0

    0

    1

    Returns: 1

  7. 0

    1

    0

    1

    Returns: 1

  8. 0

    0

    0

    1

    Returns: 0

  9. 1

    1

    1

    1

    Returns: 3

  10. 1

    1

    1

    2

    Returns: 1

  11. 0

    1

    2

    2

    Returns: 0

  12. 1

    0

    1

    1

    Returns: 2

  13. 2

    2

    2

    1

    Returns: 6

  14. 2

    2

    2

    2

    Returns: 2

  15. 3

    3

    3

    1

    Returns: 9

  16. 3

    3

    3

    2

    Returns: 3

  17. 3

    3

    3

    3

    Returns: 1

  18. 4

    3

    3

    2

    Returns: 3

  19. 4

    4

    3

    2

    Returns: 3

  20. 1000000000000000000

    0

    0

    2

    Returns: 0

  21. 0

    1000000000000000000

    0

    1

    Returns: 1000000000000000000

  22. 1000000000000000000

    1000000000000000000

    3

    4

    Returns: 1

  23. 5

    5

    5

    5

    Returns: 1

  24. 6

    6

    6

    6

    Returns: 0

  25. 7

    7

    7

    6

    Returns: 1

  26. 9

    9

    9

    7

    Returns: 0

  27. 10

    9

    9

    7

    Returns: 1

  28. 20

    18

    18

    7

    Returns: 2

  29. 19

    19

    18

    7

    Returns: 2

  30. 30

    27

    27

    7

    Returns: 3

  31. 28

    29

    27

    7

    Returns: 3

  32. 28

    28

    28

    7

    Returns: 3

  33. 1000000000000000000

    1000000000000000000

    1000000000000000000

    1

    Returns: 3000000000000000000

  34. 1000000000000000000

    1000000000000000000

    1000000000000000000

    4

    Returns: 300000000000000000

  35. 949185738472857384

    819402738175983874

    905384829619493856

    4

    Returns: 267397330626833511

  36. 434532807763425372

    912245252707409536

    721365743254593093

    31414801

    Returns: 2641

  37. 678784925379051339

    10400178261775338

    596597756820352946

    219585852

    Returns: 1

  38. 410337216597617089

    386302845330165482

    418056928079112265

    706013973

    Returns: 4

  39. 972188503299304012

    409126227317276821

    995258269701504023

    49615093

    Returns: 997

  40. 599621438406050095

    698609304892017589

    787796959604382653

    690733962

    Returns: 7

  41. 141432426644410478

    523068564992268257

    3968030436189050

    515162458

    Returns: 0

  42. 254628413341806822

    566715091027788844

    879582218386129339

    675919335

    Returns: 3

  43. 507439108017966407

    215717761963116220

    945999661289213983

    366606129

    Returns: 9

  44. 199071957438966662

    39288696435238117

    284416158721260667

    18754549

    Returns: 670

  45. 983736091909044788

    702333263235925397

    7736674995425306

    132651710

    Returns: 2

  46. 569236532697503079

    359905201510005491

    368202917314669897

    729169499

    Returns: 4

  47. 10467327035807453

    880124072793239679

    990334133647510853

    522284156

    Returns: 0

  48. 869468770771426074

    654142812520614050

    316191939090744226

    271490006

    Returns: 25

  49. 581857340557919457

    126509045080352385

    552851871392234657

    326592752

    Returns: 7

  50. 647366618592656593

    256087226025013360

    640836616989961093

    543804583

    Returns: 5

  51. 766158796809697016

    366549826517977430

    739434029035185553

    502785481

    Returns: 8

  52. 171859595078689544

    94382729514372910

    873631019476369348

    559594700

    Returns: 1

  53. 850357130417442178

    54925571384856154

    925783176400092567

    180057968

    Returns: 10

  54. 415939394452830858

    825021880708597642

    439171514174899099

    472920443

    Returns: 11

  55. 20761386065312160

    350806678810220275

    235110673638246110

    534340919

    Returns: 0

  56. 300247799199144451

    298066591896670306

    906025349749616686

    17

    Returns: 5844442978366084

  57. 721673323105071141

    203949908126125056

    377546143339611000

    2

    Returns: 203949908126125056

  58. 424089261602786391

    228127905195220341

    867852640395653859

    20

    Returns: 3258970074217433

  59. 597666940660802864

    353285014788433562

    796366346613886003

    20

    Returns: 5046928782691908

  60. 875395507329539035

    361768382604152564

    732770400499242701

    24

    Returns: 3617683826041525

  61. 469629003818947099

    466014803897807155

    8740647170953527

    15

    Returns: 218516179273838

  62. 714394451425081416

    934383015997870113

    437765390693388432

    16

    Returns: 9728119793186409

  63. 868134492197118126

    838282259575541163

    693354686219975066

    17

    Returns: 13595189925881864

  64. 741245874030733510

    364572418091271939

    120695531315088765

    28

    Returns: 894040972704361

  65. 978517292632498505

    288013197731675107

    867413781183444535

    8

    Returns: 24001099810972925

  66. 21149663609246215

    768508198421360005

    417798430934155076

    7

    Returns: 2349962623249579

  67. 394281996341375734

    911909099833936580

    87140857515851980

    13

    Returns: 2904695250528399

  68. 960944295171171344

    687623549733004805

    513199817045212536

    24

    Returns: 5131998170452125

  69. 595165730234648309

    57201505479204008

    112537623951448996

    20

    Returns: 817164363988628

  70. 525482445223521345

    623000890791532501

    601360662936882125

    11

    Returns: 23885565691978242

  71. 414003689480975178

    444893071864914782

    911216048589144303

    18

    Returns: 7263222622473248

  72. 388214781534238435

    296926208814985411

    759202342234524695

    17

    Returns: 5822082525784027

  73. 745787960733907063

    751612625711023250

    873841571278977575

    20

    Returns: 10654113724770100

  74. 242760377566309954

    528576742527990434

    170285625210596976

    18

    Returns: 2987467108957841

  75. 573220895197092962

    342556405012238046

    57017734782977031

    14

    Returns: 1629078136656486

  76. 866371492869738380

    866371492869738437

    866371492869738418

    478076429

    Returns: 22

  77. 90640277124104481

    90640277124104500

    90640277124104553

    194606200

    Returns: 14

  78. 921015884493001641

    921015884493001653

    921015884493001661

    606524717

    Returns: 15

  79. 426095736033883130

    426095736033883165

    426095736033883077

    390495974

    Returns: 16

  80. 841146992876139473

    841146992876139407

    841146992876139291

    912691565

    Returns: 6

  81. 568627451507658226

    568627451507658085

    568627451507658064

    862083986

    Returns: 4

  82. 383098163497752052

    383098163497752107

    383098163497752123

    649123799

    Returns: 5

  83. 469397376150686270

    469397376150686319

    469397376150686191

    977494083

    Returns: 2

  84. 338594055324770179

    338594055324770216

    338594055324770203

    464735843

    Returns: 9

  85. 770226248969126024

    770226248969126067

    770226248969125965

    127140587

    Returns: 285

  86. 48932907154432024

    48932907154432174

    48932907154432072

    523579054

    Returns: 1

  87. 953756049150593126

    953756049150593155

    953756049150593254

    945836614

    Returns: 6

  88. 921567783946494978

    921567783946495044

    921567783946494938

    67103100

    Returns: 1227

  89. 938603508209546223

    938603508209546327

    938603508209546190

    246728026

    Returns: 92

  90. 180563567070190582

    180563567070190700

    180563567070190663

    78419658

    Returns: 176

  91. 765178045830717532

    765178045830717546

    765178045830717479

    704612361

    Returns: 9

  92. 590733514181997590

    590733514181997558

    590733514181997593

    695340729

    Returns: 7

  93. 540849015002207908

    540849015002207889

    540849015002207770

    733793060

    Returns: 6

  94. 448232396775595482

    448232396775595511

    448232396775595525

    908506983

    Returns: 3

  95. 750925177042368293

    750925177042368234

    750925177042368167

    403311295

    Returns: 27

  96. 440104302960949798

    440104302960949652

    440104302960949818

    935144910

    Returns: 3

  97. 128219221160872551

    128219221160872532

    128219221160872513

    249402199

    Returns: 12

  98. 926803537328012521

    926803537328012590

    926803537328012509

    886385758

    Returns: 7

  99. 638355527147559025

    638355527147559108

    638355527147558983

    402165992

    Returns: 23

  100. 671505422387382102

    671505422387381991

    671505422387382010

    414785576

    Returns: 23

  101. 19330428391852493

    48815737582834113

    11451481019198930

    3456

    Returns: 5750952686

  102. 1

    1

    1

    1

    Returns: 3

  103. 19330428391852493

    48815737582834113

    11451481019198930

    1000000000

    Returns: 0

  104. 1000000000000000000

    500000000000000000

    250000000000000000

    4

    Returns: 83333333333333333

  105. 1000000000000000000

    1000000000

    1000000000000000000

    1000000000

    Returns: 0

  106. 19330428391852493

    48815737582834113

    11451481019198930

    4

    Returns: 3817160339732976

  107. 19330428391852493

    48815737582834113

    11451481019198930

    345600

    Returns: 575260

  108. 458775

    4874487

    4588754

    1000000000

    Returns: 0

  109. 543556563565654567

    23423454565656

    23463453472345

    1000000000

    Returns: 0

  110. 19330428391852493

    48815737582834113

    11451481019198930

    3457

    Returns: 5747627475

  111. 1000000000000000

    1000000000000000

    1000000000000000

    2342352

    Returns: 1093

  112. 1000000000000000000

    1000000000000000000

    1

    1

    Returns: 2000000000000000001

  113. 100000

    404040

    202020

    1000000000

    Returns: 0

  114. 1000000000000

    1000000000000

    1000000000000

    5000000

    Returns: 0

  115. 1000000000000000000

    1000000000000000000

    1000000000000000000

    1000000000

    Returns: 5

  116. 500

    500

    500

    1

    Returns: 1500

  117. 1000000000000000000

    1000000000000000000

    1000000000000000000

    1000000

    Returns: 5999994

  118. 1000000000000000

    1000000000000000

    1000000000000000

    1

    Returns: 3000000000000000

  119. 100

    0

    0

    1

    Returns: 100

  120. 999999999999999999

    999999999999999999

    999999999999999997

    999878477

    Returns: 6

  121. 3265873456834

    6354857389734

    345345847583

    1000000000

    Returns: 0

  122. 1247612373918741

    273593827409184

    2385789472398

    20394

    Returns: 34415

  123. 1000000000000000000

    10000000000000000

    100000000000000000

    1000000000

    Returns: 0

  124. 1000000000000000000

    90000000000000000

    800000000000000

    1000000

    Returns: 4799

  125. 10

    0

    0

    1

    Returns: 10

  126. 4324324234234234

    4324234324234324

    42324324424324344

    1000000000

    Returns: 0

  127. 19330428391852493

    48815737582834113

    11451481019198930

    100000000

    Returns: 6

  128. 1000000000000000000

    1000000000000000000

    1000000000000000000

    100000000

    Returns: 599

  129. 1000000000

    1000000000

    1000000000

    1000000000

    Returns: 0

  130. 1000000000000000000

    1000000000000000000

    1000000000000000000

    100000

    Returns: 599994000

  131. 9

    9

    12

    4

    Returns: 3

  132. 100000000

    100000000

    100000000

    1000000000

    Returns: 0

  133. 2

    4

    4

    4

    Returns: 0

  134. 10

    10

    10

    1

    Returns: 30

  135. 1000000000000000

    1000000000000023

    1000000000000015

    10000000

    Returns: 59

  136. 4564121

    1111111

    47711

    4

    Returns: 15903

  137. 100

    100

    1

    4

    Returns: 0

  138. 12

    12

    12

    1

    Returns: 36

  139. 50000000500000003

    50000000500000003

    50000000500000003

    100000000

    Returns: 30

  140. 100

    10000000000

    10000000000

    4

    Returns: 33

  141. 100000000000000

    100000000000000

    100000000000000

    1000000

    Returns: 599

  142. 100

    100

    1

    7

    Returns: 0

  143. 100000000000

    100000000000

    200000000000

    4

    Returns: 33333333333

  144. 400

    30

    30

    4

    Returns: 10

  145. 1000000000000000000

    1

    1

    1

    Returns: 1000000000000000002

  146. 1000

    1000

    1000

    999999999

    Returns: 0

  147. 1000000000000000

    1000000000000000

    1000000000000000

    1000000

    Returns: 5999

  148. 0

    100

    200

    1

    Returns: 300

  149. 19330428391852493

    48815737582834113

    11451481019198999

    345634

    Returns: 575146

  150. 30

    30

    40

    4

    Returns: 10

  151. 100000000000000

    100000000000000

    100000000000000

    7

    Returns: 10714285714285

  152. 7

    6

    6

    4

    Returns: 1

  153. 100000000000000

    100000000000000

    100000000000000

    100000002

    Returns: 0

  154. 1000000000000000

    1000000000000000

    1000000000000000

    4

    Returns: 300000000000000

  155. 900000000000000041

    800000000000018467

    700000000000006334

    650019169

    Returns: 9

  156. 19330428391852493

    48815737585554113

    11451481019198999

    345634232

    Returns: 0

  157. 1000000000000000

    1000000000000000

    999999999999999

    4

    Returns: 299999999999999

  158. 1

    2

    1000000000

    2

    Returns: 1

  159. 100000000000006700

    111000000000000000

    100000000990000000

    1000000000

    Returns: 0

  160. 1000000000000000

    1000000000000000

    1000000000000000

    100000

    Returns: 599994

  161. 100

    102

    140

    4

    Returns: 33

  162. 100

    100

    1432

    4

    Returns: 33

  163. 19330428391852493

    48815737585554113

    11451481019198999

    345634231

    Returns: 0

  164. 350000000000000000

    320000000000000000

    330000000000000000

    4

    Returns: 100000000000000000

  165. 1000000000000000000

    1000000000000000000

    1000000000000000000

    999999998

    Returns: 6

  166. 0

    1

    1

    1

    Returns: 2

  167. 19000

    18000

    18000

    10

    Returns: 1000

  168. 100

    100

    0

    4

    Returns: 0

  169. 8

    1

    11

    4

    Returns: 0

  170. 999999999

    888888888

    777777777

    999999999

    Returns: 0

  171. 100000000000000000

    100000000000000000

    100000000000000000

    1000000

    Returns: 599999

  172. 100000000000000000

    100000000000000000

    100000000000000000

    4

    Returns: 30000000000000000

  173. 1000000000000000000

    999999999999999999

    999999999999999998

    1000000000

    Returns: 5

  174. 3

    10

    10

    4

    Returns: 1

  175. 3

    3

    4

    7

    Returns: 0

  176. 1000000000000000000

    1000000000000000000

    1000000000000000000

    10000000

    Returns: 59999

  177. 1000000000000000000

    1000000000000000000

    1000000000000000000

    900000000

    Returns: 7

  178. 2345

    334563635

    434534

    1000000000

    Returns: 0

  179. 19330428391852493

    48815737582834113

    11451481019198930

    345666

    Returns: 575040

  180. 100

    1

    1

    4

    Returns: 0

  181. 9999999999999999

    10000000000000000

    10000000000000000

    100

    Returns: 5940594059405

  182. 1000000000000000000

    500000000000000000

    700000000000000002

    1

    Returns: 2200000000000000002

  183. 0

    100

    100

    4

    Returns: 0

  184. 1000

    0

    0

    1

    Returns: 1000

  185. 0

    100000000000000000

    100000000000000000

    1

    Returns: 200000000000000000

  186. 999999999999999999

    999999999999999999

    999999999999999999

    4

    Returns: 299999999999999999

  187. 123

    456

    789

    4

    Returns: 41

  188. 2

    3

    4

    1

    Returns: 9

  189. 11

    10

    9

    1

    Returns: 30

  190. 856674609788912520

    791809296233191086

    711066335916901716

    11380

    Returns: 32941144942

  191. 1000000000000000000

    1000000000000000000

    1000000000000000000

    7

    Returns: 107142857142857142

  192. 1000000000000000

    1000000000000000

    1000000000000000

    1000000000

    Returns: 0

  193. 1000000000000000000

    1000000000000000000

    1000000000000000000

    999999

    Returns: 6000006

  194. 32

    32

    36

    4

    Returns: 10

  195. 16683300000000000

    166833000000

    166833

    1000

    Returns: 1

  196. 1000000000000000

    1000000000000000

    1000000000000000

    7

    Returns: 107142857142857

  197. 400

    300

    300

    4

    Returns: 100

  198. 324234

    2333

    5666232552

    12534523

    Returns: 0

  199. 10000000000000

    1000000000000

    10000000000000

    1

    Returns: 21000000000000

  200. 0

    0

    2

    4

    Returns: 0

  201. 29

    28

    27

    7

    Returns: 3

  202. 100

    100000000

    100000000

    4

    Returns: 33

  203. 567

    1246

    2871

    64

    Returns: 0

  204. 100000000000000000

    100000000000000000

    100000000000000000

    6395098

    Returns: 14670

  205. 2

    2

    0

    1

    Returns: 4

  206. 5

    100

    10000000000000

    4

    Returns: 1

  207. 1

    1

    1001

    4

    Returns: 0

  208. 1000000000000000000

    999999999999999999

    999999999999999998

    4

    Returns: 299999999999999999

  209. 100000000000000000

    100000000000000000

    100000000000000000

    1

    Returns: 300000000000000000

  210. 100000000000000

    100000000000000

    100000000000000

    1

    Returns: 300000000000000

  211. 1000000000231213

    10000000002311345

    10000000002312139

    999999997

    Returns: 0

  212. 22

    22

    19

    4

    Returns: 6

  213. 1000000000000000000

    1000000000000000000

    1000000000000000000

    1000001

    Returns: 5999982

  214. 93

    1

    1

    13

    Returns: 0

  215. 822981258385599122

    28316248989464292

    779547115376367011

    57307

    Returns: 51732569

  216. 9

    9

    11

    4

    Returns: 2

  217. 10001

    10010

    10005

    4

    Returns: 3001

  218. 1000000000000000000

    1000000000000000000

    999999999999999999

    4

    Returns: 299999999999999999

  219. 100000000000

    100000000000

    100000000000

    1000000000

    Returns: 0

  220. 66630362332990648

    79343508172661713

    73842408503145400

    4

    Returns: 21981627900879776

  221. 1000000000

    1000000000

    10000000

    4

    Returns: 3333333

  222. 18

    19

    19

    4

    Returns: 5

  223. 33

    33

    33

    4

    Returns: 9

  224. 1

    100

    199

    4

    Returns: 0

  225. 1000000000000

    1000000000000

    1000000000000

    4

    Returns: 300000000000

  226. 3

    3

    3

    4

    Returns: 0

  227. 100000000000000000

    1000000

    1000000

    4

    Returns: 333333

  228. 6

    6

    6

    4

    Returns: 1

  229. 2

    2

    2

    1000000000

    Returns: 0

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