This page was generated from unit-6.2-contact/contact.ipynb.
6.2 Contact Problems¶
work in progress …
[1]:
from netgen.occ import *
from ngsolve import *
from ngsolve.solvers import *
from ngsolve.webgui import Draw
from netgen.webgui import Draw as DrawGeo
rect = MoveTo(0,-0.02).Rectangle(0.04, 0.02).Face()
ball = MoveTo(0,0).Arc(0.005, 90).Rotate(90).Line(0.005).Close().Face()
rect.edges.Min(X).name="sym"
rect.edges.Max(X).name="free"
rect.edges.Min(Y).name="fix"
rect.edges.Max(Y).name="contact1"
ball.edges.Min(X).name="sym"
ball.edges.Max(Y).name="disp"
ball.edges.Max(X-Y).name="contact2"
ball.faces.name="ball"
rect.faces.name="rect"
rect = Glue ([rect, Vertex((0.001,0,0))])
rect.vertices.Max(Y-X).maxh=0.0002
rect.edges.Max(Y-0.1*X).maxh=0.00002
geo = Compound([rect,ball])
DrawGeo (geo)
mesh = Mesh(OCCGeometry(geo, dim=2).GenerateMesh(maxh=0.002))
mesh.Curve(4)
Draw(mesh);
[2]:
mesh.GetBoundaries(), mesh.GetMaterials()
[2]:
(('fix', 'free', 'contact1', 'contact1', 'sym', 'contact2', 'disp', 'sym'),
('rect', 'ball'))
[3]:
E = 2.1e11
nu = 0.2
rho = 7e3
mu = E / 2 / (1+nu)
lam = E * nu / ((1+nu)*(1-2*nu))
I = Id(mesh.dim)
def Pow(a, b):
return a**b # exp (log(a)*b)
def C(u):
# F = Id(2) + Grad(u)
G = Grad(u)
F = Id(3) + CoefficientFunction( (G[0,0], G[1,0], 0, G[1,0], G[1,1], 0, 0, 0, u[0]/(x+1e-16) ) )
return F.trans*F
def NeoHooke (C):
return 0.5 * mu * (Trace(C-Id(C.dims[0])) + 2*mu/lam * Det(C)**(-lam/2/mu) - 1)
fes = VectorH1(mesh, order=4, dirichletx="sym", dirichlety="fix|disp")
u,v = fes.TnT()
a = BilinearForm(fes)
a += Variation((x*NeoHooke(C(u))).Compile()*dx)
contact = ContactBoundary(mesh.Boundaries("contact1"), mesh.Boundaries("contact2"))
X = CoefficientFunction((x,y))
cf = (X + u - (X.Other() + u.Other())) * contact.normal
# energy formulation
# contact.AddEnergy(IfPos(cf, 1e14*cf*cf, 0))
# or integrator
contact.AddIntegrator(IfPos(cf, 1e14*cf*(v-v.Other())*contact.normal, 0))
gfu = GridFunction(fes)
disp = -10e-6
gfu.Set((0, disp), definedon=mesh.Materials("ball"))
sceneu = Draw(gfu, deformation=gfu)
C_ = C(gfu).MakeVariable()
sigma = NeoHooke(C_).Diff(C_)
scenesigma = Draw(sigma[1,1], mesh, "sigmazz", min=-2e9, max=2e9)
with TaskManager():
contact.Update(gfu, a, 200, 1e-4)
NewtonMinimization(a=a, u=gfu, printing=False, inverse="sparsecholesky")
sceneu.Redraw()
scenesigma.Redraw()
Draw(sigma[1,1], mesh, "sigmazz", min=-5e9, max=0, deformation=gfu);
Dynamic Contact¶
[4]:
from netgen.occ import *
from ngsolve import *
from ngsolve.solvers import *
from ngsolve.webgui import Draw
from netgen.webgui import Draw as DrawGeo
[5]:
bowl = MoveTo(0,-0.01).Arc(0.2,70).Rotate(90).Line(0.01).Rotate(90) \
.Arc(0.19,-140).Rotate(90).Line(0.01).Rotate(90).Arc(0.2,70).Face()
ball1 = Circle((0,0.1),0.01).Face()
ball2 = Circle((0.05,0.1),0.01).Face()
ball3 = Circle((-0.05,0.1),0.01).Face()
balls = Compound([ball1, ball2, ball3])
balls.edges.name = "balls"
geo = Compound([bowl, balls])
bowl.edges.name="contact"
bowl.edges.Min(Y+0.01*X).name="fix"
bowl.edges.Min(Y-0.01*X).name="fix"
DrawGeo(geo);
[6]:
mesh = Mesh(OCCGeometry(geo, dim=2).GenerateMesh(maxh=0.005))
mesh.Curve(4)
Draw(mesh);
[7]:
mesh.GetBoundaries()
[7]:
('fix', 'contact', 'contact', 'contact', 'fix', 'balls', 'balls', 'balls')
[8]:
E, nu = 210e6, 0.2
rho = 7e3
mu = E / 2 / (1+nu)
lam = E * nu / ((1+nu)*(1-2*nu))
I = Id(mesh.dim)
def C(u):
F = I+Grad(u)
return F.trans*F
def NeoHooke (C):
return 0.5 * mu * (Trace(C-I) + 2*mu/lam * Det(C)**(-lam/2/mu) - 1)
fes = VectorH1(mesh, order=3, dirichlet="fix")
u,v = fes.TnT()
force = CF((0,-9.81*rho))
uold = GridFunction(fes)
unew = GridFunction(fes)
vel = GridFunction(fes)
anew = GridFunction(fes)
aold = GridFunction(fes)
tau = 2e-4
bfmstar = BilinearForm(fes)
bfmstar += Variation( NeoHooke (C(u)).Compile(False)*dx )
bfmstar += Variation( -force*u*dx )
bfmstar += Variation( rho/2* 2/tau**2 * (u-uold-tau*vel-tau**2/4*aold)**2 * dx )
tend = 1
scene = Draw (unew, mesh, "disp", deformation=unew)
t = 0
unew.Set( (0,0) )
vel.Set( (0,0) )
contact = ContactBoundary(mesh.Boundaries("contact|balls"), mesh.Boundaries("contact|balls"))
X = CoefficientFunction((x,y))
if True:
cf = (X + u-uold - (X.Other() + u.Other() - uold.Other())) * (-specialcf.normal(2).Other())
# cf = (X + u-uold)*specialcf.normal(2) + \
# (X.Other() + u.Other() - uold.Other()) * specialcf.normal(2).Other()
contact.AddEnergy(IfPos(cf, 1e9*cf*cf, 0), deformed=True)
else:
cf = (X + u - (X.Other() + u.Other())) * contact.normal
contact.AddEnergy(IfPos(cf, 1e9*cf*cf, 0), deformed=False)
[9]:
with TaskManager():
while t < tend:
print ("time", t)
t += tau
uold.vec.data = unew.vec
aold.vec.data = anew.vec
contact.Update(uold, bfmstar, 5, 0.01)
NewtonMinimization (a=bfmstar, u=unew, printing=False, inverse="sparsecholesky")
anew.vec.data = unew.vec-uold.vec-tau*vel.vec-tau**2/4*aold.vec
anew.vec.data *= 4/tau**2
vel.vec.data += 0.5*tau*aold.vec
vel.vec.data += 0.5*tau*anew.vec
scene.Redraw()
time 0
time 0.0002
time 0.0004
time 0.0006000000000000001
time 0.0008
time 0.001
time 0.0012000000000000001
time 0.0014000000000000002
time 0.0016000000000000003
time 0.0018000000000000004
time 0.0020000000000000005
time 0.0022000000000000006
time 0.0024000000000000007
time 0.0026000000000000007
time 0.002800000000000001
time 0.003000000000000001
time 0.003200000000000001
time 0.003400000000000001
time 0.003600000000000001
time 0.0038000000000000013
time 0.004000000000000001
time 0.004200000000000001
time 0.0044
time 0.0046
time 0.0048
time 0.004999999999999999
time 0.005199999999999999
time 0.0053999999999999986
time 0.005599999999999998
time 0.005799999999999998
time 0.0059999999999999975
time 0.006199999999999997
time 0.006399999999999997
time 0.0065999999999999965
time 0.006799999999999996
time 0.006999999999999996
time 0.0071999999999999955
time 0.007399999999999995
time 0.007599999999999995
time 0.0077999999999999944
time 0.007999999999999995
time 0.008199999999999995
time 0.008399999999999996
time 0.008599999999999997
time 0.008799999999999997
time 0.008999999999999998
time 0.009199999999999998
time 0.009399999999999999
time 0.0096
time 0.0098
time 0.01
time 0.0102
time 0.010400000000000001
time 0.010600000000000002
time 0.010800000000000002
time 0.011000000000000003
time 0.011200000000000003
time 0.011400000000000004
time 0.011600000000000004
time 0.011800000000000005
time 0.012000000000000005
time 0.012200000000000006
time 0.012400000000000007
time 0.012600000000000007
time 0.012800000000000008
time 0.013000000000000008
time 0.013200000000000009
time 0.013400000000000009
time 0.01360000000000001
time 0.01380000000000001
time 0.01400000000000001
time 0.014200000000000011
time 0.014400000000000012
time 0.014600000000000012
time 0.014800000000000013
time 0.015000000000000013
time 0.015200000000000014
time 0.015400000000000014
time 0.015600000000000015
time 0.015800000000000015
time 0.016000000000000014
time 0.016200000000000013
time 0.016400000000000012
time 0.01660000000000001
time 0.01680000000000001
time 0.017000000000000008
time 0.017200000000000007
time 0.017400000000000006
time 0.017600000000000005
time 0.017800000000000003
time 0.018000000000000002
time 0.0182
time 0.0184
time 0.0186
time 0.018799999999999997
time 0.018999999999999996
time 0.019199999999999995
time 0.019399999999999994
time 0.019599999999999992
time 0.01979999999999999
time 0.01999999999999999
time 0.02019999999999999
time 0.020399999999999988
time 0.020599999999999986
time 0.020799999999999985
time 0.020999999999999984
time 0.021199999999999983
time 0.02139999999999998
time 0.02159999999999998
time 0.02179999999999998
time 0.021999999999999978
time 0.022199999999999977
time 0.022399999999999975
time 0.022599999999999974
time 0.022799999999999973
time 0.022999999999999972
time 0.02319999999999997
time 0.02339999999999997
time 0.023599999999999968
time 0.023799999999999967
time 0.023999999999999966
time 0.024199999999999965
time 0.024399999999999963
time 0.024599999999999962
time 0.02479999999999996
time 0.02499999999999996
time 0.02519999999999996
time 0.025399999999999957
time 0.025599999999999956
time 0.025799999999999955
time 0.025999999999999954
time 0.026199999999999952
time 0.02639999999999995
time 0.02659999999999995
time 0.02679999999999995
time 0.026999999999999948
time 0.027199999999999946
time 0.027399999999999945
time 0.027599999999999944
time 0.027799999999999943
time 0.02799999999999994
time 0.02819999999999994
time 0.02839999999999994
time 0.028599999999999938
time 0.028799999999999937
time 0.028999999999999936
time 0.029199999999999934
time 0.029399999999999933
time 0.029599999999999932
time 0.02979999999999993
time 0.02999999999999993
time 0.03019999999999993
time 0.030399999999999927
time 0.030599999999999926
time 0.030799999999999925
time 0.030999999999999923
time 0.031199999999999922
time 0.03139999999999992
time 0.03159999999999992
time 0.03179999999999992
time 0.03199999999999992
time 0.032199999999999916
time 0.032399999999999915
time 0.032599999999999914
time 0.03279999999999991
time 0.03299999999999991
time 0.03319999999999991
time 0.03339999999999991
time 0.03359999999999991
time 0.033799999999999907
time 0.033999999999999905
time 0.034199999999999904
time 0.0343999999999999
time 0.0345999999999999
time 0.0347999999999999
time 0.0349999999999999
time 0.0351999999999999
time 0.0353999999999999
time 0.035599999999999896
time 0.035799999999999894
time 0.03599999999999989
time 0.03619999999999989
time 0.03639999999999989
time 0.03659999999999989
time 0.03679999999999989
time 0.03699999999999989
time 0.037199999999999886
time 0.037399999999999885
time 0.037599999999999884
time 0.03779999999999988
time 0.03799999999999988
time 0.03819999999999988
time 0.03839999999999988
time 0.03859999999999988
time 0.038799999999999876
time 0.038999999999999875
time 0.039199999999999874
time 0.03939999999999987
time 0.03959999999999987
time 0.03979999999999987
time 0.03999999999999987
time 0.04019999999999987
time 0.04039999999999987
time 0.040599999999999865
time 0.040799999999999864
time 0.04099999999999986
time 0.04119999999999986
time 0.04139999999999986
time 0.04159999999999986
time 0.04179999999999986
time 0.04199999999999986
time 0.042199999999999856
time 0.042399999999999854
time 0.04259999999999985
time 0.04279999999999985
time 0.04299999999999985
time 0.04319999999999985
time 0.04339999999999985
time 0.04359999999999985
time 0.043799999999999846
time 0.043999999999999845
time 0.044199999999999844
time 0.04439999999999984
time 0.04459999999999984
time 0.04479999999999984
time 0.04499999999999984
time 0.04519999999999984
time 0.045399999999999836
time 0.045599999999999835
time 0.045799999999999834
time 0.04599999999999983
time 0.04619999999999983
time 0.04639999999999983
time 0.04659999999999983
time 0.04679999999999983
time 0.04699999999999983
time 0.047199999999999825
time 0.047399999999999824
time 0.04759999999999982
time 0.04779999999999982
time 0.04799999999999982
time 0.04819999999999982
time 0.04839999999999982
time 0.04859999999999982
time 0.048799999999999816
time 0.048999999999999815
time 0.04919999999999981
time 0.04939999999999981
time 0.04959999999999981
time 0.04979999999999981
time 0.04999999999999981
time 0.05019999999999981
time 0.050399999999999806
time 0.050599999999999805
time 0.050799999999999804
time 0.0509999999999998
time 0.0511999999999998
time 0.0513999999999998
time 0.0515999999999998
time 0.0517999999999998
time 0.051999999999999796
time 0.052199999999999795
time 0.052399999999999794
time 0.05259999999999979
time 0.05279999999999979
time 0.05299999999999979
time 0.05319999999999979
time 0.05339999999999979
time 0.05359999999999979
time 0.053799999999999785
time 0.053999999999999784
time 0.05419999999999978
time 0.05439999999999978
time 0.05459999999999978
time 0.05479999999999978
time 0.05499999999999978
time 0.05519999999999978
time 0.055399999999999776
time 0.055599999999999775
time 0.05579999999999977
time 0.05599999999999977
time 0.05619999999999977
time 0.05639999999999977
time 0.05659999999999977
time 0.05679999999999977
time 0.056999999999999766
time 0.057199999999999765
time 0.057399999999999764
time 0.05759999999999976
time 0.05779999999999976
time 0.05799999999999976
time 0.05819999999999976
time 0.05839999999999976
time 0.058599999999999756
time 0.058799999999999755
time 0.058999999999999754
time 0.05919999999999975
time 0.05939999999999975
time 0.05959999999999975
time 0.05979999999999975
time 0.05999999999999975
time 0.06019999999999975
time 0.060399999999999746
time 0.060599999999999744
time 0.06079999999999974
time 0.06099999999999974
time 0.06119999999999974
time 0.06139999999999974
time 0.06159999999999974
time 0.06179999999999974
time 0.061999999999999736
time 0.062199999999999735
time 0.06239999999999973
time 0.06259999999999974
time 0.06279999999999974
time 0.06299999999999975
time 0.06319999999999976
time 0.06339999999999976
time 0.06359999999999977
time 0.06379999999999977
time 0.06399999999999978
time 0.06419999999999979
time 0.06439999999999979
time 0.0645999999999998
time 0.0647999999999998
time 0.06499999999999981
time 0.06519999999999981
time 0.06539999999999982
time 0.06559999999999983
time 0.06579999999999983
time 0.06599999999999984
time 0.06619999999999984
time 0.06639999999999985
time 0.06659999999999985
time 0.06679999999999986
time 0.06699999999999987
time 0.06719999999999987
time 0.06739999999999988
time 0.06759999999999988
time 0.06779999999999989
time 0.0679999999999999
time 0.0681999999999999
time 0.0683999999999999
time 0.06859999999999991
time 0.06879999999999992
time 0.06899999999999992
time 0.06919999999999993
time 0.06939999999999993
time 0.06959999999999994
time 0.06979999999999995
time 0.06999999999999995
time 0.07019999999999996
time 0.07039999999999996
time 0.07059999999999997
time 0.07079999999999997
time 0.07099999999999998
time 0.07119999999999999
time 0.07139999999999999
time 0.0716
time 0.0718
time 0.07200000000000001
time 0.07220000000000001
time 0.07240000000000002
time 0.07260000000000003
time 0.07280000000000003
time 0.07300000000000004
time 0.07320000000000004
time 0.07340000000000005
time 0.07360000000000005
time 0.07380000000000006
time 0.07400000000000007
time 0.07420000000000007
time 0.07440000000000008
time 0.07460000000000008
time 0.07480000000000009
time 0.0750000000000001
time 0.0752000000000001
time 0.0754000000000001
time 0.07560000000000011
time 0.07580000000000012
time 0.07600000000000012
time 0.07620000000000013
time 0.07640000000000013
time 0.07660000000000014
time 0.07680000000000015
time 0.07700000000000015
time 0.07720000000000016
time 0.07740000000000016
time 0.07760000000000017
time 0.07780000000000017
time 0.07800000000000018
time 0.07820000000000019
time 0.07840000000000019
time 0.0786000000000002
time 0.0788000000000002
time 0.07900000000000021
time 0.07920000000000021
time 0.07940000000000022
time 0.07960000000000023
time 0.07980000000000023
time 0.08000000000000024
time 0.08020000000000024
time 0.08040000000000025
time 0.08060000000000025
time 0.08080000000000026
time 0.08100000000000027
time 0.08120000000000027
time 0.08140000000000028
time 0.08160000000000028
time 0.08180000000000029
time 0.0820000000000003
time 0.0822000000000003
time 0.0824000000000003
time 0.08260000000000031
time 0.08280000000000032
time 0.08300000000000032
time 0.08320000000000033
time 0.08340000000000033
time 0.08360000000000034
time 0.08380000000000035
time 0.08400000000000035
time 0.08420000000000036
time 0.08440000000000036
time 0.08460000000000037
time 0.08480000000000038
time 0.08500000000000038
time 0.08520000000000039
time 0.08540000000000039
time 0.0856000000000004
time 0.0858000000000004
time 0.08600000000000041
time 0.08620000000000042
time 0.08640000000000042
time 0.08660000000000043
time 0.08680000000000043
time 0.08700000000000044
time 0.08720000000000044
time 0.08740000000000045
time 0.08760000000000046
time 0.08780000000000046
time 0.08800000000000047
time 0.08820000000000047
time 0.08840000000000048
time 0.08860000000000048
time 0.08880000000000049
time 0.0890000000000005
time 0.0892000000000005
time 0.0894000000000005
time 0.08960000000000051
time 0.08980000000000052
time 0.09000000000000052
time 0.09020000000000053
time 0.09040000000000054
time 0.09060000000000054
time 0.09080000000000055
time 0.09100000000000055
time 0.09120000000000056
time 0.09140000000000056
time 0.09160000000000057
time 0.09180000000000058
time 0.09200000000000058
time 0.09220000000000059
time 0.09240000000000059
time 0.0926000000000006
time 0.0928000000000006
time 0.09300000000000061
time 0.09320000000000062
time 0.09340000000000062
time 0.09360000000000063
time 0.09380000000000063
time 0.09400000000000064
time 0.09420000000000064
time 0.09440000000000065
time 0.09460000000000066
time 0.09480000000000066
time 0.09500000000000067
time 0.09520000000000067
time 0.09540000000000068
time 0.09560000000000068
time 0.09580000000000069
time 0.0960000000000007
time 0.0962000000000007
time 0.09640000000000071
time 0.09660000000000071
time 0.09680000000000072
time 0.09700000000000072
time 0.09720000000000073
time 0.09740000000000074
time 0.09760000000000074
time 0.09780000000000075
time 0.09800000000000075
time 0.09820000000000076
time 0.09840000000000076
time 0.09860000000000077
time 0.09880000000000078
time 0.09900000000000078
time 0.09920000000000079
time 0.0994000000000008
time 0.0996000000000008
time 0.0998000000000008
time 0.10000000000000081
time 0.10020000000000082
time 0.10040000000000082
time 0.10060000000000083
time 0.10080000000000083
time 0.10100000000000084
time 0.10120000000000084
time 0.10140000000000085
time 0.10160000000000086
time 0.10180000000000086
time 0.10200000000000087
time 0.10220000000000087
time 0.10240000000000088
time 0.10260000000000088
time 0.10280000000000089
time 0.1030000000000009
time 0.1032000000000009
time 0.10340000000000091
time 0.10360000000000091
time 0.10380000000000092
time 0.10400000000000093
time 0.10420000000000093
time 0.10440000000000094
time 0.10460000000000094
time 0.10480000000000095
time 0.10500000000000095
time 0.10520000000000096
time 0.10540000000000097
time 0.10560000000000097
time 0.10580000000000098
time 0.10600000000000098
time 0.10620000000000099
time 0.106400000000001
time 0.106600000000001
time 0.106800000000001
time 0.10700000000000101
time 0.10720000000000102
time 0.10740000000000102
time 0.10760000000000103
time 0.10780000000000103
time 0.10800000000000104
time 0.10820000000000105
time 0.10840000000000105
time 0.10860000000000106
time 0.10880000000000106
time 0.10900000000000107
time 0.10920000000000107
time 0.10940000000000108
time 0.10960000000000109
time 0.10980000000000109
time 0.1100000000000011
time 0.1102000000000011
time 0.11040000000000111
time 0.11060000000000111
time 0.11080000000000112
time 0.11100000000000113
time 0.11120000000000113
time 0.11140000000000114
time 0.11160000000000114
time 0.11180000000000115
time 0.11200000000000115
time 0.11220000000000116
time 0.11240000000000117
time 0.11260000000000117
time 0.11280000000000118
time 0.11300000000000118
time 0.11320000000000119
time 0.1134000000000012
time 0.1136000000000012
time 0.1138000000000012
time 0.11400000000000121
time 0.11420000000000122
time 0.11440000000000122
time 0.11460000000000123
time 0.11480000000000123
time 0.11500000000000124
time 0.11520000000000125
time 0.11540000000000125
time 0.11560000000000126
time 0.11580000000000126
time 0.11600000000000127
time 0.11620000000000127
time 0.11640000000000128
time 0.11660000000000129
time 0.11680000000000129
time 0.1170000000000013
time 0.1172000000000013
time 0.11740000000000131
time 0.11760000000000131
time 0.11780000000000132
time 0.11800000000000133
time 0.11820000000000133
time 0.11840000000000134
time 0.11860000000000134
time 0.11880000000000135
time 0.11900000000000135
time 0.11920000000000136
time 0.11940000000000137
time 0.11960000000000137
time 0.11980000000000138
time 0.12000000000000138
time 0.12020000000000139
time 0.1204000000000014
time 0.1206000000000014
time 0.1208000000000014
time 0.12100000000000141
time 0.12120000000000142
time 0.12140000000000142
time 0.12160000000000143
time 0.12180000000000143
time 0.12200000000000144
time 0.12220000000000145
time 0.12240000000000145
time 0.12260000000000146
time 0.12280000000000146
time 0.12300000000000147
time 0.12320000000000147
time 0.12340000000000148
time 0.12360000000000149
time 0.12380000000000149
time 0.1240000000000015
time 0.1242000000000015
time 0.12440000000000151
time 0.12460000000000152
time 0.12480000000000152
time 0.12500000000000153
time 0.12520000000000153
time 0.12540000000000154
time 0.12560000000000154
time 0.12580000000000155
time 0.12600000000000156
time 0.12620000000000156
time 0.12640000000000157
time 0.12660000000000157
time 0.12680000000000158
time 0.12700000000000158
time 0.1272000000000016
time 0.1274000000000016
time 0.1276000000000016
time 0.1278000000000016
time 0.1280000000000016
time 0.12820000000000162
time 0.12840000000000162
time 0.12860000000000163
time 0.12880000000000164
time 0.12900000000000164
time 0.12920000000000165
time 0.12940000000000165
time 0.12960000000000166
time 0.12980000000000166
time 0.13000000000000167
time 0.13020000000000168
time 0.13040000000000168
time 0.1306000000000017
time 0.1308000000000017
time 0.1310000000000017
time 0.1312000000000017
time 0.1314000000000017
time 0.13160000000000172
time 0.13180000000000172
time 0.13200000000000173
time 0.13220000000000173
time 0.13240000000000174
time 0.13260000000000174
time 0.13280000000000175
time 0.13300000000000176
time 0.13320000000000176
time 0.13340000000000177
time 0.13360000000000177
time 0.13380000000000178
time 0.13400000000000178
time 0.1342000000000018
time 0.1344000000000018
time 0.1346000000000018
time 0.1348000000000018
time 0.1350000000000018
time 0.13520000000000182
time 0.13540000000000182
time 0.13560000000000183
time 0.13580000000000184
time 0.13600000000000184
time 0.13620000000000185
time 0.13640000000000185
time 0.13660000000000186
time 0.13680000000000186
time 0.13700000000000187
time 0.13720000000000188
time 0.13740000000000188
time 0.1376000000000019
time 0.1378000000000019
time 0.1380000000000019
time 0.1382000000000019
time 0.1384000000000019
time 0.13860000000000192
time 0.13880000000000192
time 0.13900000000000193
time 0.13920000000000193
time 0.13940000000000194
time 0.13960000000000194
time 0.13980000000000195
time 0.14000000000000196
time 0.14020000000000196
time 0.14040000000000197
time 0.14060000000000197
time 0.14080000000000198
time 0.14100000000000198
time 0.141200000000002
time 0.141400000000002
time 0.141600000000002
time 0.141800000000002
time 0.142000000000002
time 0.14220000000000202
time 0.14240000000000202
time 0.14260000000000203
time 0.14280000000000204
time 0.14300000000000204
time 0.14320000000000205
time 0.14340000000000205
time 0.14360000000000206
time 0.14380000000000207
time 0.14400000000000207
time 0.14420000000000208
time 0.14440000000000208
time 0.1446000000000021
time 0.1448000000000021
time 0.1450000000000021
time 0.1452000000000021
time 0.1454000000000021
time 0.14560000000000212
time 0.14580000000000212
time 0.14600000000000213
time 0.14620000000000213
time 0.14640000000000214
time 0.14660000000000215
time 0.14680000000000215
time 0.14700000000000216
time 0.14720000000000216
time 0.14740000000000217
time 0.14760000000000217
time 0.14780000000000218
time 0.14800000000000219
time 0.1482000000000022
time 0.1484000000000022
time 0.1486000000000022
time 0.1488000000000022
time 0.14900000000000221
time 0.14920000000000222
time 0.14940000000000223
time 0.14960000000000223
time 0.14980000000000224
time 0.15000000000000224
time 0.15020000000000225
time 0.15040000000000225
time 0.15060000000000226
time 0.15080000000000227
time 0.15100000000000227
time 0.15120000000000228
time 0.15140000000000228
time 0.1516000000000023
time 0.1518000000000023
time 0.1520000000000023
time 0.1522000000000023
time 0.1524000000000023
time 0.15260000000000232
time 0.15280000000000232
time 0.15300000000000233
time 0.15320000000000233
time 0.15340000000000234
time 0.15360000000000235
time 0.15380000000000235
time 0.15400000000000236
time 0.15420000000000236
time 0.15440000000000237
time 0.15460000000000237
time 0.15480000000000238
time 0.15500000000000239
time 0.1552000000000024
time 0.1554000000000024
time 0.1556000000000024
time 0.1558000000000024
time 0.15600000000000241
time 0.15620000000000242
time 0.15640000000000243
time 0.15660000000000243
time 0.15680000000000244
time 0.15700000000000244
time 0.15720000000000245
time 0.15740000000000245
time 0.15760000000000246
time 0.15780000000000247
time 0.15800000000000247
time 0.15820000000000248
time 0.15840000000000248
time 0.1586000000000025
time 0.1588000000000025
time 0.1590000000000025
time 0.1592000000000025
time 0.1594000000000025
time 0.15960000000000252
time 0.15980000000000252
time 0.16000000000000253
time 0.16020000000000253
time 0.16040000000000254
time 0.16060000000000255
time 0.16080000000000255
time 0.16100000000000256
time 0.16120000000000256
time 0.16140000000000257
time 0.16160000000000257
time 0.16180000000000258
time 0.1620000000000026
time 0.1622000000000026
time 0.1624000000000026
time 0.1626000000000026
time 0.1628000000000026
time 0.16300000000000262
time 0.16320000000000262
time 0.16340000000000263
time 0.16360000000000263
time 0.16380000000000264
time 0.16400000000000264
time 0.16420000000000265
time 0.16440000000000266
time 0.16460000000000266
time 0.16480000000000267
time 0.16500000000000267
time 0.16520000000000268
time 0.16540000000000268
time 0.1656000000000027
time 0.1658000000000027
time 0.1660000000000027
time 0.1662000000000027
time 0.1664000000000027
time 0.16660000000000272
time 0.16680000000000272
time 0.16700000000000273
time 0.16720000000000274
time 0.16740000000000274
time 0.16760000000000275
time 0.16780000000000275
time 0.16800000000000276
time 0.16820000000000276
time 0.16840000000000277
time 0.16860000000000278
time 0.16880000000000278
time 0.1690000000000028
time 0.1692000000000028
time 0.1694000000000028
time 0.1696000000000028
time 0.1698000000000028
time 0.17000000000000282
time 0.17020000000000282
time 0.17040000000000283
time 0.17060000000000283
time 0.17080000000000284
time 0.17100000000000284
time 0.17120000000000285
time 0.17140000000000286
time 0.17160000000000286
time 0.17180000000000287
time 0.17200000000000287
time 0.17220000000000288
time 0.17240000000000288
time 0.1726000000000029
time 0.1728000000000029
time 0.1730000000000029
time 0.1732000000000029
time 0.1734000000000029
time 0.17360000000000292
time 0.17380000000000292
time 0.17400000000000293
time 0.17420000000000294
time 0.17440000000000294
time 0.17460000000000295
time 0.17480000000000295
time 0.17500000000000296
time 0.17520000000000296
time 0.17540000000000297
time 0.17560000000000298
time 0.17580000000000298
time 0.176000000000003
time 0.176200000000003
time 0.176400000000003
time 0.176600000000003
time 0.176800000000003
time 0.17700000000000302
time 0.17720000000000302
time 0.17740000000000303
time 0.17760000000000303
time 0.17780000000000304
time 0.17800000000000304
time 0.17820000000000305
time 0.17840000000000306
time 0.17860000000000306
time 0.17880000000000307
time 0.17900000000000307
time 0.17920000000000308
time 0.17940000000000308
time 0.1796000000000031
time 0.1798000000000031
time 0.1800000000000031
time 0.1802000000000031
time 0.1804000000000031
time 0.18060000000000312
time 0.18080000000000312
time 0.18100000000000313
time 0.18120000000000314
time 0.18140000000000314
time 0.18160000000000315
time 0.18180000000000315
time 0.18200000000000316
time 0.18220000000000316
time 0.18240000000000317
time 0.18260000000000318
time 0.18280000000000318
time 0.1830000000000032
time 0.1832000000000032
time 0.1834000000000032
time 0.1836000000000032
time 0.1838000000000032
time 0.18400000000000322
time 0.18420000000000322
time 0.18440000000000323
time 0.18460000000000323
time 0.18480000000000324
time 0.18500000000000325
time 0.18520000000000325
time 0.18540000000000326
time 0.18560000000000326
time 0.18580000000000327
time 0.18600000000000327
time 0.18620000000000328
time 0.18640000000000329
time 0.1866000000000033
time 0.1868000000000033
time 0.1870000000000033
time 0.1872000000000033
time 0.18740000000000331
time 0.18760000000000332
time 0.18780000000000333
time 0.18800000000000333
time 0.18820000000000334
time 0.18840000000000334
time 0.18860000000000335
time 0.18880000000000335
time 0.18900000000000336
time 0.18920000000000337
time 0.18940000000000337
time 0.18960000000000338
time 0.18980000000000338
time 0.1900000000000034
time 0.1902000000000034
time 0.1904000000000034
time 0.1906000000000034
time 0.1908000000000034
time 0.19100000000000342
time 0.19120000000000342
time 0.19140000000000343
time 0.19160000000000343
time 0.19180000000000344
time 0.19200000000000345
time 0.19220000000000345
time 0.19240000000000346
time 0.19260000000000346
time 0.19280000000000347
time 0.19300000000000347
time 0.19320000000000348
time 0.19340000000000349
time 0.1936000000000035
time 0.1938000000000035
time 0.1940000000000035
time 0.1942000000000035
time 0.19440000000000351
time 0.19460000000000352
time 0.19480000000000353
time 0.19500000000000353
time 0.19520000000000354
time 0.19540000000000354
time 0.19560000000000355
time 0.19580000000000355
time 0.19600000000000356
time 0.19620000000000357
time 0.19640000000000357
time 0.19660000000000358
time 0.19680000000000358
time 0.1970000000000036
time 0.1972000000000036
time 0.1974000000000036
time 0.1976000000000036
time 0.1978000000000036
time 0.19800000000000362
time 0.19820000000000362
time 0.19840000000000363
time 0.19860000000000363
time 0.19880000000000364
time 0.19900000000000365
time 0.19920000000000365
time 0.19940000000000366
time 0.19960000000000366
time 0.19980000000000367
time 0.20000000000000367
time 0.20020000000000368
time 0.2004000000000037
time 0.2006000000000037
time 0.2008000000000037
time 0.2010000000000037
time 0.2012000000000037
time 0.20140000000000371
time 0.20160000000000372
time 0.20180000000000373
time 0.20200000000000373
time 0.20220000000000374
time 0.20240000000000374
time 0.20260000000000375
time 0.20280000000000376
time 0.20300000000000376
time 0.20320000000000377
time 0.20340000000000377
time 0.20360000000000378
time 0.20380000000000378
time 0.2040000000000038
time 0.2042000000000038
time 0.2044000000000038
time 0.2046000000000038
time 0.2048000000000038
time 0.20500000000000382
time 0.20520000000000382
time 0.20540000000000383
time 0.20560000000000384
time 0.20580000000000384
time 0.20600000000000385
time 0.20620000000000385
time 0.20640000000000386
time 0.20660000000000386
time 0.20680000000000387
time 0.20700000000000388
time 0.20720000000000388
time 0.2074000000000039
time 0.2076000000000039
time 0.2078000000000039
time 0.2080000000000039
time 0.2082000000000039
time 0.20840000000000392
time 0.20860000000000392
time 0.20880000000000393
time 0.20900000000000393
time 0.20920000000000394
time 0.20940000000000394
time 0.20960000000000395
time 0.20980000000000396
time 0.21000000000000396
time 0.21020000000000397
time 0.21040000000000397
time 0.21060000000000398
time 0.21080000000000398
time 0.211000000000004
time 0.211200000000004
time 0.211400000000004
time 0.211600000000004
time 0.211800000000004
time 0.21200000000000402
time 0.21220000000000402
time 0.21240000000000403
time 0.21260000000000404
time 0.21280000000000404
time 0.21300000000000405
time 0.21320000000000405
time 0.21340000000000406
time 0.21360000000000406
time 0.21380000000000407
time 0.21400000000000408
time 0.21420000000000408
time 0.2144000000000041
time 0.2146000000000041
time 0.2148000000000041
time 0.2150000000000041
time 0.2152000000000041
time 0.21540000000000412
time 0.21560000000000412
time 0.21580000000000413
time 0.21600000000000413
time 0.21620000000000414
time 0.21640000000000414
time 0.21660000000000415
time 0.21680000000000416
time 0.21700000000000416
time 0.21720000000000417
time 0.21740000000000417
time 0.21760000000000418
time 0.21780000000000418
time 0.2180000000000042
time 0.2182000000000042
time 0.2184000000000042
time 0.2186000000000042
time 0.2188000000000042
time 0.21900000000000422
time 0.21920000000000422
time 0.21940000000000423
time 0.21960000000000424
time 0.21980000000000424
time 0.22000000000000425
time 0.22020000000000425
time 0.22040000000000426
time 0.22060000000000426
time 0.22080000000000427
time 0.22100000000000428
time 0.22120000000000428
time 0.2214000000000043
time 0.2216000000000043
time 0.2218000000000043
time 0.2220000000000043
time 0.2222000000000043
time 0.22240000000000432
time 0.22260000000000432
time 0.22280000000000433
time 0.22300000000000433
time 0.22320000000000434
time 0.22340000000000435
time 0.22360000000000435
time 0.22380000000000436
time 0.22400000000000436
time 0.22420000000000437
time 0.22440000000000437
time 0.22460000000000438
time 0.22480000000000439
time 0.2250000000000044
time 0.2252000000000044
time 0.2254000000000044
time 0.2256000000000044
time 0.2258000000000044
time 0.22600000000000442
time 0.22620000000000443
time 0.22640000000000443
time 0.22660000000000444
time 0.22680000000000444
time 0.22700000000000445
time 0.22720000000000445
time 0.22740000000000446
time 0.22760000000000447
time 0.22780000000000447
time 0.22800000000000448
time 0.22820000000000448
time 0.2284000000000045
time 0.2286000000000045
time 0.2288000000000045
time 0.2290000000000045
time 0.2292000000000045
time 0.22940000000000452
time 0.22960000000000452
time 0.22980000000000453
time 0.23000000000000453
time 0.23020000000000454
time 0.23040000000000455
time 0.23060000000000455
time 0.23080000000000456
time 0.23100000000000456
time 0.23120000000000457
time 0.23140000000000457
time 0.23160000000000458
time 0.23180000000000459
time 0.2320000000000046
time 0.2322000000000046
time 0.2324000000000046
time 0.2326000000000046
time 0.23280000000000461
time 0.23300000000000462
time 0.23320000000000463
time 0.23340000000000463
time 0.23360000000000464
time 0.23380000000000464
time 0.23400000000000465
time 0.23420000000000465
time 0.23440000000000466
time 0.23460000000000467
time 0.23480000000000467
time 0.23500000000000468
time 0.23520000000000468
time 0.2354000000000047
time 0.2356000000000047
time 0.2358000000000047
time 0.2360000000000047
time 0.2362000000000047
time 0.23640000000000472
time 0.23660000000000472
time 0.23680000000000473
time 0.23700000000000473
time 0.23720000000000474
time 0.23740000000000475
time 0.23760000000000475
time 0.23780000000000476
time 0.23800000000000476
time 0.23820000000000477
time 0.23840000000000477
time 0.23860000000000478
time 0.2388000000000048
time 0.2390000000000048
time 0.2392000000000048
time 0.2394000000000048
time 0.2396000000000048
time 0.23980000000000481
time 0.24000000000000482
time 0.24020000000000483
time 0.24040000000000483
time 0.24060000000000484
time 0.24080000000000484
time 0.24100000000000485
time 0.24120000000000485
time 0.24140000000000486
time 0.24160000000000487
time 0.24180000000000487
time 0.24200000000000488
time 0.24220000000000488
time 0.2424000000000049
time 0.2426000000000049
time 0.2428000000000049
time 0.2430000000000049
time 0.2432000000000049
time 0.24340000000000492
time 0.24360000000000492
time 0.24380000000000493
time 0.24400000000000494
time 0.24420000000000494
time 0.24440000000000495
time 0.24460000000000495
time 0.24480000000000496
time 0.24500000000000496
time 0.24520000000000497
time 0.24540000000000498
time 0.24560000000000498
time 0.245800000000005
time 0.246000000000005
time 0.246200000000005
time 0.246400000000005
time 0.246600000000005
time 0.24680000000000502
time 0.24700000000000502
time 0.24720000000000503
time 0.24740000000000503
time 0.24760000000000504
time 0.24780000000000504
time 0.24800000000000505
time 0.24820000000000506
time 0.24840000000000506
time 0.24860000000000507
time 0.24880000000000507
time 0.24900000000000508
time 0.24920000000000508
time 0.2494000000000051
time 0.2496000000000051
time 0.2498000000000051
time 0.2500000000000051
time 0.2502000000000051
time 0.25040000000000506
time 0.25060000000000504
time 0.250800000000005
time 0.251000000000005
time 0.251200000000005
time 0.25140000000000495
time 0.25160000000000493
time 0.2518000000000049
time 0.2520000000000049
time 0.25220000000000486
time 0.25240000000000484
time 0.2526000000000048
time 0.2528000000000048
time 0.2530000000000048
time 0.25320000000000475
time 0.25340000000000473
time 0.2536000000000047
time 0.2538000000000047
time 0.25400000000000467
time 0.25420000000000464
time 0.2544000000000046
time 0.2546000000000046
time 0.2548000000000046
time 0.25500000000000456
time 0.25520000000000453
time 0.2554000000000045
time 0.2556000000000045
time 0.25580000000000447
time 0.25600000000000445
time 0.2562000000000044
time 0.2564000000000044
time 0.2566000000000044
time 0.25680000000000436
time 0.25700000000000434
time 0.2572000000000043
time 0.2574000000000043
time 0.25760000000000427
time 0.25780000000000425
time 0.2580000000000042
time 0.2582000000000042
time 0.2584000000000042
time 0.25860000000000416
time 0.25880000000000414
time 0.2590000000000041
time 0.2592000000000041
time 0.25940000000000407
time 0.25960000000000405
time 0.259800000000004
time 0.260000000000004
time 0.260200000000004
time 0.26040000000000396
time 0.26060000000000394
time 0.2608000000000039
time 0.2610000000000039
time 0.2612000000000039
time 0.26140000000000385
time 0.26160000000000383
time 0.2618000000000038
time 0.2620000000000038
time 0.26220000000000376
time 0.26240000000000374
time 0.2626000000000037
time 0.2628000000000037
time 0.2630000000000037
time 0.26320000000000365
time 0.26340000000000363
time 0.2636000000000036
time 0.2638000000000036
time 0.26400000000000357
time 0.26420000000000354
time 0.2644000000000035
time 0.2646000000000035
time 0.2648000000000035
time 0.26500000000000346
time 0.26520000000000343
time 0.2654000000000034
time 0.2656000000000034
time 0.26580000000000337
time 0.26600000000000334
time 0.2662000000000033
time 0.2664000000000033
time 0.2666000000000033
time 0.26680000000000326
time 0.26700000000000323
time 0.2672000000000032
time 0.2674000000000032
time 0.26760000000000317
time 0.26780000000000315
time 0.2680000000000031
time 0.2682000000000031
time 0.2684000000000031
time 0.26860000000000306
time 0.26880000000000304
time 0.269000000000003
time 0.269200000000003
time 0.26940000000000297
time 0.26960000000000295
time 0.2698000000000029
time 0.2700000000000029
time 0.2702000000000029
time 0.27040000000000286
time 0.27060000000000284
time 0.2708000000000028
time 0.2710000000000028
time 0.27120000000000277
time 0.27140000000000275
time 0.27160000000000273
time 0.2718000000000027
time 0.2720000000000027
time 0.27220000000000266
time 0.27240000000000264
time 0.2726000000000026
time 0.2728000000000026
time 0.2730000000000026
time 0.27320000000000255
time 0.27340000000000253
time 0.2736000000000025
time 0.2738000000000025
time 0.27400000000000246
time 0.27420000000000244
time 0.2744000000000024
time 0.2746000000000024
time 0.2748000000000024
time 0.27500000000000235
time 0.27520000000000233
time 0.2754000000000023
time 0.2756000000000023
time 0.27580000000000227
time 0.27600000000000224
time 0.2762000000000022
time 0.2764000000000022
time 0.2766000000000022
time 0.27680000000000216
time 0.27700000000000213
time 0.2772000000000021
time 0.2774000000000021
time 0.27760000000000207
time 0.27780000000000205
time 0.278000000000002
time 0.278200000000002
time 0.278400000000002
time 0.27860000000000196
time 0.27880000000000194
time 0.2790000000000019
time 0.2792000000000019
time 0.27940000000000187
time 0.27960000000000185
time 0.2798000000000018
time 0.2800000000000018
time 0.2802000000000018
time 0.28040000000000176
time 0.28060000000000174
time 0.2808000000000017
time 0.2810000000000017
time 0.28120000000000167
time 0.28140000000000165
time 0.2816000000000016
time 0.2818000000000016
time 0.2820000000000016
time 0.28220000000000156
time 0.28240000000000154
time 0.2826000000000015
time 0.2828000000000015
time 0.2830000000000015
time 0.28320000000000145
time 0.28340000000000143
time 0.2836000000000014
time 0.2838000000000014
time 0.28400000000000136
time 0.28420000000000134
time 0.2844000000000013
time 0.2846000000000013
time 0.2848000000000013
time 0.28500000000000125
time 0.28520000000000123
time 0.2854000000000012
time 0.2856000000000012
time 0.28580000000000116
time 0.28600000000000114
time 0.2862000000000011
time 0.2864000000000011
time 0.2866000000000011
time 0.28680000000000105
time 0.28700000000000103
time 0.287200000000001
time 0.287400000000001
time 0.28760000000000097
time 0.28780000000000094
time 0.2880000000000009
time 0.2882000000000009
time 0.2884000000000009
time 0.28860000000000086
time 0.28880000000000083
time 0.2890000000000008
time 0.2892000000000008
time 0.28940000000000077
time 0.28960000000000075
time 0.2898000000000007
time 0.2900000000000007
time 0.2902000000000007
time 0.29040000000000066
time 0.29060000000000064
time 0.2908000000000006
time 0.2910000000000006
time 0.29120000000000057
time 0.29140000000000055
time 0.2916000000000005
time 0.2918000000000005
time 0.2920000000000005
time 0.29220000000000046
time 0.29240000000000044
time 0.2926000000000004
time 0.2928000000000004
time 0.29300000000000037
time 0.29320000000000035
time 0.2934000000000003
time 0.2936000000000003
time 0.2938000000000003
time 0.29400000000000026
time 0.29420000000000024
time 0.2944000000000002
time 0.2946000000000002
time 0.2948000000000002
time 0.29500000000000015
time 0.29520000000000013
time 0.2954000000000001
time 0.2956000000000001
time 0.29580000000000006
time 0.29600000000000004
time 0.2962
time 0.2964
time 0.2966
time 0.29679999999999995
time 0.29699999999999993
time 0.2971999999999999
time 0.2973999999999999
time 0.29759999999999986
time 0.29779999999999984
time 0.2979999999999998
time 0.2981999999999998
time 0.2983999999999998
time 0.29859999999999975
time 0.29879999999999973
time 0.2989999999999997
time 0.2991999999999997
time 0.29939999999999967
time 0.29959999999999964
time 0.2997999999999996
time 0.2999999999999996
time 0.3001999999999996
time 0.30039999999999956
time 0.30059999999999953
time 0.3007999999999995
time 0.3009999999999995
time 0.30119999999999947
time 0.30139999999999945
time 0.3015999999999994
time 0.3017999999999994
time 0.3019999999999994
time 0.30219999999999936
time 0.30239999999999934
time 0.3025999999999993
time 0.3027999999999993
time 0.30299999999999927
time 0.30319999999999925
time 0.3033999999999992
time 0.3035999999999992
time 0.3037999999999992
time 0.30399999999999916
time 0.30419999999999914
time 0.3043999999999991
time 0.3045999999999991
time 0.30479999999999907
time 0.30499999999999905
time 0.305199999999999
time 0.305399999999999
time 0.305599999999999
time 0.30579999999999896
time 0.30599999999999894
time 0.3061999999999989
time 0.3063999999999989
time 0.3065999999999989
time 0.30679999999999885
time 0.30699999999999883
time 0.3071999999999988
time 0.3073999999999988
time 0.30759999999999876
time 0.30779999999999874
time 0.3079999999999987
time 0.3081999999999987
time 0.3083999999999987
time 0.30859999999999865
time 0.30879999999999863
time 0.3089999999999986
time 0.3091999999999986
time 0.30939999999999857
time 0.30959999999999854
time 0.3097999999999985
time 0.3099999999999985
time 0.3101999999999985
time 0.31039999999999845
time 0.31059999999999843
time 0.3107999999999984
time 0.3109999999999984
time 0.31119999999999837
time 0.31139999999999834
time 0.3115999999999983
time 0.3117999999999983
time 0.3119999999999983
time 0.31219999999999826
time 0.31239999999999823
time 0.3125999999999982
time 0.3127999999999982
time 0.31299999999999817
time 0.31319999999999815
time 0.3133999999999981
time 0.3135999999999981
time 0.3137999999999981
time 0.31399999999999806
time 0.31419999999999804
time 0.314399999999998
time 0.314599999999998
time 0.31479999999999797
time 0.31499999999999795
time 0.3151999999999979
time 0.3153999999999979
time 0.3155999999999979
time 0.31579999999999786
time 0.31599999999999784
time 0.3161999999999978
time 0.3163999999999978
time 0.31659999999999777
time 0.31679999999999775
time 0.31699999999999773
time 0.3171999999999977
time 0.3173999999999977
time 0.31759999999999766
time 0.31779999999999764
time 0.3179999999999976
time 0.3181999999999976
time 0.3183999999999976
time 0.31859999999999755
time 0.31879999999999753
time 0.3189999999999975
time 0.3191999999999975
time 0.31939999999999746
time 0.31959999999999744
time 0.3197999999999974
time 0.3199999999999974
time 0.3201999999999974
time 0.32039999999999735
time 0.32059999999999733
time 0.3207999999999973
time 0.3209999999999973
time 0.32119999999999727
time 0.32139999999999724
time 0.3215999999999972
time 0.3217999999999972
time 0.3219999999999972
time 0.32219999999999716
time 0.32239999999999713
time 0.3225999999999971
time 0.3227999999999971
time 0.32299999999999707
time 0.32319999999999705
time 0.323399999999997
time 0.323599999999997
time 0.323799999999997
time 0.32399999999999696
time 0.32419999999999694
time 0.3243999999999969
time 0.3245999999999969
time 0.32479999999999687
time 0.32499999999999685
time 0.3251999999999968
time 0.3253999999999968
time 0.3255999999999968
time 0.32579999999999676
time 0.32599999999999674
time 0.3261999999999967
time 0.3263999999999967
time 0.32659999999999667
time 0.32679999999999665
time 0.3269999999999966
time 0.3271999999999966
time 0.3273999999999966
time 0.32759999999999656
time 0.32779999999999654
time 0.3279999999999965
time 0.3281999999999965
time 0.3283999999999965
time 0.32859999999999645
time 0.32879999999999643
time 0.3289999999999964
time 0.3291999999999964
time 0.32939999999999636
time 0.32959999999999634
time 0.3297999999999963
time 0.3299999999999963
time 0.3301999999999963
time 0.33039999999999625
time 0.33059999999999623
time 0.3307999999999962
time 0.3309999999999962
time 0.33119999999999616
time 0.33139999999999614
time 0.3315999999999961
time 0.3317999999999961
time 0.3319999999999961
time 0.33219999999999605
time 0.33239999999999603
time 0.332599999999996
time 0.332799999999996
time 0.33299999999999597
time 0.33319999999999594
time 0.3333999999999959
time 0.3335999999999959
time 0.3337999999999959
time 0.33399999999999586
time 0.33419999999999583
time 0.3343999999999958
time 0.3345999999999958
time 0.33479999999999577
time 0.33499999999999575
time 0.3351999999999957
time 0.3353999999999957
time 0.3355999999999957
time 0.33579999999999566
time 0.33599999999999564
time 0.3361999999999956
time 0.3363999999999956
time 0.33659999999999557
time 0.33679999999999555
time 0.3369999999999955
time 0.3371999999999955
time 0.3373999999999955
time 0.33759999999999546
time 0.33779999999999544
time 0.3379999999999954
time 0.3381999999999954
time 0.33839999999999537
time 0.33859999999999535
time 0.3387999999999953
time 0.3389999999999953
time 0.3391999999999953
time 0.33939999999999526
time 0.33959999999999524
time 0.3397999999999952
time 0.3399999999999952
time 0.3401999999999952
time 0.34039999999999515
time 0.34059999999999513
time 0.3407999999999951
time 0.3409999999999951
time 0.34119999999999506
time 0.34139999999999504
time 0.341599999999995
time 0.341799999999995
time 0.341999999999995
time 0.34219999999999495
time 0.34239999999999493
time 0.3425999999999949
time 0.3427999999999949
time 0.34299999999999486
time 0.34319999999999484
time 0.3433999999999948
time 0.3435999999999948
time 0.3437999999999948
time 0.34399999999999475
time 0.34419999999999473
time 0.3443999999999947
time 0.3445999999999947
time 0.34479999999999467
time 0.34499999999999464
time 0.3451999999999946
time 0.3453999999999946
time 0.3455999999999946
time 0.34579999999999456
time 0.34599999999999453
time 0.3461999999999945
time 0.3463999999999945
time 0.34659999999999447
time 0.34679999999999445
time 0.3469999999999944
time 0.3471999999999944
time 0.3473999999999944
time 0.34759999999999436
time 0.34779999999999434
time 0.3479999999999943
time 0.3481999999999943
time 0.34839999999999427
time 0.34859999999999425
time 0.3487999999999942
time 0.3489999999999942
time 0.3491999999999942
time 0.34939999999999416
time 0.34959999999999414
time 0.3497999999999941
time 0.3499999999999941
time 0.35019999999999407
time 0.35039999999999405
time 0.350599999999994
time 0.350799999999994
time 0.350999999999994
time 0.35119999999999396
time 0.35139999999999394
time 0.3515999999999939
time 0.3517999999999939
time 0.3519999999999939
time 0.35219999999999385
time 0.35239999999999383
time 0.3525999999999938
time 0.3527999999999938
time 0.35299999999999376
time 0.35319999999999374
time 0.3533999999999937
time 0.3535999999999937
time 0.3537999999999937
time 0.35399999999999365
time 0.35419999999999363
time 0.3543999999999936
time 0.3545999999999936
time 0.35479999999999356
time 0.35499999999999354
time 0.3551999999999935
time 0.3553999999999935
time 0.3555999999999935
time 0.35579999999999345
time 0.35599999999999343
time 0.3561999999999934
time 0.3563999999999934
time 0.35659999999999337
time 0.35679999999999334
time 0.3569999999999933
time 0.3571999999999933
time 0.3573999999999933
time 0.35759999999999326
time 0.35779999999999323
time 0.3579999999999932
time 0.3581999999999932
time 0.35839999999999317
time 0.35859999999999315
time 0.3587999999999931
time 0.3589999999999931
time 0.3591999999999931
time 0.35939999999999306
time 0.35959999999999304
time 0.359799999999993
time 0.359999999999993
time 0.36019999999999297
time 0.36039999999999295
time 0.3605999999999929
time 0.3607999999999929
time 0.3609999999999929
time 0.36119999999999286
time 0.36139999999999284
time 0.3615999999999928
time 0.3617999999999928
time 0.36199999999999277
time 0.36219999999999275
time 0.36239999999999273
time 0.3625999999999927
time 0.3627999999999927
time 0.36299999999999266
time 0.36319999999999264
time 0.3633999999999926
time 0.3635999999999926
time 0.3637999999999926
time 0.36399999999999255
time 0.36419999999999253
time 0.3643999999999925
time 0.3645999999999925
time 0.36479999999999246
time 0.36499999999999244
time 0.3651999999999924
time 0.3653999999999924
time 0.3655999999999924
time 0.36579999999999235
time 0.36599999999999233
time 0.3661999999999923
time 0.3663999999999923
time 0.36659999999999227
time 0.36679999999999224
time 0.3669999999999922
time 0.3671999999999922
time 0.3673999999999922
time 0.36759999999999216
time 0.36779999999999213
time 0.3679999999999921
time 0.3681999999999921
time 0.36839999999999207
time 0.36859999999999205
time 0.368799999999992
time 0.368999999999992
time 0.369199999999992
time 0.36939999999999196
time 0.36959999999999193
time 0.3697999999999919
time 0.3699999999999919
time 0.37019999999999187
time 0.37039999999999185
time 0.3705999999999918
time 0.3707999999999918
time 0.3709999999999918
time 0.37119999999999176
time 0.37139999999999174
time 0.3715999999999917
time 0.3717999999999917
time 0.37199999999999167
time 0.37219999999999165
time 0.3723999999999916
time 0.3725999999999916
time 0.3727999999999916
time 0.37299999999999156
time 0.37319999999999154
time 0.3733999999999915
time 0.3735999999999915
time 0.3737999999999915
time 0.37399999999999145
time 0.37419999999999143
time 0.3743999999999914
time 0.3745999999999914
time 0.37479999999999136
time 0.37499999999999134
time 0.3751999999999913
time 0.3753999999999913
time 0.3755999999999913
time 0.37579999999999125
time 0.37599999999999123
time 0.3761999999999912
time 0.3763999999999912
time 0.37659999999999116
time 0.37679999999999114
time 0.3769999999999911
time 0.3771999999999911
time 0.3773999999999911
time 0.37759999999999105
time 0.37779999999999103
time 0.377999999999991
time 0.378199999999991
time 0.37839999999999097
time 0.37859999999999094
time 0.3787999999999909
time 0.3789999999999909
time 0.3791999999999909
time 0.37939999999999086
time 0.37959999999999083
time 0.3797999999999908
time 0.3799999999999908
time 0.38019999999999077
time 0.38039999999999075
time 0.3805999999999907
time 0.3807999999999907
time 0.3809999999999907
time 0.38119999999999066
time 0.38139999999999064
time 0.3815999999999906
time 0.3817999999999906
time 0.38199999999999057
time 0.38219999999999055
time 0.3823999999999905
time 0.3825999999999905
time 0.3827999999999905
time 0.38299999999999046
time 0.38319999999999044
time 0.3833999999999904
time 0.3835999999999904
time 0.38379999999999037
time 0.38399999999999035
time 0.3841999999999903
time 0.3843999999999903
time 0.3845999999999903
time 0.38479999999999026
time 0.38499999999999024
time 0.3851999999999902
time 0.3853999999999902
time 0.3855999999999902
time 0.38579999999999015
time 0.38599999999999013
time 0.3861999999999901
time 0.3863999999999901
time 0.38659999999999006
time 0.38679999999999004
time 0.38699999999999
time 0.38719999999999
time 0.38739999999999
time 0.38759999999998995
time 0.38779999999998993
time 0.3879999999999899
time 0.3881999999999899
time 0.38839999999998986
time 0.38859999999998984
time 0.3887999999999898
time 0.3889999999999898
time 0.3891999999999898
time 0.38939999999998975
time 0.38959999999998973
time 0.3897999999999897
time 0.3899999999999897
time 0.39019999999998967
time 0.39039999999998964
time 0.3905999999999896
time 0.3907999999999896
time 0.3909999999999896
time 0.39119999999998956
time 0.39139999999998953
time 0.3915999999999895
time 0.3917999999999895
time 0.39199999999998947
time 0.39219999999998945
time 0.3923999999999894
time 0.3925999999999894
time 0.3927999999999894
time 0.39299999999998936
time 0.39319999999998934
time 0.3933999999999893
time 0.3935999999999893
time 0.39379999999998927
time 0.39399999999998925
time 0.3941999999999892
time 0.3943999999999892
time 0.3945999999999892
time 0.39479999999998916
time 0.39499999999998914
time 0.3951999999999891
time 0.3953999999999891
time 0.39559999999998907
time 0.39579999999998905
time 0.395999999999989
time 0.396199999999989
time 0.396399999999989
time 0.39659999999998896
time 0.39679999999998894
time 0.3969999999999889
time 0.3971999999999889
time 0.3973999999999889
time 0.39759999999998885
time 0.39779999999998883
time 0.3979999999999888
time 0.3981999999999888
time 0.39839999999998876
time 0.39859999999998874
time 0.3987999999999887
time 0.3989999999999887
time 0.3991999999999887
time 0.39939999999998865
time 0.39959999999998863
time 0.3997999999999886
time 0.3999999999999886
time 0.40019999999998856
time 0.40039999999998854
time 0.4005999999999885
time 0.4007999999999885
time 0.4009999999999885
time 0.40119999999998845
time 0.40139999999998843
time 0.4015999999999884
time 0.4017999999999884
time 0.40199999999998837
time 0.40219999999998834
time 0.4023999999999883
time 0.4025999999999883
time 0.4027999999999883
time 0.40299999999998826
time 0.40319999999998823
time 0.4033999999999882
time 0.4035999999999882
time 0.40379999999998817
time 0.40399999999998815
time 0.4041999999999881
time 0.4043999999999881
time 0.4045999999999881
time 0.40479999999998806
time 0.40499999999998804
time 0.405199999999988
time 0.405399999999988
time 0.40559999999998797
time 0.40579999999998795
time 0.4059999999999879
time 0.4061999999999879
time 0.4063999999999879
time 0.40659999999998786
time 0.40679999999998784
time 0.4069999999999878
time 0.4071999999999878
time 0.40739999999998777
time 0.40759999999998775
time 0.40779999999998773
time 0.4079999999999877
time 0.4081999999999877
time 0.40839999999998766
time 0.40859999999998764
time 0.4087999999999876
time 0.4089999999999876
time 0.4091999999999876
time 0.40939999999998755
time 0.40959999999998753
time 0.4097999999999875
time 0.4099999999999875
time 0.41019999999998746
time 0.41039999999998744
time 0.4105999999999874
time 0.4107999999999874
time 0.4109999999999874
time 0.41119999999998735
time 0.41139999999998733
time 0.4115999999999873
time 0.4117999999999873
time 0.41199999999998727
time 0.41219999999998724
time 0.4123999999999872
time 0.4125999999999872
time 0.4127999999999872
time 0.41299999999998716
time 0.41319999999998713
time 0.4133999999999871
time 0.4135999999999871
time 0.41379999999998707
time 0.41399999999998705
time 0.414199999999987
time 0.414399999999987
time 0.414599999999987
time 0.41479999999998696
time 0.41499999999998693
time 0.4151999999999869
time 0.4153999999999869
time 0.41559999999998687
time 0.41579999999998685
time 0.4159999999999868
time 0.4161999999999868
time 0.4163999999999868
time 0.41659999999998676
time 0.41679999999998674
time 0.4169999999999867
time 0.4171999999999867
time 0.41739999999998667
time 0.41759999999998665
time 0.4177999999999866
time 0.4179999999999866
time 0.4181999999999866
time 0.41839999999998656
time 0.41859999999998654
time 0.4187999999999865
time 0.4189999999999865
time 0.4191999999999865
time 0.41939999999998645
time 0.41959999999998643
time 0.4197999999999864
time 0.4199999999999864
time 0.42019999999998636
time 0.42039999999998634
time 0.4205999999999863
time 0.4207999999999863
time 0.4209999999999863
time 0.42119999999998625
time 0.42139999999998623
time 0.4215999999999862
time 0.4217999999999862
time 0.42199999999998616
time 0.42219999999998614
time 0.4223999999999861
time 0.4225999999999861
time 0.4227999999999861
time 0.42299999999998605
time 0.42319999999998603
time 0.423399999999986
time 0.423599999999986
time 0.42379999999998597
time 0.42399999999998594
time 0.4241999999999859
time 0.4243999999999859
time 0.4245999999999859
time 0.42479999999998586
time 0.42499999999998583
time 0.4251999999999858
time 0.4253999999999858
time 0.42559999999998577
time 0.42579999999998575
time 0.4259999999999857
time 0.4261999999999857
time 0.4263999999999857
time 0.42659999999998566
time 0.42679999999998564
time 0.4269999999999856
time 0.4271999999999856
time 0.42739999999998557
time 0.42759999999998555
time 0.4277999999999855
time 0.4279999999999855
time 0.4281999999999855
time 0.42839999999998546
time 0.42859999999998544
time 0.4287999999999854
time 0.4289999999999854
time 0.42919999999998537
time 0.42939999999998535
time 0.4295999999999853
time 0.4297999999999853
time 0.4299999999999853
time 0.43019999999998526
time 0.43039999999998524
time 0.4305999999999852
time 0.4307999999999852
time 0.4309999999999852
time 0.43119999999998515
time 0.43139999999998513
time 0.4315999999999851
time 0.4317999999999851
time 0.43199999999998506
time 0.43219999999998504
time 0.432399999999985
time 0.432599999999985
time 0.432799999999985
time 0.43299999999998495
time 0.43319999999998493
time 0.4333999999999849
time 0.4335999999999849
time 0.43379999999998486
time 0.43399999999998484
time 0.4341999999999848
time 0.4343999999999848
time 0.4345999999999848
time 0.43479999999998475
time 0.43499999999998473
time 0.4351999999999847
time 0.4353999999999847
time 0.43559999999998467
time 0.43579999999998464
time 0.4359999999999846
time 0.4361999999999846
time 0.4363999999999846
time 0.43659999999998456
time 0.43679999999998453
time 0.4369999999999845
time 0.4371999999999845
time 0.43739999999998447
time 0.43759999999998445
time 0.4377999999999844
time 0.4379999999999844
time 0.4381999999999844
time 0.43839999999998436
time 0.43859999999998434
time 0.4387999999999843
time 0.4389999999999843
time 0.43919999999998427
time 0.43939999999998425
time 0.4395999999999842
time 0.4397999999999842
time 0.4399999999999842
time 0.44019999999998416
time 0.44039999999998414
time 0.4405999999999841
time 0.4407999999999841
time 0.44099999999998407
time 0.44119999999998405
time 0.441399999999984
time 0.441599999999984
time 0.441799999999984
time 0.44199999999998396
time 0.44219999999998394
time 0.4423999999999839
time 0.4425999999999839
time 0.4427999999999839
time 0.44299999999998385
time 0.44319999999998383
time 0.4433999999999838
time 0.4435999999999838
time 0.44379999999998376
time 0.44399999999998374
time 0.4441999999999837
time 0.4443999999999837
time 0.4445999999999837
time 0.44479999999998365
time 0.44499999999998363
time 0.4451999999999836
time 0.4453999999999836
time 0.44559999999998356
time 0.44579999999998354
time 0.4459999999999835
time 0.4461999999999835
time 0.4463999999999835
time 0.44659999999998345
time 0.44679999999998343
time 0.4469999999999834
time 0.4471999999999834
time 0.44739999999998337
time 0.44759999999998334
time 0.4477999999999833
time 0.4479999999999833
time 0.4481999999999833
time 0.44839999999998326
time 0.44859999999998323
time 0.4487999999999832
time 0.4489999999999832
time 0.44919999999998317
time 0.44939999999998315
time 0.4495999999999831
time 0.4497999999999831
time 0.4499999999999831
time 0.45019999999998306
time 0.45039999999998304
time 0.450599999999983
time 0.450799999999983
time 0.45099999999998297
time 0.45119999999998295
time 0.4513999999999829
time 0.4515999999999829
time 0.4517999999999829
time 0.45199999999998286
time 0.45219999999998284
time 0.4523999999999828
time 0.4525999999999828
time 0.45279999999998277
time 0.45299999999998275
time 0.45319999999998273
time 0.4533999999999827
time 0.4535999999999827
time 0.45379999999998266
time 0.45399999999998264
time 0.4541999999999826
time 0.4543999999999826
time 0.4545999999999826
time 0.45479999999998255
time 0.45499999999998253
time 0.4551999999999825
time 0.4553999999999825
time 0.45559999999998246
time 0.45579999999998244
time 0.4559999999999824
time 0.4561999999999824
time 0.4563999999999824
time 0.45659999999998235
time 0.45679999999998233
time 0.4569999999999823
time 0.4571999999999823
time 0.45739999999998227
time 0.45759999999998224
time 0.4577999999999822
time 0.4579999999999822
time 0.4581999999999822
time 0.45839999999998216
time 0.45859999999998213
time 0.4587999999999821
time 0.4589999999999821
time 0.45919999999998207
time 0.45939999999998204
time 0.459599999999982
time 0.459799999999982
time 0.459999999999982
time 0.46019999999998196
time 0.46039999999998193
time 0.4605999999999819
time 0.4607999999999819
time 0.46099999999998187
time 0.46119999999998185
time 0.4613999999999818
time 0.4615999999999818
time 0.4617999999999818
time 0.46199999999998176
time 0.46219999999998174
time 0.4623999999999817
time 0.4625999999999817
time 0.46279999999998167
time 0.46299999999998165
time 0.4631999999999816
time 0.4633999999999816
time 0.4635999999999816
time 0.46379999999998156
time 0.46399999999998154
time 0.4641999999999815
time 0.4643999999999815
time 0.46459999999998147
time 0.46479999999998145
time 0.46499999999998143
time 0.4651999999999814
time 0.4653999999999814
time 0.46559999999998136
time 0.46579999999998134
time 0.4659999999999813
time 0.4661999999999813
time 0.4663999999999813
time 0.46659999999998125
time 0.46679999999998123
time 0.4669999999999812
time 0.4671999999999812
time 0.46739999999998116
time 0.46759999999998114
time 0.4677999999999811
time 0.4679999999999811
time 0.4681999999999811
time 0.46839999999998105
time 0.46859999999998103
time 0.468799999999981
time 0.468999999999981
time 0.46919999999998097
time 0.46939999999998094
time 0.4695999999999809
time 0.4697999999999809
time 0.4699999999999809
time 0.47019999999998086
time 0.47039999999998083
time 0.4705999999999808
time 0.4707999999999808
time 0.47099999999998077
time 0.47119999999998075
time 0.4713999999999807
time 0.4715999999999807
time 0.4717999999999807
time 0.47199999999998066
time 0.47219999999998064
time 0.4723999999999806
time 0.4725999999999806
time 0.47279999999998057
time 0.47299999999998055
time 0.4731999999999805
time 0.4733999999999805
time 0.4735999999999805
time 0.47379999999998046
time 0.47399999999998044
time 0.4741999999999804
time 0.4743999999999804
time 0.47459999999998037
time 0.47479999999998035
time 0.4749999999999803
time 0.4751999999999803
time 0.4753999999999803
time 0.47559999999998026
time 0.47579999999998024
time 0.4759999999999802
time 0.4761999999999802
time 0.4763999999999802
time 0.47659999999998015
time 0.47679999999998013
time 0.4769999999999801
time 0.4771999999999801
time 0.47739999999998006
time 0.47759999999998004
time 0.47779999999998
time 0.47799999999998
time 0.47819999999998
time 0.47839999999997995
time 0.47859999999997993
time 0.4787999999999799
time 0.4789999999999799
time 0.47919999999997986
time 0.47939999999997984
time 0.4795999999999798
time 0.4797999999999798
time 0.4799999999999798
time 0.48019999999997975
time 0.48039999999997973
time 0.4805999999999797
time 0.4807999999999797
time 0.48099999999997967
time 0.48119999999997964
time 0.4813999999999796
time 0.4815999999999796
time 0.4817999999999796
time 0.48199999999997956
time 0.48219999999997953
time 0.4823999999999795
time 0.4825999999999795
time 0.48279999999997947
time 0.48299999999997945
time 0.4831999999999794
time 0.4833999999999794
time 0.4835999999999794
time 0.48379999999997936
time 0.48399999999997934
time 0.4841999999999793
time 0.4843999999999793
time 0.48459999999997927
time 0.48479999999997925
time 0.4849999999999792
time 0.4851999999999792
time 0.4853999999999792
time 0.48559999999997916
time 0.48579999999997914
time 0.4859999999999791
time 0.4861999999999791
time 0.48639999999997907
time 0.48659999999997905
time 0.486799999999979
time 0.486999999999979
time 0.487199999999979
time 0.48739999999997896
time 0.48759999999997894
time 0.4877999999999789
time 0.4879999999999789
time 0.4881999999999789
time 0.48839999999997885
time 0.48859999999997883
time 0.4887999999999788
time 0.4889999999999788
time 0.48919999999997876
time 0.48939999999997874
time 0.4895999999999787
time 0.4897999999999787
time 0.4899999999999787
time 0.49019999999997865
time 0.49039999999997863
time 0.4905999999999786
time 0.4907999999999786
time 0.49099999999997856
time 0.49119999999997854
time 0.4913999999999785
time 0.4915999999999785
time 0.4917999999999785
time 0.49199999999997845
time 0.49219999999997843
time 0.4923999999999784
time 0.4925999999999784
time 0.49279999999997837
time 0.49299999999997834
time 0.4931999999999783
time 0.4933999999999783
time 0.4935999999999783
time 0.49379999999997826
time 0.49399999999997823
time 0.4941999999999782
time 0.4943999999999782
time 0.49459999999997817
time 0.49479999999997815
time 0.4949999999999781
time 0.4951999999999781
time 0.4953999999999781
time 0.49559999999997806
time 0.49579999999997804
time 0.495999999999978
time 0.496199999999978
time 0.49639999999997797
time 0.49659999999997795
time 0.4967999999999779
time 0.4969999999999779
time 0.4971999999999779
time 0.49739999999997786
time 0.49759999999997784
time 0.4977999999999778
time 0.4979999999999778
time 0.49819999999997777
time 0.49839999999997775
time 0.4985999999999777
time 0.4987999999999777
time 0.4989999999999777
time 0.49919999999997766
time 0.49939999999997764
time 0.4995999999999776
time 0.4997999999999776
time 0.4999999999999776
time 0.5001999999999776
time 0.5003999999999775
time 0.5005999999999775
time 0.5007999999999775
time 0.5009999999999775
time 0.5011999999999774
time 0.5013999999999774
time 0.5015999999999774
time 0.5017999999999774
time 0.5019999999999774
time 0.5021999999999773
time 0.5023999999999773
time 0.5025999999999773
time 0.5027999999999773
time 0.5029999999999772
time 0.5031999999999772
time 0.5033999999999772
time 0.5035999999999772
time 0.5037999999999772
time 0.5039999999999771
time 0.5041999999999771
time 0.5043999999999771
time 0.5045999999999771
time 0.504799999999977
time 0.504999999999977
time 0.505199999999977
time 0.505399999999977
time 0.505599999999977
time 0.5057999999999769
time 0.5059999999999769
time 0.5061999999999769
time 0.5063999999999769
time 0.5065999999999768
time 0.5067999999999768
time 0.5069999999999768
time 0.5071999999999768
time 0.5073999999999768
time 0.5075999999999767
time 0.5077999999999767
time 0.5079999999999767
time 0.5081999999999767
time 0.5083999999999766
time 0.5085999999999766
time 0.5087999999999766
time 0.5089999999999766
time 0.5091999999999766
time 0.5093999999999765
time 0.5095999999999765
time 0.5097999999999765
time 0.5099999999999765
time 0.5101999999999765
time 0.5103999999999764
time 0.5105999999999764
time 0.5107999999999764
time 0.5109999999999764
time 0.5111999999999763
time 0.5113999999999763
time 0.5115999999999763
time 0.5117999999999763
time 0.5119999999999763
time 0.5121999999999762
time 0.5123999999999762
time 0.5125999999999762
time 0.5127999999999762
time 0.5129999999999761
time 0.5131999999999761
time 0.5133999999999761
time 0.5135999999999761
time 0.513799999999976
time 0.513999999999976
time 0.514199999999976
time 0.514399999999976
time 0.514599999999976
time 0.5147999999999759
time 0.5149999999999759
time 0.5151999999999759
time 0.5153999999999759
time 0.5155999999999759
time 0.5157999999999758
time 0.5159999999999758
time 0.5161999999999758
time 0.5163999999999758
time 0.5165999999999757
time 0.5167999999999757
time 0.5169999999999757
time 0.5171999999999757
time 0.5173999999999757
time 0.5175999999999756
time 0.5177999999999756
time 0.5179999999999756
time 0.5181999999999756
time 0.5183999999999755
time 0.5185999999999755
time 0.5187999999999755
time 0.5189999999999755
time 0.5191999999999755
time 0.5193999999999754
time 0.5195999999999754
time 0.5197999999999754
time 0.5199999999999754
time 0.5201999999999753
time 0.5203999999999753
time 0.5205999999999753
time 0.5207999999999753
time 0.5209999999999753
time 0.5211999999999752
time 0.5213999999999752
time 0.5215999999999752
time 0.5217999999999752
time 0.5219999999999752
time 0.5221999999999751
time 0.5223999999999751
time 0.5225999999999751
time 0.5227999999999751
time 0.522999999999975
time 0.523199999999975
time 0.523399999999975
time 0.523599999999975
time 0.523799999999975
time 0.5239999999999749
time 0.5241999999999749
time 0.5243999999999749
time 0.5245999999999749
time 0.5247999999999748
time 0.5249999999999748
time 0.5251999999999748
time 0.5253999999999748
time 0.5255999999999748
time 0.5257999999999747
time 0.5259999999999747
time 0.5261999999999747
time 0.5263999999999747
time 0.5265999999999746
time 0.5267999999999746
time 0.5269999999999746
time 0.5271999999999746
time 0.5273999999999746
time 0.5275999999999745
time 0.5277999999999745
time 0.5279999999999745
time 0.5281999999999745
time 0.5283999999999744
time 0.5285999999999744
time 0.5287999999999744
time 0.5289999999999744
time 0.5291999999999744
time 0.5293999999999743
time 0.5295999999999743
time 0.5297999999999743
time 0.5299999999999743
time 0.5301999999999742
time 0.5303999999999742
time 0.5305999999999742
time 0.5307999999999742
time 0.5309999999999742
time 0.5311999999999741
time 0.5313999999999741
time 0.5315999999999741
time 0.5317999999999741
time 0.531999999999974
time 0.532199999999974
time 0.532399999999974
time 0.532599999999974
time 0.532799999999974
time 0.5329999999999739
time 0.5331999999999739
time 0.5333999999999739
time 0.5335999999999739
time 0.5337999999999739
time 0.5339999999999738
time 0.5341999999999738
time 0.5343999999999738
time 0.5345999999999738
time 0.5347999999999737
time 0.5349999999999737
time 0.5351999999999737
time 0.5353999999999737
time 0.5355999999999737
time 0.5357999999999736
time 0.5359999999999736
time 0.5361999999999736
time 0.5363999999999736
time 0.5365999999999735
time 0.5367999999999735
time 0.5369999999999735
time 0.5371999999999735
time 0.5373999999999735
time 0.5375999999999734
time 0.5377999999999734
time 0.5379999999999734
time 0.5381999999999734
time 0.5383999999999733
time 0.5385999999999733
time 0.5387999999999733
time 0.5389999999999733
time 0.5391999999999733
time 0.5393999999999732
time 0.5395999999999732
time 0.5397999999999732
time 0.5399999999999732
time 0.5401999999999731
time 0.5403999999999731
time 0.5405999999999731
time 0.5407999999999731
time 0.5409999999999731
time 0.541199999999973
time 0.541399999999973
time 0.541599999999973
time 0.541799999999973
time 0.541999999999973
time 0.5421999999999729
time 0.5423999999999729
time 0.5425999999999729
time 0.5427999999999729
time 0.5429999999999728
time 0.5431999999999728
time 0.5433999999999728
time 0.5435999999999728
time 0.5437999999999727
time 0.5439999999999727
time 0.5441999999999727
time 0.5443999999999727
time 0.5445999999999727
time 0.5447999999999726
time 0.5449999999999726
time 0.5451999999999726
time 0.5453999999999726
time 0.5455999999999726
time 0.5457999999999725
time 0.5459999999999725
time 0.5461999999999725
time 0.5463999999999725
time 0.5465999999999724
time 0.5467999999999724
time 0.5469999999999724
time 0.5471999999999724
time 0.5473999999999724
time 0.5475999999999723
time 0.5477999999999723
time 0.5479999999999723
time 0.5481999999999723
time 0.5483999999999722
time 0.5485999999999722
time 0.5487999999999722
time 0.5489999999999722
time 0.5491999999999722
time 0.5493999999999721
time 0.5495999999999721
time 0.5497999999999721
time 0.5499999999999721
time 0.550199999999972
time 0.550399999999972
time 0.550599999999972
time 0.550799999999972
time 0.550999999999972
time 0.5511999999999719
time 0.5513999999999719
time 0.5515999999999719
time 0.5517999999999719
time 0.5519999999999718
time 0.5521999999999718
time 0.5523999999999718
time 0.5525999999999718
time 0.5527999999999718
time 0.5529999999999717
time 0.5531999999999717
time 0.5533999999999717
time 0.5535999999999717
time 0.5537999999999716
time 0.5539999999999716
time 0.5541999999999716
time 0.5543999999999716
time 0.5545999999999716
time 0.5547999999999715
time 0.5549999999999715
time 0.5551999999999715
time 0.5553999999999715
time 0.5555999999999715
time 0.5557999999999714
time 0.5559999999999714
time 0.5561999999999714
time 0.5563999999999714
time 0.5565999999999713
time 0.5567999999999713
time 0.5569999999999713
time 0.5571999999999713
time 0.5573999999999713
time 0.5575999999999712
time 0.5577999999999712
time 0.5579999999999712
time 0.5581999999999712
time 0.5583999999999711
time 0.5585999999999711
time 0.5587999999999711
time 0.5589999999999711
time 0.559199999999971
time 0.559399999999971
time 0.559599999999971
time 0.559799999999971
time 0.559999999999971
time 0.5601999999999709
time 0.5603999999999709
time 0.5605999999999709
time 0.5607999999999709
time 0.5609999999999709
time 0.5611999999999708
time 0.5613999999999708
time 0.5615999999999708
time 0.5617999999999708
time 0.5619999999999707
time 0.5621999999999707
time 0.5623999999999707
time 0.5625999999999707
time 0.5627999999999707
time 0.5629999999999706
time 0.5631999999999706
time 0.5633999999999706
time 0.5635999999999706
time 0.5637999999999705
time 0.5639999999999705
time 0.5641999999999705
time 0.5643999999999705
time 0.5645999999999705
time 0.5647999999999704
time 0.5649999999999704
time 0.5651999999999704
time 0.5653999999999704
time 0.5655999999999703
time 0.5657999999999703
time 0.5659999999999703
time 0.5661999999999703
time 0.5663999999999703
time 0.5665999999999702
time 0.5667999999999702
time 0.5669999999999702
time 0.5671999999999702
time 0.5673999999999702
time 0.5675999999999701
time 0.5677999999999701
time 0.5679999999999701
time 0.5681999999999701
time 0.56839999999997
time 0.56859999999997
time 0.56879999999997
time 0.56899999999997
time 0.56919999999997
time 0.5693999999999699
time 0.5695999999999699
time 0.5697999999999699
time 0.5699999999999699
time 0.5701999999999698
time 0.5703999999999698
time 0.5705999999999698
time 0.5707999999999698
time 0.5709999999999698
time 0.5711999999999697
time 0.5713999999999697
time 0.5715999999999697
time 0.5717999999999697
time 0.5719999999999696
time 0.5721999999999696
time 0.5723999999999696
time 0.5725999999999696
time 0.5727999999999696
time 0.5729999999999695
time 0.5731999999999695
time 0.5733999999999695
time 0.5735999999999695
time 0.5737999999999694
time 0.5739999999999694
time 0.5741999999999694
time 0.5743999999999694
time 0.5745999999999694
time 0.5747999999999693
time 0.5749999999999693
time 0.5751999999999693
time 0.5753999999999693
time 0.5755999999999692
time 0.5757999999999692
time 0.5759999999999692
time 0.5761999999999692
time 0.5763999999999692
time 0.5765999999999691
time 0.5767999999999691
time 0.5769999999999691
time 0.5771999999999691
time 0.577399999999969
time 0.577599999999969
time 0.577799999999969
time 0.577999999999969
time 0.578199999999969
time 0.5783999999999689
time 0.5785999999999689
time 0.5787999999999689
time 0.5789999999999689
time 0.5791999999999689
time 0.5793999999999688
time 0.5795999999999688
time 0.5797999999999688
time 0.5799999999999688
time 0.5801999999999687
time 0.5803999999999687
time 0.5805999999999687
time 0.5807999999999687
time 0.5809999999999687
time 0.5811999999999686
time 0.5813999999999686
time 0.5815999999999686
time 0.5817999999999686
time 0.5819999999999685
time 0.5821999999999685
time 0.5823999999999685
time 0.5825999999999685
time 0.5827999999999685
time 0.5829999999999684
time 0.5831999999999684
time 0.5833999999999684
time 0.5835999999999684
time 0.5837999999999683
time 0.5839999999999683
time 0.5841999999999683
time 0.5843999999999683
time 0.5845999999999683
time 0.5847999999999682
time 0.5849999999999682
time 0.5851999999999682
time 0.5853999999999682
time 0.5855999999999681
time 0.5857999999999681
time 0.5859999999999681
time 0.5861999999999681
time 0.5863999999999681
time 0.586599999999968
time 0.586799999999968
time 0.586999999999968
time 0.587199999999968
time 0.587399999999968
time 0.5875999999999679
time 0.5877999999999679
time 0.5879999999999679
time 0.5881999999999679
time 0.5883999999999678
time 0.5885999999999678
time 0.5887999999999678
time 0.5889999999999678
time 0.5891999999999677
time 0.5893999999999677
time 0.5895999999999677
time 0.5897999999999677
time 0.5899999999999677
time 0.5901999999999676
time 0.5903999999999676
time 0.5905999999999676
time 0.5907999999999676
time 0.5909999999999676
time 0.5911999999999675
time 0.5913999999999675
time 0.5915999999999675
time 0.5917999999999675
time 0.5919999999999674
time 0.5921999999999674
time 0.5923999999999674
time 0.5925999999999674
time 0.5927999999999674
time 0.5929999999999673
time 0.5931999999999673
time 0.5933999999999673
time 0.5935999999999673
time 0.5937999999999672
time 0.5939999999999672
time 0.5941999999999672
time 0.5943999999999672
time 0.5945999999999672
time 0.5947999999999671
time 0.5949999999999671
time 0.5951999999999671
time 0.5953999999999671
time 0.595599999999967
time 0.595799999999967
time 0.595999999999967
time 0.596199999999967
time 0.596399999999967
time 0.5965999999999669
time 0.5967999999999669
time 0.5969999999999669
time 0.5971999999999669
time 0.5973999999999668
time 0.5975999999999668
time 0.5977999999999668
time 0.5979999999999668
time 0.5981999999999668
time 0.5983999999999667
time 0.5985999999999667
time 0.5987999999999667
time 0.5989999999999667
time 0.5991999999999666
time 0.5993999999999666
time 0.5995999999999666
time 0.5997999999999666
time 0.5999999999999666
time 0.6001999999999665
time 0.6003999999999665
time 0.6005999999999665
time 0.6007999999999665
time 0.6009999999999664
time 0.6011999999999664
time 0.6013999999999664
time 0.6015999999999664
time 0.6017999999999664
time 0.6019999999999663
time 0.6021999999999663
time 0.6023999999999663
time 0.6025999999999663
time 0.6027999999999663
time 0.6029999999999662
time 0.6031999999999662
time 0.6033999999999662
time 0.6035999999999662
time 0.6037999999999661
time 0.6039999999999661
time 0.6041999999999661
time 0.6043999999999661
time 0.604599999999966
time 0.604799999999966
time 0.604999999999966
time 0.605199999999966
time 0.605399999999966
time 0.6055999999999659
time 0.6057999999999659
time 0.6059999999999659
time 0.6061999999999659
time 0.6063999999999659
time 0.6065999999999658
time 0.6067999999999658
time 0.6069999999999658
time 0.6071999999999658
time 0.6073999999999657
time 0.6075999999999657
time 0.6077999999999657
time 0.6079999999999657
time 0.6081999999999657
time 0.6083999999999656
time 0.6085999999999656
time 0.6087999999999656
time 0.6089999999999656
time 0.6091999999999655
time 0.6093999999999655
time 0.6095999999999655
time 0.6097999999999655
time 0.6099999999999655
time 0.6101999999999654
time 0.6103999999999654
time 0.6105999999999654
time 0.6107999999999654
time 0.6109999999999653
time 0.6111999999999653
time 0.6113999999999653
time 0.6115999999999653
time 0.6117999999999653
time 0.6119999999999652
time 0.6121999999999652
time 0.6123999999999652
time 0.6125999999999652
time 0.6127999999999652
time 0.6129999999999651
time 0.6131999999999651
time 0.6133999999999651
time 0.6135999999999651
time 0.613799999999965
time 0.613999999999965
time 0.614199999999965
time 0.614399999999965
time 0.614599999999965
time 0.6147999999999649
time 0.6149999999999649
time 0.6151999999999649
time 0.6153999999999649
time 0.6155999999999648
time 0.6157999999999648
time 0.6159999999999648
time 0.6161999999999648
time 0.6163999999999648
time 0.6165999999999647
time 0.6167999999999647
time 0.6169999999999647
time 0.6171999999999647
time 0.6173999999999646
time 0.6175999999999646
time 0.6177999999999646
time 0.6179999999999646
time 0.6181999999999646
time 0.6183999999999645
time 0.6185999999999645
time 0.6187999999999645
time 0.6189999999999645
time 0.6191999999999644
time 0.6193999999999644
time 0.6195999999999644
time 0.6197999999999644
time 0.6199999999999644
time 0.6201999999999643
time 0.6203999999999643
time 0.6205999999999643
time 0.6207999999999643
time 0.6209999999999642
time 0.6211999999999642
time 0.6213999999999642
time 0.6215999999999642
time 0.6217999999999642
time 0.6219999999999641
time 0.6221999999999641
time 0.6223999999999641
time 0.6225999999999641
time 0.622799999999964
time 0.622999999999964
time 0.623199999999964
time 0.623399999999964
time 0.623599999999964
time 0.6237999999999639
time 0.6239999999999639
time 0.6241999999999639
time 0.6243999999999639
time 0.6245999999999639
time 0.6247999999999638
time 0.6249999999999638
time 0.6251999999999638
time 0.6253999999999638
time 0.6255999999999637
time 0.6257999999999637
time 0.6259999999999637
time 0.6261999999999637
time 0.6263999999999637
time 0.6265999999999636
time 0.6267999999999636
time 0.6269999999999636
time 0.6271999999999636
time 0.6273999999999635
time 0.6275999999999635
time 0.6277999999999635
time 0.6279999999999635
time 0.6281999999999635
time 0.6283999999999634
time 0.6285999999999634
time 0.6287999999999634
time 0.6289999999999634
time 0.6291999999999633
time 0.6293999999999633
time 0.6295999999999633
time 0.6297999999999633
time 0.6299999999999633
time 0.6301999999999632
time 0.6303999999999632
time 0.6305999999999632
time 0.6307999999999632
time 0.6309999999999631
time 0.6311999999999631
time 0.6313999999999631
time 0.6315999999999631
time 0.6317999999999631
time 0.631999999999963
time 0.632199999999963
time 0.632399999999963
time 0.632599999999963
time 0.632799999999963
time 0.6329999999999629
time 0.6331999999999629
time 0.6333999999999629
time 0.6335999999999629
time 0.6337999999999628
time 0.6339999999999628
time 0.6341999999999628
time 0.6343999999999628
time 0.6345999999999627
time 0.6347999999999627
time 0.6349999999999627
time 0.6351999999999627
time 0.6353999999999627
time 0.6355999999999626
time 0.6357999999999626
time 0.6359999999999626
time 0.6361999999999626
time 0.6363999999999626
time 0.6365999999999625
time 0.6367999999999625
time 0.6369999999999625
time 0.6371999999999625
time 0.6373999999999624
time 0.6375999999999624
time 0.6377999999999624
time 0.6379999999999624
time 0.6381999999999624
time 0.6383999999999623
time 0.6385999999999623
time 0.6387999999999623
time 0.6389999999999623
time 0.6391999999999622
time 0.6393999999999622
time 0.6395999999999622
time 0.6397999999999622
time 0.6399999999999622
time 0.6401999999999621
time 0.6403999999999621
time 0.6405999999999621
time 0.6407999999999621
time 0.640999999999962
time 0.641199999999962
time 0.641399999999962
time 0.641599999999962
time 0.641799999999962
time 0.6419999999999619
time 0.6421999999999619
time 0.6423999999999619
time 0.6425999999999619
time 0.6427999999999618
time 0.6429999999999618
time 0.6431999999999618
time 0.6433999999999618
time 0.6435999999999618
time 0.6437999999999617
time 0.6439999999999617
time 0.6441999999999617
time 0.6443999999999617
time 0.6445999999999616
time 0.6447999999999616
time 0.6449999999999616
time 0.6451999999999616
time 0.6453999999999616
time 0.6455999999999615
time 0.6457999999999615
time 0.6459999999999615
time 0.6461999999999615
time 0.6463999999999614
time 0.6465999999999614
time 0.6467999999999614
time 0.6469999999999614
time 0.6471999999999614
time 0.6473999999999613
time 0.6475999999999613
time 0.6477999999999613
time 0.6479999999999613
time 0.6481999999999613
time 0.6483999999999612
time 0.6485999999999612
time 0.6487999999999612
time 0.6489999999999612
time 0.6491999999999611
time 0.6493999999999611
time 0.6495999999999611
time 0.6497999999999611
time 0.649999999999961
time 0.650199999999961
time 0.650399999999961
time 0.650599999999961
time 0.650799999999961
time 0.6509999999999609
time 0.6511999999999609
time 0.6513999999999609
time 0.6515999999999609
time 0.6517999999999609
time 0.6519999999999608
time 0.6521999999999608
time 0.6523999999999608
time 0.6525999999999608
time 0.6527999999999607
time 0.6529999999999607
time 0.6531999999999607
time 0.6533999999999607
time 0.6535999999999607
time 0.6537999999999606
time 0.6539999999999606
time 0.6541999999999606
time 0.6543999999999606
time 0.6545999999999605
time 0.6547999999999605
time 0.6549999999999605
time 0.6551999999999605
time 0.6553999999999605
time 0.6555999999999604
time 0.6557999999999604
time 0.6559999999999604
time 0.6561999999999604
time 0.6563999999999603
time 0.6565999999999603
time 0.6567999999999603
time 0.6569999999999603
time 0.6571999999999603
time 0.6573999999999602
time 0.6575999999999602
time 0.6577999999999602
time 0.6579999999999602
time 0.6581999999999602
time 0.6583999999999601
time 0.6585999999999601
time 0.6587999999999601
time 0.6589999999999601
time 0.65919999999996
time 0.65939999999996
time 0.65959999999996
time 0.65979999999996
time 0.65999999999996
time 0.6601999999999599
time 0.6603999999999599
time 0.6605999999999599
time 0.6607999999999599
time 0.6609999999999598
time 0.6611999999999598
time 0.6613999999999598
time 0.6615999999999598
time 0.6617999999999598
time 0.6619999999999597
time 0.6621999999999597
time 0.6623999999999597
time 0.6625999999999597
time 0.6627999999999596
time 0.6629999999999596
time 0.6631999999999596
time 0.6633999999999596
time 0.6635999999999596
time 0.6637999999999595
time 0.6639999999999595
time 0.6641999999999595
time 0.6643999999999595
time 0.6645999999999594
time 0.6647999999999594
time 0.6649999999999594
time 0.6651999999999594
time 0.6653999999999594
time 0.6655999999999593
time 0.6657999999999593
time 0.6659999999999593
time 0.6661999999999593
time 0.6663999999999592
time 0.6665999999999592
time 0.6667999999999592
time 0.6669999999999592
time 0.6671999999999592
time 0.6673999999999591
time 0.6675999999999591
time 0.6677999999999591
time 0.6679999999999591
time 0.668199999999959
time 0.668399999999959
time 0.668599999999959
time 0.668799999999959
time 0.668999999999959
time 0.6691999999999589
time 0.6693999999999589
time 0.6695999999999589
time 0.6697999999999589
time 0.6699999999999589
time 0.6701999999999588
time 0.6703999999999588
time 0.6705999999999588
time 0.6707999999999588
time 0.6709999999999587
time 0.6711999999999587
time 0.6713999999999587
time 0.6715999999999587
time 0.6717999999999587
time 0.6719999999999586
time 0.6721999999999586
time 0.6723999999999586
time 0.6725999999999586
time 0.6727999999999585
time 0.6729999999999585
time 0.6731999999999585
time 0.6733999999999585
time 0.6735999999999585
time 0.6737999999999584
time 0.6739999999999584
time 0.6741999999999584
time 0.6743999999999584
time 0.6745999999999583
time 0.6747999999999583
time 0.6749999999999583
time 0.6751999999999583
time 0.6753999999999583
time 0.6755999999999582
time 0.6757999999999582
time 0.6759999999999582
time 0.6761999999999582
time 0.6763999999999581
time 0.6765999999999581
time 0.6767999999999581
time 0.6769999999999581
time 0.6771999999999581
time 0.677399999999958
time 0.677599999999958
time 0.677799999999958
time 0.677999999999958
time 0.678199999999958
time 0.6783999999999579
time 0.6785999999999579
time 0.6787999999999579
time 0.6789999999999579
time 0.6791999999999578
time 0.6793999999999578
time 0.6795999999999578
time 0.6797999999999578
time 0.6799999999999577
time 0.6801999999999577
time 0.6803999999999577
time 0.6805999999999577
time 0.6807999999999577
time 0.6809999999999576
time 0.6811999999999576
time 0.6813999999999576
time 0.6815999999999576
time 0.6817999999999576
time 0.6819999999999575
time 0.6821999999999575
time 0.6823999999999575
time 0.6825999999999575
time 0.6827999999999574
time 0.6829999999999574
time 0.6831999999999574
time 0.6833999999999574
time 0.6835999999999574
time 0.6837999999999573
time 0.6839999999999573
time 0.6841999999999573
time 0.6843999999999573
time 0.6845999999999572
time 0.6847999999999572
time 0.6849999999999572
time 0.6851999999999572
time 0.6853999999999572
time 0.6855999999999571
time 0.6857999999999571
time 0.6859999999999571
time 0.6861999999999571
time 0.686399999999957
time 0.686599999999957
time 0.686799999999957
time 0.686999999999957
time 0.687199999999957
time 0.6873999999999569
time 0.6875999999999569
time 0.6877999999999569
time 0.6879999999999569
time 0.6881999999999568
time 0.6883999999999568
time 0.6885999999999568
time 0.6887999999999568
time 0.6889999999999568
time 0.6891999999999567
time 0.6893999999999567
time 0.6895999999999567
time 0.6897999999999567
time 0.6899999999999566
time 0.6901999999999566
time 0.6903999999999566
time 0.6905999999999566
time 0.6907999999999566
time 0.6909999999999565
time 0.6911999999999565
time 0.6913999999999565
time 0.6915999999999565
time 0.6917999999999564
time 0.6919999999999564
time 0.6921999999999564
time 0.6923999999999564
time 0.6925999999999564
time 0.6927999999999563
time 0.6929999999999563
time 0.6931999999999563
time 0.6933999999999563
time 0.6935999999999563
time 0.6937999999999562
time 0.6939999999999562
time 0.6941999999999562
time 0.6943999999999562
time 0.6945999999999561
time 0.6947999999999561
time 0.6949999999999561
time 0.6951999999999561
time 0.695399999999956
time 0.695599999999956
time 0.695799999999956
time 0.695999999999956
time 0.696199999999956
time 0.6963999999999559
time 0.6965999999999559
time 0.6967999999999559
time 0.6969999999999559
time 0.6971999999999559
time 0.6973999999999558
time 0.6975999999999558
time 0.6977999999999558
time 0.6979999999999558
time 0.6981999999999557
time 0.6983999999999557
time 0.6985999999999557
time 0.6987999999999557
time 0.6989999999999557
time 0.6991999999999556
time 0.6993999999999556
time 0.6995999999999556
time 0.6997999999999556
time 0.6999999999999555
time 0.7001999999999555
time 0.7003999999999555
time 0.7005999999999555
time 0.7007999999999555
time 0.7009999999999554
time 0.7011999999999554
time 0.7013999999999554
time 0.7015999999999554
time 0.7017999999999553
time 0.7019999999999553
time 0.7021999999999553
time 0.7023999999999553
time 0.7025999999999553
time 0.7027999999999552
time 0.7029999999999552
time 0.7031999999999552
time 0.7033999999999552
time 0.7035999999999552
time 0.7037999999999551
time 0.7039999999999551
time 0.7041999999999551
time 0.7043999999999551
time 0.704599999999955
time 0.704799999999955
time 0.704999999999955
time 0.705199999999955
time 0.705399999999955
time 0.7055999999999549
time 0.7057999999999549
time 0.7059999999999549
time 0.7061999999999549
time 0.7063999999999548
time 0.7065999999999548
time 0.7067999999999548
time 0.7069999999999548
time 0.7071999999999548
time 0.7073999999999547
time 0.7075999999999547
time 0.7077999999999547
time 0.7079999999999547
time 0.7081999999999546
time 0.7083999999999546
time 0.7085999999999546
time 0.7087999999999546
time 0.7089999999999546
time 0.7091999999999545
time 0.7093999999999545
time 0.7095999999999545
time 0.7097999999999545
time 0.7099999999999544
time 0.7101999999999544
time 0.7103999999999544
time 0.7105999999999544
time 0.7107999999999544
time 0.7109999999999543
time 0.7111999999999543
time 0.7113999999999543
time 0.7115999999999543
time 0.7117999999999542
time 0.7119999999999542
time 0.7121999999999542
time 0.7123999999999542
time 0.7125999999999542
time 0.7127999999999541
time 0.7129999999999541
time 0.7131999999999541
time 0.7133999999999541
time 0.713599999999954
time 0.713799999999954
time 0.713999999999954
time 0.714199999999954
time 0.714399999999954
time 0.7145999999999539
time 0.7147999999999539
time 0.7149999999999539
time 0.7151999999999539
time 0.7153999999999539
time 0.7155999999999538
time 0.7157999999999538
time 0.7159999999999538
time 0.7161999999999538
time 0.7163999999999537
time 0.7165999999999537
time 0.7167999999999537
time 0.7169999999999537
time 0.7171999999999537
time 0.7173999999999536
time 0.7175999999999536
time 0.7177999999999536
time 0.7179999999999536
time 0.7181999999999535
time 0.7183999999999535
time 0.7185999999999535
time 0.7187999999999535
time 0.7189999999999535
time 0.7191999999999534
time 0.7193999999999534
time 0.7195999999999534
time 0.7197999999999534
time 0.7199999999999533
time 0.7201999999999533
time 0.7203999999999533
time 0.7205999999999533
time 0.7207999999999533
time 0.7209999999999532
time 0.7211999999999532
time 0.7213999999999532
time 0.7215999999999532
time 0.7217999999999531
time 0.7219999999999531
time 0.7221999999999531
time 0.7223999999999531
time 0.7225999999999531
time 0.722799999999953
time 0.722999999999953
time 0.723199999999953
time 0.723399999999953
time 0.723599999999953
time 0.7237999999999529
time 0.7239999999999529
time 0.7241999999999529
time 0.7243999999999529
time 0.7245999999999528
time 0.7247999999999528
time 0.7249999999999528
time 0.7251999999999528
time 0.7253999999999527
time 0.7255999999999527
time 0.7257999999999527
time 0.7259999999999527
time 0.7261999999999527
time 0.7263999999999526
time 0.7265999999999526
time 0.7267999999999526
time 0.7269999999999526
time 0.7271999999999526
time 0.7273999999999525
time 0.7275999999999525
time 0.7277999999999525
time 0.7279999999999525
time 0.7281999999999524
time 0.7283999999999524
time 0.7285999999999524
time 0.7287999999999524
time 0.7289999999999524
time 0.7291999999999523
time 0.7293999999999523
time 0.7295999999999523
time 0.7297999999999523
time 0.7299999999999522
time 0.7301999999999522
time 0.7303999999999522
time 0.7305999999999522
time 0.7307999999999522
time 0.7309999999999521
time 0.7311999999999521
time 0.7313999999999521
time 0.7315999999999521
time 0.731799999999952
time 0.731999999999952
time 0.732199999999952
time 0.732399999999952
time 0.732599999999952
time 0.7327999999999519
time 0.7329999999999519
time 0.7331999999999519
time 0.7333999999999519
time 0.7335999999999518
time 0.7337999999999518
time 0.7339999999999518
time 0.7341999999999518
time 0.7343999999999518
time 0.7345999999999517
time 0.7347999999999517
time 0.7349999999999517
time 0.7351999999999517
time 0.7353999999999516
time 0.7355999999999516
time 0.7357999999999516
time 0.7359999999999516
time 0.7361999999999516
time 0.7363999999999515
time 0.7365999999999515
time 0.7367999999999515
time 0.7369999999999515
time 0.7371999999999514
time 0.7373999999999514
time 0.7375999999999514
time 0.7377999999999514
time 0.7379999999999514
time 0.7381999999999513
time 0.7383999999999513
time 0.7385999999999513
time 0.7387999999999513
time 0.7389999999999513
time 0.7391999999999512
time 0.7393999999999512
time 0.7395999999999512
time 0.7397999999999512
time 0.7399999999999511
time 0.7401999999999511
time 0.7403999999999511
time 0.7405999999999511
time 0.740799999999951
time 0.740999999999951
time 0.741199999999951
time 0.741399999999951
time 0.741599999999951
time 0.7417999999999509
time 0.7419999999999509
time 0.7421999999999509
time 0.7423999999999509
time 0.7425999999999509
time 0.7427999999999508
time 0.7429999999999508
time 0.7431999999999508
time 0.7433999999999508
time 0.7435999999999507
time 0.7437999999999507
time 0.7439999999999507
time 0.7441999999999507
time 0.7443999999999507
time 0.7445999999999506
time 0.7447999999999506
time 0.7449999999999506
time 0.7451999999999506
time 0.7453999999999505
time 0.7455999999999505
time 0.7457999999999505
time 0.7459999999999505
time 0.7461999999999505
time 0.7463999999999504
time 0.7465999999999504
time 0.7467999999999504
time 0.7469999999999504
time 0.7471999999999503
time 0.7473999999999503
time 0.7475999999999503
time 0.7477999999999503
time 0.7479999999999503
time 0.7481999999999502
time 0.7483999999999502
time 0.7485999999999502
time 0.7487999999999502
time 0.7489999999999502
time 0.7491999999999501
time 0.7493999999999501
time 0.7495999999999501
time 0.7497999999999501
time 0.74999999999995
time 0.75019999999995
time 0.75039999999995
time 0.75059999999995
time 0.75079999999995
time 0.7509999999999499
time 0.7511999999999499
time 0.7513999999999499
time 0.7515999999999499
time 0.7517999999999498
time 0.7519999999999498
time 0.7521999999999498
time 0.7523999999999498
time 0.7525999999999498
time 0.7527999999999497
time 0.7529999999999497
time 0.7531999999999497
time 0.7533999999999497
time 0.7535999999999496
time 0.7537999999999496
time 0.7539999999999496
time 0.7541999999999496
time 0.7543999999999496
time 0.7545999999999495
time 0.7547999999999495
time 0.7549999999999495
time 0.7551999999999495
time 0.7553999999999494
time 0.7555999999999494
time 0.7557999999999494
time 0.7559999999999494
time 0.7561999999999494
time 0.7563999999999493
time 0.7565999999999493
time 0.7567999999999493
time 0.7569999999999493
time 0.7571999999999492
time 0.7573999999999492
time 0.7575999999999492
time 0.7577999999999492
time 0.7579999999999492
time 0.7581999999999491
time 0.7583999999999491
time 0.7585999999999491
time 0.7587999999999491
time 0.758999999999949
time 0.759199999999949
time 0.759399999999949
time 0.759599999999949
time 0.759799999999949
time 0.7599999999999489
time 0.7601999999999489
time 0.7603999999999489
time 0.7605999999999489
time 0.7607999999999489
time 0.7609999999999488
time 0.7611999999999488
time 0.7613999999999488
time 0.7615999999999488
time 0.7617999999999487
time 0.7619999999999487
time 0.7621999999999487
time 0.7623999999999487
time 0.7625999999999487
time 0.7627999999999486
time 0.7629999999999486
time 0.7631999999999486
time 0.7633999999999486
time 0.7635999999999485
time 0.7637999999999485
time 0.7639999999999485
time 0.7641999999999485
time 0.7643999999999485
time 0.7645999999999484
time 0.7647999999999484
time 0.7649999999999484
time 0.7651999999999484
time 0.7653999999999483
time 0.7655999999999483
time 0.7657999999999483
time 0.7659999999999483
time 0.7661999999999483
time 0.7663999999999482
time 0.7665999999999482
time 0.7667999999999482
time 0.7669999999999482
time 0.7671999999999481
time 0.7673999999999481
time 0.7675999999999481
time 0.7677999999999481
time 0.7679999999999481
time 0.768199999999948
time 0.768399999999948
time 0.768599999999948
time 0.768799999999948
time 0.768999999999948
time 0.7691999999999479
time 0.7693999999999479
time 0.7695999999999479
time 0.7697999999999479
time 0.7699999999999478
time 0.7701999999999478
time 0.7703999999999478
time 0.7705999999999478
time 0.7707999999999477
time 0.7709999999999477
time 0.7711999999999477
time 0.7713999999999477
time 0.7715999999999477
time 0.7717999999999476
time 0.7719999999999476
time 0.7721999999999476
time 0.7723999999999476
time 0.7725999999999476
time 0.7727999999999475
time 0.7729999999999475
time 0.7731999999999475
time 0.7733999999999475
time 0.7735999999999474
time 0.7737999999999474
time 0.7739999999999474
time 0.7741999999999474
time 0.7743999999999474
time 0.7745999999999473
time 0.7747999999999473
time 0.7749999999999473
time 0.7751999999999473
time 0.7753999999999472
time 0.7755999999999472
time 0.7757999999999472
time 0.7759999999999472
time 0.7761999999999472
time 0.7763999999999471
time 0.7765999999999471
time 0.7767999999999471
time 0.7769999999999471
time 0.777199999999947
time 0.777399999999947
time 0.777599999999947
time 0.777799999999947
time 0.777999999999947
time 0.7781999999999469
time 0.7783999999999469
time 0.7785999999999469
time 0.7787999999999469
time 0.7789999999999468
time 0.7791999999999468
time 0.7793999999999468
time 0.7795999999999468
time 0.7797999999999468
time 0.7799999999999467
time 0.7801999999999467
time 0.7803999999999467
time 0.7805999999999467
time 0.7807999999999466
time 0.7809999999999466
time 0.7811999999999466
time 0.7813999999999466
time 0.7815999999999466
time 0.7817999999999465
time 0.7819999999999465
time 0.7821999999999465
time 0.7823999999999465
time 0.7825999999999464
time 0.7827999999999464
time 0.7829999999999464
time 0.7831999999999464
time 0.7833999999999464
time 0.7835999999999463
time 0.7837999999999463
time 0.7839999999999463
time 0.7841999999999463
time 0.7843999999999463
time 0.7845999999999462
time 0.7847999999999462
time 0.7849999999999462
time 0.7851999999999462
time 0.7853999999999461
time 0.7855999999999461
time 0.7857999999999461
time 0.7859999999999461
time 0.786199999999946
time 0.786399999999946
time 0.786599999999946
time 0.786799999999946
time 0.786999999999946
time 0.7871999999999459
time 0.7873999999999459
time 0.7875999999999459
time 0.7877999999999459
time 0.7879999999999459
time 0.7881999999999458
time 0.7883999999999458
time 0.7885999999999458
time 0.7887999999999458
time 0.7889999999999457
time 0.7891999999999457
time 0.7893999999999457
time 0.7895999999999457
time 0.7897999999999457
time 0.7899999999999456
time 0.7901999999999456
time 0.7903999999999456
time 0.7905999999999456
time 0.7907999999999455
time 0.7909999999999455
time 0.7911999999999455
time 0.7913999999999455
time 0.7915999999999455
time 0.7917999999999454
time 0.7919999999999454
time 0.7921999999999454
time 0.7923999999999454
time 0.7925999999999453
time 0.7927999999999453
time 0.7929999999999453
time 0.7931999999999453
time 0.7933999999999453
time 0.7935999999999452
time 0.7937999999999452
time 0.7939999999999452
time 0.7941999999999452
time 0.7943999999999452
time 0.7945999999999451
time 0.7947999999999451
time 0.7949999999999451
time 0.7951999999999451
time 0.795399999999945
time 0.795599999999945
time 0.795799999999945
time 0.795999999999945
time 0.796199999999945
time 0.7963999999999449
time 0.7965999999999449
time 0.7967999999999449
time 0.7969999999999449
time 0.7971999999999448
time 0.7973999999999448
time 0.7975999999999448
time 0.7977999999999448
time 0.7979999999999448
time 0.7981999999999447
time 0.7983999999999447
time 0.7985999999999447
time 0.7987999999999447
time 0.7989999999999446
time 0.7991999999999446
time 0.7993999999999446
time 0.7995999999999446
time 0.7997999999999446
time 0.7999999999999445
time 0.8001999999999445
time 0.8003999999999445
time 0.8005999999999445
time 0.8007999999999444
time 0.8009999999999444
time 0.8011999999999444
time 0.8013999999999444
time 0.8015999999999444
time 0.8017999999999443
time 0.8019999999999443
time 0.8021999999999443
time 0.8023999999999443
time 0.8025999999999442
time 0.8027999999999442
time 0.8029999999999442
time 0.8031999999999442
time 0.8033999999999442
time 0.8035999999999441
time 0.8037999999999441
time 0.8039999999999441
time 0.8041999999999441
time 0.804399999999944
time 0.804599999999944
time 0.804799999999944
time 0.804999999999944
time 0.805199999999944
time 0.8053999999999439
time 0.8055999999999439
time 0.8057999999999439
time 0.8059999999999439
time 0.8061999999999439
time 0.8063999999999438
time 0.8065999999999438
time 0.8067999999999438
time 0.8069999999999438
time 0.8071999999999437
time 0.8073999999999437
time 0.8075999999999437
time 0.8077999999999437
time 0.8079999999999437
time 0.8081999999999436
time 0.8083999999999436
time 0.8085999999999436
time 0.8087999999999436
time 0.8089999999999435
time 0.8091999999999435
time 0.8093999999999435
time 0.8095999999999435
time 0.8097999999999435
time 0.8099999999999434
time 0.8101999999999434
time 0.8103999999999434
time 0.8105999999999434
time 0.8107999999999433
time 0.8109999999999433
time 0.8111999999999433
time 0.8113999999999433
time 0.8115999999999433
time 0.8117999999999432
time 0.8119999999999432
time 0.8121999999999432
time 0.8123999999999432
time 0.8125999999999431
time 0.8127999999999431
time 0.8129999999999431
time 0.8131999999999431
time 0.8133999999999431
time 0.813599999999943
time 0.813799999999943
time 0.813999999999943
time 0.814199999999943
time 0.814399999999943
time 0.8145999999999429
time 0.8147999999999429
time 0.8149999999999429
time 0.8151999999999429
time 0.8153999999999428
time 0.8155999999999428
time 0.8157999999999428
time 0.8159999999999428
time 0.8161999999999427
time 0.8163999999999427
time 0.8165999999999427
time 0.8167999999999427
time 0.8169999999999427
time 0.8171999999999426
time 0.8173999999999426
time 0.8175999999999426
time 0.8177999999999426
time 0.8179999999999426
time 0.8181999999999425
time 0.8183999999999425
time 0.8185999999999425
time 0.8187999999999425
time 0.8189999999999424
time 0.8191999999999424
time 0.8193999999999424
time 0.8195999999999424
time 0.8197999999999424
time 0.8199999999999423
time 0.8201999999999423
time 0.8203999999999423
time 0.8205999999999423
time 0.8207999999999422
time 0.8209999999999422
time 0.8211999999999422
time 0.8213999999999422
time 0.8215999999999422
time 0.8217999999999421
time 0.8219999999999421
time 0.8221999999999421
time 0.8223999999999421
time 0.822599999999942
time 0.822799999999942
time 0.822999999999942
time 0.823199999999942
time 0.823399999999942
time 0.8235999999999419
time 0.8237999999999419
time 0.8239999999999419
time 0.8241999999999419
time 0.8243999999999418
time 0.8245999999999418
time 0.8247999999999418
time 0.8249999999999418
time 0.8251999999999418
time 0.8253999999999417
time 0.8255999999999417
time 0.8257999999999417
time 0.8259999999999417
time 0.8261999999999416
time 0.8263999999999416
time 0.8265999999999416
time 0.8267999999999416
time 0.8269999999999416
time 0.8271999999999415
time 0.8273999999999415
time 0.8275999999999415
time 0.8277999999999415
time 0.8279999999999414
time 0.8281999999999414
time 0.8283999999999414
time 0.8285999999999414
time 0.8287999999999414
time 0.8289999999999413
time 0.8291999999999413
time 0.8293999999999413
time 0.8295999999999413
time 0.8297999999999413
time 0.8299999999999412
time 0.8301999999999412
time 0.8303999999999412
time 0.8305999999999412
time 0.8307999999999411
time 0.8309999999999411
time 0.8311999999999411
time 0.8313999999999411
time 0.831599999999941
time 0.831799999999941
time 0.831999999999941
time 0.832199999999941
time 0.832399999999941
time 0.8325999999999409
time 0.8327999999999409
time 0.8329999999999409
time 0.8331999999999409
time 0.8333999999999409
time 0.8335999999999408
time 0.8337999999999408
time 0.8339999999999408
time 0.8341999999999408
time 0.8343999999999407
time 0.8345999999999407
time 0.8347999999999407
time 0.8349999999999407
time 0.8351999999999407
time 0.8353999999999406
time 0.8355999999999406
time 0.8357999999999406
time 0.8359999999999406
time 0.8361999999999405
time 0.8363999999999405
time 0.8365999999999405
time 0.8367999999999405
time 0.8369999999999405
time 0.8371999999999404
time 0.8373999999999404
time 0.8375999999999404
time 0.8377999999999404
time 0.8379999999999403
time 0.8381999999999403
time 0.8383999999999403
time 0.8385999999999403
time 0.8387999999999403
time 0.8389999999999402
time 0.8391999999999402
time 0.8393999999999402
time 0.8395999999999402
time 0.8397999999999401
time 0.8399999999999401
time 0.8401999999999401
time 0.8403999999999401
time 0.8405999999999401
time 0.84079999999994
time 0.84099999999994
time 0.84119999999994
time 0.84139999999994
time 0.84159999999994
time 0.8417999999999399
time 0.8419999999999399
time 0.8421999999999399
time 0.8423999999999399
time 0.8425999999999398
time 0.8427999999999398
time 0.8429999999999398
time 0.8431999999999398
time 0.8433999999999398
time 0.8435999999999397
time 0.8437999999999397
time 0.8439999999999397
time 0.8441999999999397
time 0.8443999999999396
time 0.8445999999999396
time 0.8447999999999396
time 0.8449999999999396
time 0.8451999999999396
time 0.8453999999999395
time 0.8455999999999395
time 0.8457999999999395
time 0.8459999999999395
time 0.8461999999999394
time 0.8463999999999394
time 0.8465999999999394
time 0.8467999999999394
time 0.8469999999999394
time 0.8471999999999393
time 0.8473999999999393
time 0.8475999999999393
time 0.8477999999999393
time 0.8479999999999392
time 0.8481999999999392
time 0.8483999999999392
time 0.8485999999999392
time 0.8487999999999392
time 0.8489999999999391
time 0.8491999999999391
time 0.8493999999999391
time 0.8495999999999391
time 0.849799999999939
time 0.849999999999939
time 0.850199999999939
time 0.850399999999939
time 0.850599999999939
time 0.8507999999999389
time 0.8509999999999389
time 0.8511999999999389
time 0.8513999999999389
time 0.8515999999999389
time 0.8517999999999388
time 0.8519999999999388
time 0.8521999999999388
time 0.8523999999999388
time 0.8525999999999387
time 0.8527999999999387
time 0.8529999999999387
time 0.8531999999999387
time 0.8533999999999387
time 0.8535999999999386
time 0.8537999999999386
time 0.8539999999999386
time 0.8541999999999386
time 0.8543999999999385
time 0.8545999999999385
time 0.8547999999999385
time 0.8549999999999385
time 0.8551999999999385
time 0.8553999999999384
time 0.8555999999999384
time 0.8557999999999384
time 0.8559999999999384
time 0.8561999999999383
time 0.8563999999999383
time 0.8565999999999383
time 0.8567999999999383
time 0.8569999999999383
time 0.8571999999999382
time 0.8573999999999382
time 0.8575999999999382
time 0.8577999999999382
time 0.8579999999999381
time 0.8581999999999381
time 0.8583999999999381
time 0.8585999999999381
time 0.8587999999999381
time 0.858999999999938
time 0.859199999999938
time 0.859399999999938
time 0.859599999999938
time 0.859799999999938
time 0.8599999999999379
time 0.8601999999999379
time 0.8603999999999379
time 0.8605999999999379
time 0.8607999999999378
time 0.8609999999999378
time 0.8611999999999378
time 0.8613999999999378
time 0.8615999999999377
time 0.8617999999999377
time 0.8619999999999377
time 0.8621999999999377
time 0.8623999999999377
time 0.8625999999999376
time 0.8627999999999376
time 0.8629999999999376
time 0.8631999999999376
time 0.8633999999999376
time 0.8635999999999375
time 0.8637999999999375
time 0.8639999999999375
time 0.8641999999999375
time 0.8643999999999374
time 0.8645999999999374
time 0.8647999999999374
time 0.8649999999999374
time 0.8651999999999374
time 0.8653999999999373
time 0.8655999999999373
time 0.8657999999999373
time 0.8659999999999373
time 0.8661999999999372
time 0.8663999999999372
time 0.8665999999999372
time 0.8667999999999372
time 0.8669999999999372
time 0.8671999999999371
time 0.8673999999999371
time 0.8675999999999371
time 0.8677999999999371
time 0.867999999999937
time 0.868199999999937
time 0.868399999999937
time 0.868599999999937
time 0.868799999999937
time 0.8689999999999369
time 0.8691999999999369
time 0.8693999999999369
time 0.8695999999999369
time 0.8697999999999368
time 0.8699999999999368
time 0.8701999999999368
time 0.8703999999999368
time 0.8705999999999368
time 0.8707999999999367
time 0.8709999999999367
time 0.8711999999999367
time 0.8713999999999367
time 0.8715999999999366
time 0.8717999999999366
time 0.8719999999999366
time 0.8721999999999366
time 0.8723999999999366
time 0.8725999999999365
time 0.8727999999999365
time 0.8729999999999365
time 0.8731999999999365
time 0.8733999999999364
time 0.8735999999999364
time 0.8737999999999364
time 0.8739999999999364
time 0.8741999999999364
time 0.8743999999999363
time 0.8745999999999363
time 0.8747999999999363
time 0.8749999999999363
time 0.8751999999999363
time 0.8753999999999362
time 0.8755999999999362
time 0.8757999999999362
time 0.8759999999999362
time 0.8761999999999361
time 0.8763999999999361
time 0.8765999999999361
time 0.8767999999999361
time 0.876999999999936
time 0.877199999999936
time 0.877399999999936
time 0.877599999999936
time 0.877799999999936
time 0.8779999999999359
time 0.8781999999999359
time 0.8783999999999359
time 0.8785999999999359
time 0.8787999999999359
time 0.8789999999999358
time 0.8791999999999358
time 0.8793999999999358
time 0.8795999999999358
time 0.8797999999999357
time 0.8799999999999357
time 0.8801999999999357
time 0.8803999999999357
time 0.8805999999999357
time 0.8807999999999356
time 0.8809999999999356
time 0.8811999999999356
time 0.8813999999999356
time 0.8815999999999355
time 0.8817999999999355
time 0.8819999999999355
time 0.8821999999999355
time 0.8823999999999355
time 0.8825999999999354
time 0.8827999999999354
time 0.8829999999999354
time 0.8831999999999354
time 0.8833999999999353
time 0.8835999999999353
time 0.8837999999999353
time 0.8839999999999353
time 0.8841999999999353
time 0.8843999999999352
time 0.8845999999999352
time 0.8847999999999352
time 0.8849999999999352
time 0.8851999999999351
time 0.8853999999999351
time 0.8855999999999351
time 0.8857999999999351
time 0.8859999999999351
time 0.886199999999935
time 0.886399999999935
time 0.886599999999935
time 0.886799999999935
time 0.886999999999935
time 0.8871999999999349
time 0.8873999999999349
time 0.8875999999999349
time 0.8877999999999349
time 0.8879999999999348
time 0.8881999999999348
time 0.8883999999999348
time 0.8885999999999348
time 0.8887999999999348
time 0.8889999999999347
time 0.8891999999999347
time 0.8893999999999347
time 0.8895999999999347
time 0.8897999999999346
time 0.8899999999999346
time 0.8901999999999346
time 0.8903999999999346
time 0.8905999999999346
time 0.8907999999999345
time 0.8909999999999345
time 0.8911999999999345
time 0.8913999999999345
time 0.8915999999999344
time 0.8917999999999344
time 0.8919999999999344
time 0.8921999999999344
time 0.8923999999999344
time 0.8925999999999343
time 0.8927999999999343
time 0.8929999999999343
time 0.8931999999999343
time 0.8933999999999342
time 0.8935999999999342
time 0.8937999999999342
time 0.8939999999999342
time 0.8941999999999342
time 0.8943999999999341
time 0.8945999999999341
time 0.8947999999999341
time 0.8949999999999341
time 0.895199999999934
time 0.895399999999934
time 0.895599999999934
time 0.895799999999934
time 0.895999999999934
time 0.8961999999999339
time 0.8963999999999339
time 0.8965999999999339
time 0.8967999999999339
time 0.8969999999999339
time 0.8971999999999338
time 0.8973999999999338
time 0.8975999999999338
time 0.8977999999999338
time 0.8979999999999337
time 0.8981999999999337
time 0.8983999999999337
time 0.8985999999999337
time 0.8987999999999337
time 0.8989999999999336
time 0.8991999999999336
time 0.8993999999999336
time 0.8995999999999336
time 0.8997999999999335
time 0.8999999999999335
time 0.9001999999999335
time 0.9003999999999335
time 0.9005999999999335
time 0.9007999999999334
time 0.9009999999999334
time 0.9011999999999334
time 0.9013999999999334
time 0.9015999999999333
time 0.9017999999999333
time 0.9019999999999333
time 0.9021999999999333
time 0.9023999999999333
time 0.9025999999999332
time 0.9027999999999332
time 0.9029999999999332
time 0.9031999999999332
time 0.9033999999999331
time 0.9035999999999331
time 0.9037999999999331
time 0.9039999999999331
time 0.9041999999999331
time 0.904399999999933
time 0.904599999999933
time 0.904799999999933
time 0.904999999999933
time 0.905199999999933
time 0.9053999999999329
time 0.9055999999999329
time 0.9057999999999329
time 0.9059999999999329
time 0.9061999999999328
time 0.9063999999999328
time 0.9065999999999328
time 0.9067999999999328
time 0.9069999999999327
time 0.9071999999999327
time 0.9073999999999327
time 0.9075999999999327
time 0.9077999999999327
time 0.9079999999999326
time 0.9081999999999326
time 0.9083999999999326
time 0.9085999999999326
time 0.9087999999999326
time 0.9089999999999325
time 0.9091999999999325
time 0.9093999999999325
time 0.9095999999999325
time 0.9097999999999324
time 0.9099999999999324
time 0.9101999999999324
time 0.9103999999999324
time 0.9105999999999324
time 0.9107999999999323
time 0.9109999999999323
time 0.9111999999999323
time 0.9113999999999323
time 0.9115999999999322
time 0.9117999999999322
time 0.9119999999999322
time 0.9121999999999322
time 0.9123999999999322
time 0.9125999999999321
time 0.9127999999999321
time 0.9129999999999321
time 0.9131999999999321
time 0.913399999999932
time 0.913599999999932
time 0.913799999999932
time 0.913999999999932
time 0.914199999999932
time 0.9143999999999319
time 0.9145999999999319
time 0.9147999999999319
time 0.9149999999999319
time 0.9151999999999318
time 0.9153999999999318
time 0.9155999999999318
time 0.9157999999999318
time 0.9159999999999318
time 0.9161999999999317
time 0.9163999999999317
time 0.9165999999999317
time 0.9167999999999317
time 0.9169999999999316
time 0.9171999999999316
time 0.9173999999999316
time 0.9175999999999316
time 0.9177999999999316
time 0.9179999999999315
time 0.9181999999999315
time 0.9183999999999315
time 0.9185999999999315
time 0.9187999999999314
time 0.9189999999999314
time 0.9191999999999314
time 0.9193999999999314
time 0.9195999999999314
time 0.9197999999999313
time 0.9199999999999313
time 0.9201999999999313
time 0.9203999999999313
time 0.9205999999999313
time 0.9207999999999312
time 0.9209999999999312
time 0.9211999999999312
time 0.9213999999999312
time 0.9215999999999311
time 0.9217999999999311
time 0.9219999999999311
time 0.9221999999999311
time 0.922399999999931
time 0.922599999999931
time 0.922799999999931
time 0.922999999999931
time 0.923199999999931
time 0.9233999999999309
time 0.9235999999999309
time 0.9237999999999309
time 0.9239999999999309
time 0.9241999999999309
time 0.9243999999999308
time 0.9245999999999308
time 0.9247999999999308
time 0.9249999999999308
time 0.9251999999999307
time 0.9253999999999307
time 0.9255999999999307
time 0.9257999999999307
time 0.9259999999999307
time 0.9261999999999306
time 0.9263999999999306
time 0.9265999999999306
time 0.9267999999999306
time 0.9269999999999305
time 0.9271999999999305
time 0.9273999999999305
time 0.9275999999999305
time 0.9277999999999305
time 0.9279999999999304
time 0.9281999999999304
time 0.9283999999999304
time 0.9285999999999304
time 0.9287999999999303
time 0.9289999999999303
time 0.9291999999999303
time 0.9293999999999303
time 0.9295999999999303
time 0.9297999999999302
time 0.9299999999999302
time 0.9301999999999302
time 0.9303999999999302
time 0.9305999999999301
time 0.9307999999999301
time 0.9309999999999301
time 0.9311999999999301
time 0.9313999999999301
time 0.93159999999993
time 0.93179999999993
time 0.93199999999993
time 0.93219999999993
time 0.93239999999993
time 0.9325999999999299
time 0.9327999999999299
time 0.9329999999999299
time 0.9331999999999299
time 0.9333999999999298
time 0.9335999999999298
time 0.9337999999999298
time 0.9339999999999298
time 0.9341999999999298
time 0.9343999999999297
time 0.9345999999999297
time 0.9347999999999297
time 0.9349999999999297
time 0.9351999999999296
time 0.9353999999999296
time 0.9355999999999296
time 0.9357999999999296
time 0.9359999999999296
time 0.9361999999999295
time 0.9363999999999295
time 0.9365999999999295
time 0.9367999999999295
time 0.9369999999999294
time 0.9371999999999294
time 0.9373999999999294
time 0.9375999999999294
time 0.9377999999999294
time 0.9379999999999293
time 0.9381999999999293
time 0.9383999999999293
time 0.9385999999999293
time 0.9387999999999292
time 0.9389999999999292
time 0.9391999999999292
time 0.9393999999999292
time 0.9395999999999292
time 0.9397999999999291
time 0.9399999999999291
time 0.9401999999999291
time 0.9403999999999291
time 0.940599999999929
time 0.940799999999929
time 0.940999999999929
time 0.941199999999929
time 0.941399999999929
time 0.9415999999999289
time 0.9417999999999289
time 0.9419999999999289
time 0.9421999999999289
time 0.9423999999999289
time 0.9425999999999288
time 0.9427999999999288
time 0.9429999999999288
time 0.9431999999999288
time 0.9433999999999287
time 0.9435999999999287
time 0.9437999999999287
time 0.9439999999999287
time 0.9441999999999287
time 0.9443999999999286
time 0.9445999999999286
time 0.9447999999999286
time 0.9449999999999286
time 0.9451999999999285
time 0.9453999999999285
time 0.9455999999999285
time 0.9457999999999285
time 0.9459999999999285
time 0.9461999999999284
time 0.9463999999999284
time 0.9465999999999284
time 0.9467999999999284
time 0.9469999999999283
time 0.9471999999999283
time 0.9473999999999283
time 0.9475999999999283
time 0.9477999999999283
time 0.9479999999999282
time 0.9481999999999282
time 0.9483999999999282
time 0.9485999999999282
time 0.9487999999999281
time 0.9489999999999281
time 0.9491999999999281
time 0.9493999999999281
time 0.9495999999999281
time 0.949799999999928
time 0.949999999999928
time 0.950199999999928
time 0.950399999999928
time 0.950599999999928
time 0.9507999999999279
time 0.9509999999999279
time 0.9511999999999279
time 0.9513999999999279
time 0.9515999999999278
time 0.9517999999999278
time 0.9519999999999278
time 0.9521999999999278
time 0.9523999999999277
time 0.9525999999999277
time 0.9527999999999277
time 0.9529999999999277
time 0.9531999999999277
time 0.9533999999999276
time 0.9535999999999276
time 0.9537999999999276
time 0.9539999999999276
time 0.9541999999999276
time 0.9543999999999275
time 0.9545999999999275
time 0.9547999999999275
time 0.9549999999999275
time 0.9551999999999274
time 0.9553999999999274
time 0.9555999999999274
time 0.9557999999999274
time 0.9559999999999274
time 0.9561999999999273
time 0.9563999999999273
time 0.9565999999999273
time 0.9567999999999273
time 0.9569999999999272
time 0.9571999999999272
time 0.9573999999999272
time 0.9575999999999272
time 0.9577999999999272
time 0.9579999999999271
time 0.9581999999999271
time 0.9583999999999271
time 0.9585999999999271
time 0.958799999999927
time 0.958999999999927
time 0.959199999999927
time 0.959399999999927
time 0.959599999999927
time 0.9597999999999269
time 0.9599999999999269
time 0.9601999999999269
time 0.9603999999999269
time 0.9605999999999268
time 0.9607999999999268
time 0.9609999999999268
time 0.9611999999999268
time 0.9613999999999268
time 0.9615999999999267
time 0.9617999999999267
time 0.9619999999999267
time 0.9621999999999267
time 0.9623999999999266
time 0.9625999999999266
time 0.9627999999999266
time 0.9629999999999266
time 0.9631999999999266
time 0.9633999999999265
time 0.9635999999999265
time 0.9637999999999265
time 0.9639999999999265
time 0.9641999999999264
time 0.9643999999999264
time 0.9645999999999264
time 0.9647999999999264
time 0.9649999999999264
time 0.9651999999999263
time 0.9653999999999263
time 0.9655999999999263
time 0.9657999999999263
time 0.9659999999999263
time 0.9661999999999262
time 0.9663999999999262
time 0.9665999999999262
time 0.9667999999999262
time 0.9669999999999261
time 0.9671999999999261
time 0.9673999999999261
time 0.9675999999999261
time 0.967799999999926
time 0.967999999999926
time 0.968199999999926
time 0.968399999999926
time 0.968599999999926
time 0.9687999999999259
time 0.9689999999999259
time 0.9691999999999259
time 0.9693999999999259
time 0.9695999999999259
time 0.9697999999999258
time 0.9699999999999258
time 0.9701999999999258
time 0.9703999999999258
time 0.9705999999999257
time 0.9707999999999257
time 0.9709999999999257
time 0.9711999999999257
time 0.9713999999999257
time 0.9715999999999256
time 0.9717999999999256
time 0.9719999999999256
time 0.9721999999999256
time 0.9723999999999255
time 0.9725999999999255
time 0.9727999999999255
time 0.9729999999999255
time 0.9731999999999255
time 0.9733999999999254
time 0.9735999999999254
time 0.9737999999999254
time 0.9739999999999254
time 0.9741999999999253
time 0.9743999999999253
time 0.9745999999999253
time 0.9747999999999253
time 0.9749999999999253
time 0.9751999999999252
time 0.9753999999999252
time 0.9755999999999252
time 0.9757999999999252
time 0.9759999999999251
time 0.9761999999999251
time 0.9763999999999251
time 0.9765999999999251
time 0.9767999999999251
time 0.976999999999925
time 0.977199999999925
time 0.977399999999925
time 0.977599999999925
time 0.977799999999925
time 0.9779999999999249
time 0.9781999999999249
time 0.9783999999999249
time 0.9785999999999249
time 0.9787999999999248
time 0.9789999999999248
time 0.9791999999999248
time 0.9793999999999248
time 0.9795999999999248
time 0.9797999999999247
time 0.9799999999999247
time 0.9801999999999247
time 0.9803999999999247
time 0.9805999999999246
time 0.9807999999999246
time 0.9809999999999246
time 0.9811999999999246
time 0.9813999999999246
time 0.9815999999999245
time 0.9817999999999245
time 0.9819999999999245
time 0.9821999999999245
time 0.9823999999999244
time 0.9825999999999244
time 0.9827999999999244
time 0.9829999999999244
time 0.9831999999999244
time 0.9833999999999243
time 0.9835999999999243
time 0.9837999999999243
time 0.9839999999999243
time 0.9841999999999242
time 0.9843999999999242
time 0.9845999999999242
time 0.9847999999999242
time 0.9849999999999242
time 0.9851999999999241
time 0.9853999999999241
time 0.9855999999999241
time 0.9857999999999241
time 0.985999999999924
time 0.986199999999924
time 0.986399999999924
time 0.986599999999924
time 0.986799999999924
time 0.9869999999999239
time 0.9871999999999239
time 0.9873999999999239
time 0.9875999999999239
time 0.9877999999999239
time 0.9879999999999238
time 0.9881999999999238
time 0.9883999999999238
time 0.9885999999999238
time 0.9887999999999237
time 0.9889999999999237
time 0.9891999999999237
time 0.9893999999999237
time 0.9895999999999237
time 0.9897999999999236
time 0.9899999999999236
time 0.9901999999999236
time 0.9903999999999236
time 0.9905999999999235
time 0.9907999999999235
time 0.9909999999999235
time 0.9911999999999235
time 0.9913999999999235
time 0.9915999999999234
time 0.9917999999999234
time 0.9919999999999234
time 0.9921999999999234
time 0.9923999999999233
time 0.9925999999999233
time 0.9927999999999233
time 0.9929999999999233
time 0.9931999999999233
time 0.9933999999999232
time 0.9935999999999232
time 0.9937999999999232
time 0.9939999999999232
time 0.9941999999999231
time 0.9943999999999231
time 0.9945999999999231
time 0.9947999999999231
time 0.9949999999999231
time 0.995199999999923
time 0.995399999999923
time 0.995599999999923
time 0.995799999999923
time 0.995999999999923
time 0.9961999999999229
time 0.9963999999999229
time 0.9965999999999229
time 0.9967999999999229
time 0.9969999999999228
time 0.9971999999999228
time 0.9973999999999228
time 0.9975999999999228
time 0.9977999999999227
time 0.9979999999999227
time 0.9981999999999227
time 0.9983999999999227
time 0.9985999999999227
time 0.9987999999999226
time 0.9989999999999226
time 0.9991999999999226
time 0.9993999999999226
time 0.9995999999999226
time 0.9997999999999225
time 0.9999999999999225
[ ]:
A 3D example¶
[10]:
from netgen.occ import *
from ngsolve import *
from ngsolve.solvers import *
from ngsolve.webgui import Draw
from netgen.webgui import Draw as DrawGeo
[11]:
box = Box((0,0,0), (1,1,0.5))
rod = Cylinder((0.5, 0.5, -0.5),Z,0.2,1.5)
rod.faces.name="contact1"
block = box-rod
block.faces.Min(X).name="fix"
rod.faces.name="contact2"
rod.faces.Max(Z).name="force"
rod.faces.Min(Z).name="free"
geo = Compound([block, rod])
DrawGeo (geo);
mesh = Mesh(OCCGeometry(geo).GenerateMesh(maxh=0.1)).Curve(3)
Draw(mesh);
[12]:
mesh.GetBoundaries()
[12]:
('fix',
'default',
'default',
'default',
'default',
'default',
'contact1',
'contact2',
'force',
'free')
[13]:
fes = VectorH1(mesh, order=3, dirichlet="fix")
u = fes.TrialFunction()
gfu = GridFunction(fes)
a = BilinearForm(fes)
a += Variation(InnerProduct(Sym(Grad(u)), Sym(Grad(u)))*dx)
a += Variation(1e-8*u*u*dx) # regularization
a += Variation(-0.01*u[0]*ds("force"))
[14]:
contact = ContactBoundary(mesh.Boundaries("contact1"), mesh.Boundaries("contact2"))
X = CoefficientFunction((x,y,z))
cf = (X + u - (X.Other() + u.Other())) * specialcf.normal(3)
contact.AddEnergy(IfPos(cf, 1e4*cf*cf, 0))
contact.Update(gfu, a, 20, 4)
[15]:
with TaskManager(pajetrace=10**9):
NewtonMinimization(a=a, u=gfu, printing=True, inverse="sparsecholesky");
Newton iteration 0
Energy: 1.878925160437614e-06
err = 0.010437549939009761
Newton iteration 1
Energy: -5.185630751640171e-05
err = 0.0014564806368511875
Newton iteration 2
Energy: -5.303865446437123e-05
err = 0.0012067611443933898
Newton iteration 3
Energy: -5.389593983672468e-05
err = 0.0015789483885310992
Newton iteration 4
Energy: -5.52638013104644e-05
err = 0.0019503384009471015
Newton iteration 5
Energy: -5.736956658060011e-05
err = 0.0016048342147417533
Newton iteration 6
Energy: -5.876474254378248e-05
err = 0.0018084131009027942
Newton iteration 7
Energy: -6.0621014965793336e-05
err = 0.0038742223110171657
Newton iteration 8
Energy: -6.789428027913523e-05
err = 0.0018389360374545707
Newton iteration 9
Energy: -6.944231271017175e-05
err = 0.0011777291540394253
Newton iteration 10
Energy: -7.025803093193764e-05
err = 0.0013713648422986192
Newton iteration 11
Energy: -7.12577512626438e-05
err = 0.0009106923230701202
Newton iteration 12
Energy: -7.175426725228727e-05
err = 0.0011484323404433768
Newton iteration 13
Energy: -7.23727825099127e-05
err = 0.0005650840813966587
Newton iteration 14
Energy: -7.254473844748964e-05
err = 0.00037861655647394176
Newton iteration 15
Energy: -7.262547678947856e-05
err = 0.00041981841302628144
Newton iteration 16
Energy: -7.241906478182023e-05
err = 0.0008352131251081308
Newton iteration 17
Energy: -7.276878649897773e-05
err = 0.00033161403750840723
Newton iteration 18
Energy: -7.277468682814123e-05
err = 0.00038698191960818295
Newton iteration 19
Energy: -7.28503524303097e-05
err = 0.0001980097833648132
Newton iteration 20
Energy: -7.286915118966561e-05
err = 0.00017788729624589183
Newton iteration 21
Energy: -7.288333728858587e-05
err = 0.00014556020465508404
Newton iteration 22
Energy: -7.289462195481294e-05
err = 9.649102475863879e-05
Newton iteration 23
Energy: -7.289882425347345e-05
err = 7.886475521879418e-05
Newton iteration 24
Energy: -7.290222318085555e-05
err = 4.031562423735843e-05
Newton iteration 25
Energy: -7.290321366545992e-05
err = 2.3911264587440853e-05
Newton iteration 26
Energy: -7.290356158531428e-05
err = 2.2076822851387004e-05
Newton iteration 27
Energy: -7.290381364933719e-05
err = 6.375328256268167e-06
Newton iteration 28
Energy: -7.290383433796143e-05
err = 5.941419384681951e-07
Newton iteration 29
Energy: -7.290383453051025e-05
err = 1.898855834842641e-07
Newton iteration 30
Energy: -7.290383454909836e-05
err = 1.0720778479115363e-08
Newton iteration 31
Energy: -7.290383454915586e-05
err = 9.436611688698343e-16
[16]:
Draw (gfu, mesh, deformation=True);
Draw (Sym(Grad(gfu))[0,0], mesh, draw_surf=False);
[ ]: