Order of stdout and stderr is messed up

Code:

```python
import sys

print('stderr1', file=sys.stderr)
print('stdout1')
print('stderr2', file=sys.stderr)
print('stdout2')
```

Output:

```
stdout1
stdout2
stderr1
stderr2
```

Expected output:

```
stderr1
stdout1
stderr2
stdout2
```

This happens with:

python3 -m notebook
python3 -m jupyter_console

The error does not occur with:

python3 -m IPython

... where the order is as expected.

I've already reported this quite some time ago in https://github.com/jupyter/help/issues/111, where there was some chit-chat and then I was sent here.