module odeprob ! moltibody problem, 400 objects
! This file mbod4h.f90 is part of the EPPEER package by B.A.Schmitt and R.Weiner
! available at www.mathematik.uni-marburg.de\~schmitt\peer
! It contains the multi-body example from the documentation
!------------------------
  integer :: mbdy = 400, nparm=1, nprob = 2400 !=6*mbdy
  character(4) :: odename = "mbd4"
  logical :: exsol = .true. ! end solution known
  real(8), dimension(400) :: mass
  real(8) :: meps = 1D-4

contains

  pure subroutine fcn(t,u,fw,par)
!     m-body-problem, (x,y,z)\in [0,1]**3
    implicit none
    real(8), intent(in) :: t
    real(8), dimension(:), intent(in) :: u
    real(8), dimension(:), intent(in) :: par
    real(8), dimension(:), intent(out) :: fw
    integer :: i,j, ip,jp
    real(8) :: dist, f1,f2,f3
 ! 2*3-coordinates (u,u')
    do i=1,mbdy
      ip = 6*(i-1)
      fw(ip+1) = u(ip+4)
      fw(ip+2) = u(ip+5)
      fw(ip+3) = u(ip+6)
      f1 = 0D0; f2 = 0D0; f3 = 0D0
      do j=1,mbdy ! compute gravity force body j <- i
        if (j.ne.i) then
          jp = 6*(j-1)
          dist=meps+(u(ip+1)-u(jp+1))**2+(u(ip+2)-u(jp+2))**2+(u(ip+3)-u(jp+3))**2
          dist = mass(j)/(dist*sqrt(dist))
          f1 = f1+(u(jp+1)-u(ip+1))*dist
          f2 = f2+(u(jp+2)-u(ip+2))*dist
          f3 = f3+(u(jp+3)-u(ip+3))*dist
        end if
      end do
      fw(ip+4) = f1
      fw(ip+5) = f2
      fw(ip+6) = f3
    end do
  end subroutine fcn

  subroutine inivals(t0,te,u,par)
    !  initial values
    implicit none
    integer n, i,ip
    real(8), dimension(:), intent(in) :: par
    real(8), dimension(:), intent(out) :: u
    real(8) :: t0,te,pi, ci,si, rad,v,rf1,rf2
    parameter (pi=3.141592653589d0)
    t0 = 0D0
    te = 4D0
    rf1 = 4*pi/8
    rf2 = 2*pi/mbdy
    do i=1,mbdy
      mass(i) = (0.3D0 +0.1D0*(cos(i*rf1)+1D0))/mbdy
      rad = 1.7D0+cos(i*0.75D0)
      v = 0.22d0*sqrt(rad)
      ci = cos(i*rf2)
      si = sin(i*rf2)
      ip = 6*(i-1)
      u(ip+1) = rad*ci ! initial position
      u(ip+2) = rad*si
      u(ip+3) = 0.4D0*si
      u(ip+4) = -v*si ! velocity is tangential
      u(ip+5) = v*ci
      u(ip+6) = 0.D0
    end do
  end subroutine inivals

  subroutine solution(t,u,par)
    implicit none
    real(8), dimension(:), intent(in) :: par
    real(8), dimension(:), intent(out) :: u
    real(8) :: t
! reference solution with DoPri5, tol=1E-14
    u(   1)=0.186158246586595855D+01
    u(   2)=0.125672041825356517D+01
    u(   3)=-.638743521817937768D-02
    u(   4)=-.269466691089239818D+00
    u(   5)=0.224288603928422897D+00
    u(   6)=-.926040148218319412D-02
    u(   7)=0.974292884517085622D+00
    u(   8)=0.103791791403303213D+01
    u(   9)=-.538932850798164425D-02
    u(  10)=-.320517898458579087D+00
    u(  11)=0.107021403612009514D+00
    u(  12)=-.289573229413761079D-02
    u(  13)=0.364754794019629291D+00
    u(  14)=0.999190747471231044D+00
    u(  15)=0.685243109062902561D-01
    u(  16)=-.294328246876002397D+00
    u(  17)=0.297189386659420969D-01
    u(  18)=-.811957580902240711D-01
    u(  19)=0.381501751674488743D+00
    u(  20)=0.774625888881815050D+00
    u(  21)=0.330643755048046842D-01
    u(  22)=-.363466125680264943D-01
    u(  23)=0.157354643356478974D+00
    u(  24)=-.182750517897651323D-01
    u(  25)=0.455660635285889792D+00
    u(  26)=0.772916130910656474D+00
    u(  27)=0.771274954897956111D-01
    u(  28)=-.317442959889667420D+00
    u(  29)=-.504539477050278407D-01
    u(  30)=-.254665713912107568D-02
    u(  31)=0.962928248548506782D+00
    u(  32)=0.889351756256770654D+00
    u(  33)=-.250248642628246240D-01
    u(  34)=-.830134332188002949D-01
    u(  35)=0.218900434306184916D+00
    u(  36)=0.306223894960782339D-01
    u(  37)=0.150681134614429180D+01
    u(  38)=0.149306664824383639D+01
    u(  39)=0.527943711156385817D-01
    u(  40)=-.312271611605597077D+00
    u(  41)=0.291649991517766771D+00
    u(  42)=0.663577600039734830D-02
    u(  43)=0.176893710337033294D+01
    u(  44)=0.167383546971030928D+01
    u(  45)=0.588687261245065541D-01
    u(  46)=-.338229990387007129D+00
    u(  47)=0.248229517290639273D+00
    u(  48)=-.551463991352075036D-02
    u(  49)=0.172788650834762780D+01
    u(  50)=0.169714903029127995D+01
    u(  51)=0.654788205239198451D-01
    u(  52)=-.491853735670923109D+00
    u(  53)=0.351731315717725312D+00
    u(  54)=0.218476966643793742D-01
    u(  55)=0.131605887424210266D+01
    u(  56)=0.144376714063491685D+01
    u(  57)=0.591284687875665640D-01
    u(  58)=-.318162696118652222D+00
    u(  59)=0.914539750940573659D-01
    u(  60)=-.255037278946870644D-01
    u(  61)=0.195800282953423083D+00
    u(  62)=0.790286951025397699D+00
    u(  63)=0.180446802649817273D+00
    u(  64)=-.279335655121326243D+00
    u(  65)=0.258861156692793970D+00
    u(  66)=0.729842540216981972D-01
    u(  67)=0.362357040161516930D+00
    u(  68)=0.862022633043045272D+00
    u(  69)=0.124849264124152117D-01
    u(  70)=-.152168594346957925D+00
    u(  71)=0.236135347863976303D+00
    u(  72)=0.107458257177400329D-01
    u(  73)=0.406548957507127495D+00
    u(  74)=0.833276287589830633D+00
    u(  75)=0.563658254410075027D-01
    u(  76)=-.178526933857749537D+00
    u(  77)=0.155175488472572287D+00
    u(  78)=-.874729422048158844D-01
    u(  79)=0.378704732397911747D+00
    u(  80)=0.727962769215052652D+00
    u(  81)=0.185948503819312987D-01
    u(  82)=-.814019286040721934D-01
    u(  83)=0.202897180305261465D+00
    u(  84)=-.361831227353739196D-01
    u(  85)=0.134043548080897890D+01
    u(  86)=0.141464027220929522D+01
    u(  87)=0.526291324571854929D-01
    u(  88)=-.151656871902579204D+00
    u(  89)=0.280980136782021384D+00
    u(  90)=-.339615348970230112D-02
    u(  91)=0.155477749109375751D+01
    u(  92)=0.175656596503559914D+01
    u(  93)=0.857074563602218398D-01
    u(  94)=-.277740636096985016D+00
    u(  95)=0.616186247789942132D-01
    u(  96)=-.334298934600976913D-01
    u(  97)=0.156945667806479561D+01
    u(  98)=0.177283785967889362D+01
    u(  99)=0.858433633836248461D-01
    u( 100)=-.537783140224830425D+00
    u( 101)=0.357190878449564098D+00
    u( 102)=0.289578225920196566D-01
    u( 103)=0.141073076521240015D+01
    u( 104)=0.183774323138333817D+01
    u( 105)=0.110343946676329407D+00
    u( 106)=-.284975990774224419D+00
    u( 107)=0.199521427856482331D+00
    u( 108)=-.169118184960114631D-01
    u( 109)=0.668703502287290585D+00
    u( 110)=0.132909834787290104D+01
    u( 111)=0.920965124127040846D-01
    u( 112)=-.388740468655788318D+00
    u( 113)=0.237447383023755357D-01
    u( 114)=-.370555189129381096D-01
    u( 115)=0.383474862625175883D+00
    u( 116)=0.738951318767732901D+00
    u( 117)=-.418346066680453516D-01
    u( 118)=-.120722449683327987D+00
    u( 119)=0.558331696870238564D-01
    u( 120)=-.116603344330463588D-01
    u( 121)=0.112740735958278646D+00
    u( 122)=0.933397952582988633D+00
    u( 123)=0.578228301671327785D-01
    u( 124)=-.138566908216297024D+00
    u( 125)=-.152167956728096826D+00
    u( 126)=-.182707335984762687D+00
    u( 127)=0.637233128219030442D+00
    u( 128)=0.856624971119985701D+00
    u( 129)=0.137338833617370436D-01
    u( 130)=-.222629440026031133D+00
    u( 131)=0.252289235888766283D+00
    u( 132)=-.449314101953125350D-01
    u( 133)=0.685056772293151095D+00
    u( 134)=0.137173573602141396D+01
    u( 135)=0.100710299427002048D+00
    u( 136)=-.265158889213702176D+00
    u( 137)=0.207117322232178741D+00
    u( 138)=0.142074359524867015D-02
    u( 139)=0.139197434903188078D+01
    u( 140)=0.194936865369247792D+01
    u( 141)=0.121230471539719442D+00
    u( 142)=-.309601584090243909D+00
    u( 143)=0.811115347873072184D-01
    u( 144)=-.242791127655731798D-01
    u( 145)=0.124449897841425394D+01
    u( 146)=0.183299203395882015D+01
    u( 147)=0.120999802404671022D+00
    u( 148)=-.359267477284863246D+00
    u( 149)=0.639139392988770927D-01
    u( 150)=-.220775187139906036D-01
    u( 151)=0.153344902012516648D+01
    u( 152)=0.187117820637009258D+01
    u( 153)=0.104507775478235074D+00
    u( 154)=-.198126232398938035D+00
    u( 155)=0.227073072536695064D+00
    u( 156)=-.179971063340252611D-01
    u( 157)=0.718721408002056972D+00
    u( 158)=0.153695487879086823D+01
    u( 159)=0.121904371140483789D+00
    u( 160)=-.360603215472650895D+00
    u( 161)=0.627090384647261273D-01
    u( 162)=-.251929219259959189D-01
    u( 163)=0.526097252844852023D-01
    u( 164)=0.733834756531365984D+00
    u( 165)=0.566180047457515087D-01
    u( 166)=-.118697501079410406D+00
    u( 167)=-.247861433090223798D-02
    u( 168)=-.381843021729883700D-01
    u( 169)=0.266049299458867294D+00
    u( 170)=0.111486817995117193D+01
    u( 171)=0.966617631061711391D-01
    u( 172)=-.246612456094730925D+00
    u( 173)=0.154253101869905512D+00
    u( 174)=0.124658946847978677D-01
    u( 175)=0.149236447432011782D+00
    u( 176)=0.888154235063610020D+00
    u( 177)=0.837756296126319355D-01
    u( 178)=-.339785310487241143D-01
    u( 179)=0.320980157356563281D-01
    u( 180)=-.930332562831196787D-02
    u( 181)=0.172768392529347087D+00
    u( 182)=0.108349723519147600D+01
    u( 183)=0.101538690643685967D+00
    u( 184)=-.377374137493286910D+00
    u( 185)=-.187707827212056699D+00
    u( 186)=-.756074308615502511D-01
    u( 187)=0.813991211984248841D+00
    u( 188)=0.186815054698888039D+01
    u( 189)=0.163275582547894677D+00
    u( 190)=-.598805211989910435D+00
    u( 191)=0.438214980703986387D-01
    u( 192)=-.619355608667435196D-02
    u( 193)=0.109022444455593837D+01
    u( 194)=0.209567094759260675D+01
    u( 195)=0.164955868450499088D+00
    u( 196)=-.381357436680710149D+00
    u( 197)=0.459256083245994651D-01
    u( 198)=-.226992313839200557D-01
    u( 199)=0.105316205034384525D+01
    u( 200)=0.211211814809385601D+01
    u( 201)=0.169971694203693319D+00
    u( 202)=-.426957356292731904D+00
    u( 203)=0.597838154229149848D-01
    u( 204)=-.169922729968006829D-01
    u( 205)=0.811886804462033540D+00
    u( 206)=0.186450857875130849D+01
    u( 207)=0.162991006295936741D+00
    u( 208)=-.103565319864802191D-01
    u( 209)=0.196821616235048347D+00
    u( 210)=-.360639373515794642D-01
    u( 211)=0.717701264241129289D-01
    u( 212)=0.102854190141719304D+01
    u( 213)=0.103980343792658150D+00
    u( 214)=-.330616848949542186D+00
    u( 215)=-.246585332366363985D+00
    u( 216)=-.992518071627655624D-01
    u( 217)=0.124354045867963794D+00
    u( 218)=0.949220842041055723D+00
    u( 219)=0.668079718402967287D-01
    u( 220)=-.399789482691596421D+00
    u( 221)=0.123932901922988295D+00
    u( 222)=-.781223642852446609D-01
    u( 223)=0.415677822476338443D+00
    u( 224)=0.893464354555755569D+00
    u( 225)=0.407919462580085546D-01
    u( 226)=-.446198454234047914D+00
    u( 227)=0.263699831764108272D+00
    u( 228)=0.509430790744189385D-01
    u( 229)=0.115406307488491594D+00
    u( 230)=0.980309315896013667D+00
    u( 231)=0.742896024570830621D-01
    u( 232)=-.934101908192156993D-01
    u( 233)=-.954054460006312742D-02
    u( 234)=-.353799811250578994D-01
    u( 235)=0.235852088089093498D+00
    u( 236)=0.160992163552067358D+01
    u( 237)=0.189255266328234278D+00
    u( 238)=-.455037125400418352D+00
    u( 239)=-.710249709187358857D-01
    u( 240)=-.343621336332806879D-01
    u( 241)=0.707118773097792030D+00
    u( 242)=0.214248656772594614D+01
    u( 243)=0.196926355470156467D+00
    u( 244)=-.377233894371926115D+00
    u( 245)=0.257236206605491353D-01
    u( 246)=-.285416409341156148D-01
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    u( 248)=0.221382272176187112D+01
    u( 249)=0.231957000966343363D+00
    u( 250)=-.496719541994032177D+00
    u( 251)=0.113420731148144716D+00
    u( 252)=0.115930159189224746D-03
    u( 253)=0.733680934922778416D+00
    u( 254)=0.227395784819950242D+01
    u( 255)=0.217006315940587169D+00
    u( 256)=-.455952392359134595D+00
    u( 257)=0.436277624744098314D-02
    u( 258)=-.173647108085847046D-01
    u( 259)=0.235473178567580876D+00
    u( 260)=0.135567535228654190D+01
    u( 261)=0.149085911214987571D+00
    u( 262)=-.291329062705089570D+00
    u( 263)=-.562008325096479203D-01
    u( 264)=-.572083547730204006D-01
    u( 265)=-.306150421593154171D-01
    u( 266)=0.103346554979926819D+01
    u( 267)=0.109790729442144810D+00
    u( 268)=-.987831860355694313D-01
    u( 269)=0.309950187290120791D-01
    u( 270)=-.639091399785612219D-01
    u( 271)=0.277377517227625714D+00
    u( 272)=0.810365406875496297D+00
    u( 273)=0.103064320835413559D+00
    u( 274)=-.578640573734694949D-01
    u( 275)=-.167462399795483163D+00
    u( 276)=-.921448635271602534D-01
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    u( 278)=0.894972330964417861D+00
    u( 279)=0.354397412935991626D-01
    u( 280)=-.256890534231924150D-01
    u( 281)=0.237746520111108417D+00
    u( 282)=0.548661820040829487D-01
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    u( 286)=-.249076348398081376D+00
    u( 287)=-.111468036944528635D-01
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    u( 289)=0.477640139830721178D+00
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    u( 292)=-.426671511660884517D+00
    u( 293)=0.933962256930460782D-01
    u( 294)=-.116913459384096301D-01
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    u( 298)=-.206701329156758540D+00
    u( 299)=-.121580789453636204D-02
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    u( 301)=0.439350756858661262D+00
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    u( 304)=-.418636335838440454D+00
    u( 305)=-.167565622994525654D+00
    u( 306)=-.314373379090162677D-01
    u( 307)=0.489425864358032231D-01
    u( 308)=0.206640903106380502D+01
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    u( 310)=-.364558520472024916D+00
    u( 311)=0.399313087637893829D-02
    u( 312)=-.226158828111835096D-01
    u( 313)=-.234366486645890770D+00
    u( 314)=0.955785961165135256D+00
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    u( 317)=-.231763240445727159D+00
    u( 318)=-.111401067609470703D+00
    u( 319)=-.807750609588979707D+00
    u( 320)=0.580460906103685392D+00
    u( 321)=0.157587945055741085D+00
    u( 322)=-.959718729639277290D-01
    u( 323)=-.271768571483224142D+00
    u( 324)=-.246111739049280021D+00
    u( 325)=-.821796983464040287D+00
    u( 326)=0.661740240483808639D+00
    u( 327)=0.178711685206695475D+00
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    u( 329)=-.536529179944975176D+00
    u( 330)=-.131632165922807937D+00
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    u( 335)=-.164234132210981099D+00
    u( 336)=-.891709720695157970D-01
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    u( 340)=-.353309360309528142D+00
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    u( 352)=-.356275743480165552D+00
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    u( 358)=-.248710199714689995D+00
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    u(2000)=-.118669544240495251D+01
    u(2001)=-.287725608383347153D+00
    u(2002)=-.126891215309130112D+00
    u(2003)=0.152711033526661127D+00
    u(2004)=-.913594963876509791D-01
    u(2005)=0.216847441009959629D+01
    u(2006)=-.963290605097555930D+00
    u(2007)=-.322290846544661058D+00
    u(2008)=0.187237911946223662D+00
    u(2009)=0.392143327490520777D+00
    u(2010)=-.324096517483492483D-01
    u(2011)=0.214017511335100563D+01
    u(2012)=-.933413610229512081D+00
    u(2013)=-.295654921397341730D+00
    u(2014)=0.662424198982640346D-02
    u(2015)=0.429581352818895368D+00
    u(2016)=0.572642228644561976D-01
    u(2017)=0.133835326606150318D+01
    u(2018)=-.485755767285679541D+00
    u(2019)=-.253486111678351222D+00
    u(2020)=-.107368506874881406D+00
    u(2021)=0.249927236832657274D+00
    u(2022)=0.750206783243038411D-01
    u(2023)=0.860199318158065385D+00
    u(2024)=0.995076177385675609D-01
    u(2025)=-.103562076752322887D+00
    u(2026)=-.567378494119114909D-01
    u(2027)=0.375643598695657888D+00
    u(2028)=0.307676595517511697D+00
    u(2029)=0.855884863904249005D+00
    u(2030)=0.827729009101098451D-01
    u(2031)=-.825632695010612983D-01
    u(2032)=0.666862876686464129D-01
    u(2033)=0.315020099629868544D+00
    u(2034)=-.311091895072658164D+00
    u(2035)=0.767503427432368324D+00
    u(2036)=0.209445624979060940D+00
    u(2037)=-.127054885057514777D+00
    u(2038)=-.271330676664744030D+00
    u(2039)=-.614382438508089424D-02
    u(2040)=0.116337591555997558D+00
    u(2041)=0.861661356754703789D+00
    u(2042)=-.188004879614877239D-01
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    u(2044)=-.338677558455175498D+00
    u(2045)=0.216695424541844039D+00
    u(2046)=0.210215732965928048D+00
    u(2047)=0.207946094766214085D+01
    u(2048)=-.618374241323285445D+00
    u(2049)=-.259335514472086082D+00
    u(2050)=0.977612520826731252D-01
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    u(2053)=0.228037977448757223D+01
    u(2054)=-.703800381769574157D+00
    u(2055)=-.273320164174652380D+00
    u(2056)=0.318275149509858468D-01
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    u(2059)=0.226736395794351697D+01
    u(2060)=-.735149406238918668D+00
    u(2061)=-.276797307905421508D+00
    u(2062)=-.293629516953897544D-01
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    u(2064)=0.115392488076771597D-01
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    u(2066)=-.560181631150197812D+00
    u(2067)=-.257495357553964299D+00
    u(2068)=0.962649351549895865D-01
    u(2069)=0.292043914422757567D+00
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    u(2072)=-.125436139956942201D-01
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    u(2079)=-.825129877425745117D-01
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    u(2085)=-.117111828990247843D+00
    u(2086)=-.582345824378204119D-01
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    u(2096)=-.248394726314122932D+00
    u(2097)=-.224469089171608710D+00
    u(2098)=-.130359202289688728D-01
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    u(2100)=0.313651620580789672D-01
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    u(2102)=-.490252220777950498D+00
    u(2103)=-.260307274985379533D+00
    u(2104)=-.102232162486344032D-01
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    u(2106)=0.977745280944838577D-02
    u(2107)=0.226808066854728452D+01
    u(2108)=-.281927714067423452D+00
    u(2109)=-.216907649650432716D+00
    u(2110)=0.244943193601078468D-01
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    u(2114)=-.361831972940824309D+00
    u(2115)=-.234552793498760487D+00
    u(2116)=0.120949369470915204D-01
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    u(2120)=0.531252994830008207D-01
    u(2121)=-.182468147539202791D+00
    u(2122)=-.132546595037203535D+00
    u(2123)=0.281566148971133190D+00
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    u(2125)=0.100594837071450316D+01
    u(2126)=-.220615679921678715D+00
    u(2127)=-.498249104842178464D-01
    u(2128)=0.218090845773124126D-01
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    u(2130)=-.906006139473633856D-02
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    u(2132)=-.704214653939083945D-01
    u(2133)=-.875702863773559076D-01
    u(2134)=-.898967168840079378D-01
    u(2135)=-.136454565046643678D-01
    u(2136)=0.872651193953580678D-01
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    u(2139)=0.608035349093255240D-01
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    u(2146)=-.153233634954535375D+00
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    u(2176)=-.381213370747153363D-01
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    u(2202)=0.285231516821526365D-01
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    u(2205)=-.181596505843664324D+00
    u(2206)=-.135141070527313834D+00
    u(2207)=0.333391208405813988D+00
    u(2208)=0.497313154796493601D-02
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    u(2211)=-.174499362950649634D+00
    u(2212)=-.172058047254398910D+00
    u(2213)=0.368434249953156989D+00
    u(2214)=0.843459693907508239D-02
    u(2215)=0.204893855226163257D+01
    u(2216)=0.901924845517185492D-01
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    u(2218)=-.324242001787032330D-01
    u(2219)=0.289779957500719054D+00
    u(2220)=0.875509464863399346D-02
    u(2221)=0.101674327255862784D+01
    u(2222)=0.491641046523466851D+00
    u(2223)=-.100373059362009132D+00
    u(2224)=-.337959944177299076D+00
    u(2225)=0.256670122233115972D+00
    u(2226)=0.501291184886033456D-01
    u(2227)=0.739963536924124976D+00
    u(2228)=0.297765031697623916D+00
    u(2229)=-.451235056711761853D-01
    u(2230)=-.165229207368652875D+00
    u(2231)=0.356977796984895429D-01
    u(2232)=0.174969184874065292D+00
    u(2233)=0.780509010428465544D+00
    u(2234)=0.237505429935017304D+00
    u(2235)=-.106305235815778068D+00
    u(2236)=0.384669260490541620D-01
    u(2237)=0.196847814272811533D+00
    u(2238)=-.225968669030046337D+00
    u(2239)=0.848117656649530871D+00
    u(2240)=0.126907475516540413D+00
    u(2241)=-.834291677132346643D-01
    u(2242)=-.700063302594823300D-01
    u(2243)=-.246282071407684183D+00
    u(2244)=0.121321480917671018D+00
    u(2245)=0.158158440593253569D+01
    u(2246)=0.625841867251590633D+00
    u(2247)=-.926201499339833895D-01
    u(2248)=-.148886274376364536D+00
    u(2249)=0.339244062861371432D+00
    u(2250)=0.280712574645547476D-01
    u(2251)=0.224747129940272528D+01
    u(2252)=0.532700599408398312D+00
    u(2253)=-.133777608753655020D+00
    u(2254)=-.247474840209584324D+00
    u(2255)=0.344628035263918664D+00
    u(2256)=0.298351368482201798D-01
    u(2257)=0.221760406338540017D+01
    u(2258)=0.514679139729685708D+00
    u(2259)=-.114005888369744568D+00
    u(2260)=-.160665226862375082D+00
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    u(2262)=-.137827747139074100D-01
    u(2263)=0.248285699967722273D+01
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    u(2268)=-.139344735297270549D-01
    u(2269)=0.147219149207364963D+01
    u(2270)=0.579433704513016345D+00
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    u(2277)=-.861364762904893826D-02
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    u(2288)=0.355159302961344958D+00
    u(2289)=-.129427666930249680D+00
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    u(2292)=0.267620245997327762D-01
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    u(2294)=0.709664752073373206D+00
    u(2295)=-.558133444972840620D-01
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    u(2297)=0.242110433382912660D+00
    u(2298)=0.296128837911262786D-01
    u(2299)=0.190339746322341496D+01
    u(2300)=0.845772812720596234D+00
    u(2301)=-.677268575759185920D-01
    u(2302)=-.221347676050142717D+00
    u(2303)=0.373736569947611397D+00
    u(2304)=0.193286452974854757D-01
    u(2305)=0.219744821467671336D+01
    u(2306)=0.816114994442950992D+00
    u(2307)=-.843361547935959216D-01
    u(2308)=-.262045917252988814D+00
    u(2309)=0.316697077992592113D+00
    u(2310)=0.134658451139174217D-02
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    u(2312)=0.753717094525197862D+00
    u(2313)=-.966020166414762460D-01
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    u(2315)=0.301672612973514720D+00
    u(2316)=-.117340902540639014D-02
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    u(2318)=0.744986402675838932D+00
    u(2319)=-.793881541908881549D-01
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    u(2321)=0.223357487368451374D+00
    u(2322)=-.441321290043510464D-02
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    u(2324)=0.648764619761400652D+00
    u(2325)=-.262027731842998449D-01
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    u(2330)=0.134157524293633729D+00
    u(2331)=-.882600388220756427D-01
    u(2332)=-.318031037353928347D+00
    u(2333)=-.291497233778729659D+00
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    u(2340)=0.288375931885699266D+00
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    u(2348)=0.885020128901599978D+00
    u(2349)=-.548125100619314756D-01
    u(2350)=-.140332073654753642D+00
    u(2351)=0.248605054350185650D+00
    u(2352)=-.182012004369173550D-02
    u(2353)=0.208598691274348447D+01
    u(2354)=0.104821292149661915D+01
    u(2355)=-.492906613871366417D-01
    u(2356)=-.365271446492983209D+00
    u(2357)=0.214439127910421273D+00
    u(2358)=-.754038977677023905D-02
    u(2359)=0.202284197900708262D+01
    u(2360)=0.997581143914362922D+00
    u(2361)=-.532125742607589616D-01
    u(2362)=-.289030948077301786D+00
    u(2363)=0.324689055429921936D+00
    u(2364)=0.169034058807841347D-02
    u(2365)=0.195829177986893033D+01
    u(2366)=0.103839388918777153D+01
    u(2367)=-.408497237815387132D-01
    u(2368)=-.154697711563184015D+00
    u(2369)=0.216159933232731361D+00
    u(2370)=-.133438157149251575D-01
    u(2371)=0.957884644179075151D+00
    u(2372)=0.908660297073230372D+00
    u(2373)=-.140870135832787454D-01
    u(2374)=-.384233333317126391D+00
    u(2375)=0.497528214028980231D-01
    u(2376)=-.553851476985717794D-01
    u(2377)=0.360297051902733867D+00
    u(2378)=0.810251898156268191D+00
    u(2379)=0.495410018728505638D-01
    u(2380)=-.389480901409866409D+00
    u(2381)=0.236471240411461683D-01
    u(2382)=0.250018963024663211D-02
    u(2383)=0.885810387242048303D+00
    u(2384)=0.862734005464641407D+00
    u(2385)=-.873103666920269916D-01
    u(2386)=-.511231322006074976D-01
    u(2387)=0.117271756329633589D+00
    u(2388)=0.466714400465751272D-01
    u(2389)=0.563901556815160188D+00
    u(2390)=0.838174045602352091D+00
    u(2391)=0.731139540793577570D-03
    u(2392)=-.206529068306528896D+00
    u(2393)=0.103108031869488984D+00
    u(2394)=0.561484807684039383D-01
    u(2395)=0.106859366862604843D+01
    u(2396)=0.955614797091206336D+00
    u(2397)=-.138651622804090279D-01
    u(2398)=-.431151462604570379D+00
    u(2399)=0.186294943206648772D+00
    u(2400)=-.645594120097395946D-02
  end subroutine solution

  function invariant(n,u) result (en)
    integer :: i,j,ip,jp
    real(8), dimension(n) :: u
    real(8) :: en,ei,dist
    en = 0D0
    do i=1,mbdy
      ip = 6*(i-1)
      ei = 0.5D0*(u(ip+4)**2+u(ip+5)**2+u(ip+6)**2) ! kinetic energy
      do j=i+1,mbdy ! compute gravity force body j <- i
        jp = 6*(j-1)
        dist=meps+(u(ip+1)-u(jp+1))**2+(u(ip+2)-u(jp+2))**2+(u(ip+3)-u(jp+3))**2
        ei = ei - mass(j)/sqrt(dist)
      end do
      en = en+mass(i)*ei
    end do
  end function invariant
end module odeprob