How can I save the output of auto_arima() to a .txt file?

Question

When I run auto_arima() from pmdarima, the console prints these statements to the console for example:

Performing stepwise search to minimize aic
 ARIMA(2,0,2)(1,0,1)[7] intercept   : AIC=-296.496, Time=0.88 sec
 ARIMA(0,0,0)(0,0,0)[7] intercept   : AIC=-302.486, Time=0.30 sec
 ARIMA(1,0,0)(1,0,0)[7] intercept   : AIC=-299.880, Time=0.70 sec
 ARIMA(0,0,1)(0,0,1)[7] intercept   : AIC=-299.529, Time=0.70 sec
 ARIMA(0,0,0)(0,0,0)[7]             : AIC=598.722, Time=0.27 sec
 ARIMA(0,0,0)(1,0,0)[7] intercept   : AIC=-301.889, Time=0.61 sec
 ARIMA(0,0,0)(0,0,1)[7] intercept   : AIC=-301.608, Time=0.59 sec
 ARIMA(0,0,0)(1,0,1)[7] intercept   : AIC=-299.014, Time=0.64 sec
 ARIMA(1,0,0)(0,0,0)[7] intercept   : AIC=-300.553, Time=0.35 sec
 ARIMA(0,0,1)(0,0,0)[7] intercept   : AIC=-300.558, Time=0.41 sec
 ARIMA(1,0,1)(0,0,0)[7] intercept   : AIC=-299.403, Time=0.44 sec

Best model:  ARIMA(0,0,0)(0,0,0)[7] intercept
Total fit time: 5.934 seconds
Out[3]: 
ARIMA(order=(0, 0, 0), scoring_args={}, seasonal_order=(0, 0, 0, 7),
      suppress_warnings=True)

How can I save these print statements to a .txt file? I will train about 300 of these models and want to be able to log the different AIC values for each configuration. Is there a way to capture these outputs while auto_arima() finds the best model?