Don't Flip Out

You are blindfolded, and are told if you can correctly solve 
the following, the blindfold will be removed. You are given 99 
coins that are heads up, and an unknown number of coins that are 
tails up. You never remove the blindfold, you do not peak, .... 
You can count the coins, put them in arbitrary many piles, flip 
whichever coins you want, but remember, when you flip and when
you sort, you DO NOT know which ones are heads up, which are 
tails up. In the end, you must end up with just two piles, each 
containing an equal number of heads. How do you do this? 
(communicated by Eric Adelizzi).