-pc_type lu has already been used in the PETSc options. The problem could be 
caused by a bad Jacobian. I would suggest to run -snes_test_jacobian for a 
small case.

Hong (Mr.)

> On Jul 16, 2019, at 6:21 PM, Smith, Barry F. via petsc-users 
> <[email protected]> wrote:
> 
> 
>  Ahh, run with also --ksp_monitor -ksp_converged_reason 
> -ksp_monitor_singular_value and send the new output.
> 
> 
>  For smallish problems for debugging purposes you can run with -pc_type lu to 
> force a direct solve of the linear system and see what happens (if the linear 
> problems are solvable at all).
> 
> 
>> On Jul 16, 2019, at 6:11 PM, Sean Hsu <[email protected]> wrote:
>> 
>> Hi Barry,
>> 
>> I'm using a default time stepper from MOOSE, which is implicit-euler method. 
>> Here is the output from one of the examples where the timestep gets really 
>> small, I couldn't find a lot of information regarding DIVERGED LINEAR_SOLVE, 
>> thanks for your help:
>> 
>> Time Step 1, time = 0.1, dt = 0.1
>> 0 Nonlinear |R| = 4.012105e-03
>> 0 SNES Function norm 4.012104835449e-03
>>     0 Linear |R| = 4.012105e-03
>> Nonlinear solve did not converge due to DIVERGED_LINEAR_SOLVE iterations 0
>> Solve Did NOT Converge!
>> 
>> Time Step 1, time = 0.05, dt = 0.05
>> 0 Nonlinear |R| = 2.005850e-03
>> 0 SNES Function norm 2.005849521314e-03
>>     0 Linear |R| = 2.005850e-03
>> Nonlinear solve did not converge due to DIVERGED_LINEAR_SOLVE iterations 0
>> Solve Did NOT Converge!
>> 
>> Time Step 1, time = 0.025, dt = 0.025
>> 0 Nonlinear |R| = 1.002874e-03
>> 0 SNES Function norm 1.002873988124e-03
>>     0 Linear |R| = 1.002874e-03
>> Nonlinear solve did not converge due to DIVERGED_LINEAR_SOLVE iterations 0
>> Solve Did NOT Converge!
>> 
>> Time Step 1, time = 0.0125, dt = 0.0125
>> 0 Nonlinear |R| = 5.014243e-04
>> 0 SNES Function norm 5.014242948706e-04
>>     0 Linear |R| = 5.014243e-04
>> Nonlinear solve did not converge due to DIVERGED_LINEAR_SOLVE iterations 0
>> Solve Did NOT Converge!
>> 
>> Time Step 1, time = 0.00625, dt = 0.00625
>> 0 Nonlinear |R| = 2.507090e-04
>> 0 SNES Function norm 2.507089718805e-04
>>     0 Linear |R| = 2.507090e-04
>> Nonlinear solve did not converge due to DIVERGED_LINEAR_SOLVE iterations 0
>> Solve Did NOT Converge!
>> 
>> Time Step 1, time = 0.003125, dt = 0.003125
>> 0 Nonlinear |R| = 1.253537e-04
>> 0 SNES Function norm 1.253536919567e-04
>>     0 Linear |R| = 1.253537e-04
>> Nonlinear solve did not converge due to DIVERGED_LINEAR_SOLVE iterations 0
>> Solve Did NOT Converge!
>> 
>> Time Step 1, time = 0.0015625, dt = 0.0015625
>> 0 Nonlinear |R| = 6.267665e-05
>> 0 SNES Function norm 6.267664747058e-05
>>     0 Linear |R| = 6.267665e-05
>> Nonlinear solve did not converge due to DIVERGED_LINEAR_SOLVE iterations 0
>> Solve Did NOT Converge!
>> 
>> Time Step 1, time = 0.00078125, dt = 0.00078125
>> 0 Nonlinear |R| = 3.133827e-05
>> 0 SNES Function norm 3.133827410694e-05
>>     0 Linear |R| = 3.133827e-05
>> Nonlinear solve did not converge due to DIVERGED_LINEAR_SOLVE iterations 0
>> Solve Did NOT Converge!
>> 
>> Time Step 1, time = 0.000390625, dt = 0.000390625
>> 0 Nonlinear |R| = 1.566912e-05
>> 0 SNES Function norm 1.566912464487e-05
>>     0 Linear |R| = 1.566912e-05
>> Nonlinear solve did not converge due to DIVERGED_LINEAR_SOLVE iterations 0
>> Solve Did NOT Converge!
>> Time Step 1, time = 0.000195313, dt = 0.000195313
>> 0 Nonlinear |R| = 7.834559e-06
>> 0 SNES Function norm 7.834559222250e-06
>>     0 Linear |R| = 7.834559e-06
>> Nonlinear solve did not converge due to DIVERGED_LINEAR_SOLVE iterations 0
>> Solve Did NOT Converge!
>> 
>> Time Step 1, time = 9.76563e-05, dt = 9.76563e-05
>> 0 Nonlinear |R| = 3.917279e-06
>> 0 SNES Function norm 3.917278835540e-06
>>     0 Linear |R| = 3.917279e-06
>> Nonlinear solve did not converge due to DIVERGED_LINEAR_SOLVE iterations 0
>> Solve Did NOT Converge!
>> Time Step 1, time = 4.88281e-05, dt = 4.88281e-05
>> 0 Nonlinear |R| = 1.958639e-06
>> 0 SNES Function norm 1.958639223338e-06
>>     0 Linear |R| = 1.958639e-06
>> Nonlinear solve did not converge due to DIVERGED_LINEAR_SOLVE iterations 0
>> Solve Did NOT Converge!
>> Time Step 1, time = 2.44141e-05, dt = 2.44141e-05
>> 0 Nonlinear |R| = 9.793196e-07
>> 0 SNES Function norm 9.793195635958e-07
>>     0 Linear |R| = 9.793196e-07
>> Nonlinear solve did not converge due to DIVERGED_LINEAR_SOLVE iterations 0
>> Solve Did NOT Converge!
>> 
>> Time Step 1, time = 1.2207e-05, dt = 1.2207e-05
>> 0 Nonlinear |R| = 4.896598e-07
>> 0 SNES Function norm 4.896597688439e-07
>>     0 Linear |R| = 4.896598e-07
>> Nonlinear solve did not converge due to DIVERGED_LINEAR_SOLVE iterations 0
>> Solve Did NOT Converge!
>> 
>> Time Step 1, time = 6.10352e-06, dt = 6.10352e-06
>> 0 Nonlinear |R| = 2.448299e-07
>> 0 SNES Function norm 2.448298810498e-07
>>     0 Linear |R| = 2.448299e-07
>> Nonlinear solve did not converge due to DIVERGED_LINEAR_SOLVE iterations 0
>> Solve Did NOT Converge!
>> Time Step 1, time = 3.05176e-06, dt = 3.05176e-06
>> 0 Nonlinear |R| = 1.224149e-07
>> 0 SNES Function norm 1.224149403502e-07
>>     0 Linear |R| = 1.224149e-07
>> Nonlinear solve did not converge due to DIVERGED_LINEAR_SOLVE iterations 0
>> Solve Did NOT Converge!
>> 
>> Time Step 1, time = 1.52588e-06, dt = 1.52588e-06
>> 0 Nonlinear |R| = 6.120747e-08
>> 0 SNES Function norm 6.120747013139e-08
>>     0 Linear |R| = 6.120747e-08
>> Nonlinear solve did not converge due to DIVERGED_LINEAR_SOLVE iterations 0
>> Solve Did NOT Converge!
>> 
>> Time Step 1, time = 7.62939e-07, dt = 7.62939e-07
>> 0 Nonlinear |R| = 3.060373e-08
>> 0 SNES Function norm 3.060373492112e-08
>>     0 Linear |R| = 3.060373e-08
>> Nonlinear solve did not converge due to DIVERGED_LINEAR_SOLVE iterations 0
>> Solve Did NOT Converge!
>> Time Step 1, time = 3.8147e-07, dt = 3.8147e-07
>> 0 Nonlinear |R| = 1.530187e-08
>> 0 SNES Function norm 1.530186849366e-08
>>     0 Linear |R| = 1.530187e-08
>> Nonlinear solve did not converge due to DIVERGED_LINEAR_SOLVE iterations 0
>> Solve Did NOT Converge!
>> 
>> Time Step 1, time = 1.90735e-07, dt = 1.90735e-07
>> 0 Nonlinear |R| = 7.650934e-09
>> 0 SNES Function norm 7.650934237796e-09
>>     0 Linear |R| = 7.650934e-09
>> Nonlinear solve did not converge due to DIVERGED_LINEAR_SOLVE iterations 0
>> Solve Did NOT Converge!
>> 
>> Time Step 1, time = 9.53674e-08, dt = 9.53674e-08
>> 0 Nonlinear |R| = 3.825467e-09
>> 0 SNES Function norm 3.825467116639e-09
>>     0 Linear |R| = 3.825467e-09
>> Nonlinear solve did not converge due to DIVERGED_LINEAR_SOLVE iterations 0
>> Solve Did NOT Converge!
>> 
>> Time Step 1, time = 4.76837e-08, dt = 4.76837e-08
>> 0 Nonlinear |R| = 1.912734e-09
>> 0 SNES Function norm 1.912733557755e-09
>>     0 Linear |R| = 1.912734e-09
>> Nonlinear solve did not converge due to DIVERGED_LINEAR_SOLVE iterations 0
>> Solve Did NOT Converge!
>> 
>> Time Step 1, time = 2.38419e-08, dt = 2.38419e-08
>> 0 Nonlinear |R| = 9.563657e-10
>> 0 SNES Function norm 9.563657094854e-10
>>     0 Linear |R| = 9.563657e-10
>> Nonlinear solve did not converge due to DIVERGED_LINEAR_SOLVE iterations 0
>> Solve Did NOT Converge!
>> 
>> Time Step 1, time = 1.19209e-08, dt = 1.19209e-08
>> 0 Nonlinear |R| = 4.781839e-10
>> 0 SNES Function norm 4.781839239582e-10
>>     0 Linear |R| = 4.781839e-10
>> Nonlinear solve did not converge due to DIVERGED_LINEAR_SOLVE iterations 0
>> Solve Did NOT Converge!
>> 
>> Time Step 1, time = 5.96046e-09, dt = 5.96046e-09
>> 0 Nonlinear |R| = 2.390909e-10
>> 0 SNES Function norm 2.390908927195e-10
>>     0 Linear |R| = 2.390909e-10
>> Nonlinear solve did not converge due to DIVERGED_LINEAR_SOLVE iterations 0
>> Solve Did NOT Converge!
>> Time Step 1, time = 2.98023e-09, dt = 2.98023e-09
>> 0 Nonlinear |R| = 1.195465e-10
>> 0 SNES Function norm 1.195465156083e-10
>>     0 Linear |R| = 1.195465e-10
>> Nonlinear solve did not converge due to DIVERGED_LINEAR_SOLVE iterations 0
>> Solve Did NOT Converge!
>> 
>> Time Step 1, time = 1.49012e-09, dt = 1.49012e-09
>> 0 Nonlinear |R| = 5.977326e-11
>> 0 SNES Function norm 5.977325780361e-11
>> Nonlinear solve converged due to CONVERGED_FNORM_ABS iterations 0
>> Solve Converged!
>> Outlier Variable Residual Norms:
>> disp_z: 5.907986e-11
>> 
>> Best,
>> 
>> Sean
>> 
>> 
>> 
>> 
>> <https://kairospower.com/>
>> Sean Hsu   Mechanics of Materials Intern
>> p 510.808.5265   e [email protected] <mailto:[email protected]>
>> 707 W Tower Ave, Alameda, CA 94501
>> www.kairospower.com <http://www.kairospower.com>    
>> <https://www.linkedin.com/company/kairos-power-llc/>
>> 
>> 
>> 
>> On 7/16/19, 3:52 PM, "Smith, Barry F." <[email protected]> wrote:
>> 
>> 
>>     What time stepper are you using, something in PETSc or your own? If 
>> PETSc send -ts_view. If PETSc you can run with -ts_monitor -ts_adapt_monitor 
>> to see why it is making the tilmestep choices it is making. 
>> 
>>      Unfortunately I don't think MOOSE uses PETSc time-steppers so you will 
>> need to consult with the MOOSE team on how they choose time-steps, how to 
>> monitor them and determine why it is selecting such small values.
>> 
>>      You can run a case that starts to have small time steps with 
>> -snes_monitor -snes_converged_reason and send the output. At least this will 
>> give some information on how the nonlinear solver is doing. And maybe we can 
>> make suggestions on how to proceed.
>> 
>> 
>>      Barry
>> 
>> 
>>> On Jul 16, 2019, at 3:02 PM, Sean Hsu <[email protected]> wrote:
>>> 
>>> Hi Barry,
>>> 
>>> I think one of the reasons that causes this is not prescribing enough 
>>> boundary conditions in this case, resulting nan values during calculations. 
>>> The linear solver issue doesn't persist anymore when I added in enough 
>>> boundary conditions, as the linear solver doesn't have issue solving the 
>>> system. Now my issue lies in dt dropping too low during solving as the 
>>> solver failed due to timestep dropping below dtmin (2e-14). Do you have any 
>>> insight into this? Again, thanks a lot for your help!
>>> 
>>> Best,
>>> 
>>> Sean
>>> 
>>> 
>>> 
>>> 
>>> <https://kairospower.com/>
>>> Sean Hsu   Mechanics of Materials Intern
>>> p 510.808.5265   e [email protected] <mailto:[email protected]>
>>> 707 W Tower Ave, Alameda, CA 94501
>>> www.kairospower.com <http://www.kairospower.com>    
>>> <https://www.linkedin.com/company/kairos-power-llc/>
>>> 
>>> 
>>> 
>>> On 7/15/19, 5:26 PM, "Smith, Barry F." <[email protected]> wrote:
>>> 
>>> 
>>>    What is causing the Inf or Nan in the function 
>>> 
>>>    1) determine if it is inf or Nan because that can mean different things
>>> 
>>>    2) determine what the physical meaning of the inf or Nan is, that is 
>>> physically what is going wrong to cause it.
>>> 
>>>    I would back off from worrying about convergence rates a bit and instead 
>>> worry about resolving this issue first because it shows something is really 
>>> funky with the modeling aspect. That changing the solution by the 14th 
>>> digit can cause it to go from 1.e-2 to infinite or Nan is problematic.
>>> 
>>> 
>>>     Barry
>>> 
>>> 
>>> 
>>>> On Jul 15, 2019, at 7:10 PM, Sean Hsu <[email protected]> wrote:
>>>> 
>>>> Hi Barry,
>>>> 
>>>> Thanks for the quick response. 
>>>> 
>>>> This behavior shows up occasionally on coarser meshes, I don't believe I 
>>>> have non-physical constraints, the mesh doesn't change in the simulation 
>>>> and it is simply a simulation with a fix boundary on one side and a 
>>>> constant strain on the other side of a plate. 
>>>> 
>>>> I also don't have bounds on my solution.
>>>> 
>>>> Usually when the line search fails, decrease time step size can usually 
>>>> yield converged results, but if the time step size gets too small the 
>>>> simulation takes a very long time to run. Please let me know if you need 
>>>> any more information regarding this particular issue, I will be more than 
>>>> happy to provide you details of my simulation. Thanks!
>>>> 
>>>> Best,
>>>> 
>>>> Sean
>>>> 
>>>> 
>>>> 
>>>> <https://kairospower.com/>
>>>> Sean Hsu   Mechanics of Materials Intern
>>>> p 510.808.5265   e [email protected] <mailto:[email protected]>
>>>> 707 W Tower Ave, Alameda, CA 94501
>>>> www.kairospower.com <http://www.kairospower.com>    
>>>> <https://www.linkedin.com/company/kairos-power-llc/>
>>>> 
>>>> 
>>>> 
>>>> On 7/15/19, 5:00 PM, "Smith, Barry F." <[email protected]> wrote:
>>>> 
>>>> 
>>>>   Function norm was  1.078014e-02
>>>>   Linear solve is great, 
>>>> 
>>>>> Line search: objective function at lambdas = 1. is Inf or Nan, cutting 
>>>>> lambda .... 
>>>> ...
>>>>> Line search: objective function at lambdas = 9.09495e-13 is Inf or Nan, 
>>>>> cutting lambda
>>>> 
>>>>    You take a microscopically small step in space and your objective 
>>>> function is Inf or Nan. 
>>>> 
>>>>    Do you have constraints on your solution where it becomes non-physical? 
>>>> For example divide by an element of the solution (that would require the 
>>>> solution not be zero)? Is the initial solution on a constraint boundary? 
>>>> 
>>>>    If you use a coarser mesh do you get this same type of behavior? 
>>>> 
>>>>    If you have bounds on your solution you might need to consider solving 
>>>> it as a differential variational inequality (DVI)
>>>> 
>>>>    Barry
>>>> 
>>>> 
>>>> 
>>>> 
>>>> 
>>>>> On Jul 15, 2019, at 6:44 PM, Sean Hsu via petsc-users 
>>>>> <[email protected]> wrote:
>>>>> 
>>>>> Hi,
>>>>> 
>>>>> I have been using blackbear (a moose framework app) to do a simple 
>>>>> tensile test simulation on a complex material model with high amount of 
>>>>> elements. I was able to get consistent and quick solution results with 
>>>>> low amount of elements, however once the amount of element start 
>>>>> increasing, the solver won’t converge consistently and dt usually drops 
>>>>> to a very low value, causing the simulation to run for a very long time. 
>>>>> I am seeking recommendations for tips to optimize the solver so I can get 
>>>>> consistent and faster convergence rate. Here is the petsc option that I 
>>>>> am using (along with SMP preconditioner):
>>>>> 
>>>>> l_max_its = 15
>>>>> l_tol = 1e-8
>>>>> nl_max_its = 50
>>>>> nl_rel_tol = 1e-7
>>>>> nl_abs_tol = 1e-9
>>>>> petsc_options = '-snes_ksp_ew'
>>>>> petsc_options_iname = '-pc_type -snes_linesearch_type'
>>>>> petsc_options_value = 'lu bt'
>>>>> end_time = 50.0
>>>>> dt = 0.5
>>>>> 
>>>>> Here is a example output from the first few timesteps of the simulation:
>>>>> 
>>>>> Time Step 2, time = 0.75, dt = 0.5
>>>>> 0 Nonlinear |R| = 1.078014e-02
>>>>> 0 SNES Function norm 1.078014340559e-02
>>>>>   0 Linear |R| = 1.078014e-02
>>>>> 0 KSP unpreconditioned resid norm 1.078014340559e-02 true resid norm 
>>>>> 1.078014340559e-02 ||r(i)||/||b|| 1.000000000000e+00
>>>>>   1 Linear |R| = 2.319831e-13
>>>>> 1 KSP unpreconditioned resid norm 2.319831277078e-13 true resid norm 
>>>>> 2.255163534674e-13 ||r(i)||/||b|| 2.091960607412e-11
>>>>> Linear solve converged due to CONVERGED_RTOL iterations 1
>>>>> NEML stress update failed!
>>>>>   Line search: objective function at lambdas = 1. is Inf or Nan, cutting 
>>>>> lambda
>>>>> NEML stress update failed!
>>>>>   Line search: objective function at lambdas = 0.5 is Inf or Nan, cutting 
>>>>> lambda
>>>>> NEML stress update failed!
>>>>>   Line search: objective function at lambdas = 0.25 is Inf or Nan, 
>>>>> cutting lambda
>>>>> NEML stress update failed!
>>>>>   Line search: objective function at lambdas = 0.125 is Inf or Nan, 
>>>>> cutting lambda
>>>>> NEML stress update failed!
>>>>>   Line search: objective function at lambdas = 0.0625 is Inf or Nan, 
>>>>> cutting lambda
>>>>> NEML stress update failed!
>>>>>   Line search: objective function at lambdas = 0.03125 is Inf or Nan, 
>>>>> cutting lambda
>>>>>   Line search: objective function at lambdas = 0.015625 is Inf or Nan, 
>>>>> cutting lambda
>>>>>   Line search: objective function at lambdas = 0.0078125 is Inf or Nan, 
>>>>> cutting lambda
>>>>>   Line search: objective function at lambdas = 0.00390625 is Inf or Nan, 
>>>>> cutting lambda
>>>>>   Line search: objective function at lambdas = 0.00195312 is Inf or Nan, 
>>>>> cutting lambda
>>>>>   Line search: objective function at lambdas = 0.000976562 is Inf or Nan, 
>>>>> cutting lambda
>>>>>   Line search: objective function at lambdas = 0.000488281 is Inf or Nan, 
>>>>> cutting lambda
>>>>>   Line search: objective function at lambdas = 0.000244141 is Inf or Nan, 
>>>>> cutting lambda
>>>>>   Line search: objective function at lambdas = 0.00012207 is Inf or Nan, 
>>>>> cutting lambda
>>>>>   Line search: objective function at lambdas = 6.10352e-05 is Inf or Nan, 
>>>>> cutting lambda
>>>>>   Line search: objective function at lambdas = 3.05176e-05 is Inf or Nan, 
>>>>> cutting lambda
>>>>>   Line search: objective function at lambdas = 1.52588e-05 is Inf or Nan, 
>>>>> cutting lambda
>>>>>   Line search: objective function at lambdas = 7.62939e-06 is Inf or Nan, 
>>>>> cutting lambda
>>>>>   Line search: objective function at lambdas = 3.8147e-06 is Inf or Nan, 
>>>>> cutting lambda
>>>>> 
>>>>>   Line search: objective function at lambdas = 1.90735e-06 is Inf or Nan, 
>>>>> cutting lambda
>>>>>   Line search: objective function at lambdas = 9.53674e-07 is Inf or Nan, 
>>>>> cutting lambda
>>>>>   Line search: objective function at lambdas = 4.76837e-07 is Inf or Nan, 
>>>>> cutting lambda
>>>>>   Line search: objective function at lambdas = 2.38419e-07 is Inf or Nan, 
>>>>> cutting lambda
>>>>> 
>>>>>   Line search: objective function at lambdas = 1.19209e-07 is Inf or Nan, 
>>>>> cutting lambda
>>>>>   Line search: objective function at lambdas = 5.96046e-08 is Inf or Nan, 
>>>>> cutting lambda
>>>>>   Line search: objective function at lambdas = 2.98023e-08 is Inf or Nan, 
>>>>> cutting lambda
>>>>>   Line search: objective function at lambdas = 1.49012e-08 is Inf or Nan, 
>>>>> cutting lambda
>>>>>   Line search: objective function at lambdas = 7.45058e-09 is Inf or Nan, 
>>>>> cutting lambda
>>>>>   Line search: objective function at lambdas = 3.72529e-09 is Inf or Nan, 
>>>>> cutting lambda
>>>>>   Line search: objective function at lambdas = 1.86265e-09 is Inf or Nan, 
>>>>> cutting lambda
>>>>>   Line search: objective function at lambdas = 9.31323e-10 is Inf or Nan, 
>>>>> cutting lambda
>>>>>   Line search: objective function at lambdas = 4.65661e-10 is Inf or Nan, 
>>>>> cutting lambda
>>>>>   Line search: objective function at lambdas = 2.32831e-10 is Inf or Nan, 
>>>>> cutting lambda
>>>>>   Line search: objective function at lambdas = 1.16415e-10 is Inf or Nan, 
>>>>> cutting lambda
>>>>>   Line search: objective function at lambdas = 5.82077e-11 is Inf or Nan, 
>>>>> cutting lambda
>>>>>   Line search: objective function at lambdas = 2.91038e-11 is Inf or Nan, 
>>>>> cutting lambda
>>>>>   Line search: objective function at lambdas = 1.45519e-11 is Inf or Nan, 
>>>>> cutting lambda
>>>>>   Line search: objective function at lambdas = 7.27596e-12 is Inf or Nan, 
>>>>> cutting lambda
>>>>>   Line search: objective function at lambdas = 3.63798e-12 is Inf or Nan, 
>>>>> cutting lambda
>>>>>   Line search: objective function at lambdas = 1.81899e-12 is Inf or Nan, 
>>>>> cutting lambda
>>>>>   Line search: objective function at lambdas = 9.09495e-13 is Inf or Nan, 
>>>>> cutting lambda
>>>>> Nonlinear solve did not converge due to DIVERGED_LINE_SEARCH iterations 0
>>>>> Solve Did NOT Converge!
>>>>> 
>>>>> I really appreciate any inputs or insights, thanks for your time and help.
>>>>> 
>>>>> Best,
>>>>> 
>>>>> Sean
>>>>> 
>>>>> 
>>>>> <image001.png>
>>>>> Sean Hsu   Mechanics of Materials Intern
>>>>> p 510.808.5265   e [email protected]
>>>>> 707 W Tower Ave, Alameda, CA 94501
>>>>> www.kairospower.com   <image002.png>
>>>> 
>>>> 
>>>> 
>>> 
>>> 
>>> 
>> 
>> 
>> 
> 

Reply via email to