[Python-ideas] Shouldn't 'input' prompt be going to stderr?

There was a discussion on another forum that mentioned the 'input' function, and it made me wonder whether 'input' should be printing the prompt to stderr instead of stdout.

The convention is for normal output to go to stdout and error messages to go to stderr, so if a program needs to ask the user, shouldn't it be using stderr for prompts in order not to mess up the normal output?