Install and import site-packages for Python 2 and 3 on Mac

I installed brew and then

brew install python
brew install python3

Install flask with pip

pip install flask

Try

python -c 'import flask'

But I got exception

ImportError: No module named flask

Set and export PYTHONPATH

export PYTHONPATH=$PYTHONPATH:/usr/local/lib/python2.7/site-packages

So far so good. But when I tried to install a package with pip3 for Python 3, I got error message

Your PYTHONPATH points to a site-packages dir for Python 2.x but you are running Python 3.x!
     PYTHONPATH is currently: ":/usr/local/lib/python2.7/site-packages"
     You should `unset PYTHONPATH` to fix this.

How to use site-packages without the PYTHONPATH trick to make both pip and pip3 usable and both Python 2 and Python 3 able to import site-packages?