Based on a quick reading of the manual page, I don't think you are using it correctly. You are pushing but never pulling. The push method does not expect or support the passing of an argument. I also don't see how this is supposed to bring you closer to a solution.

In the meantime, the script I posted above does seem to produce the expected output for the sample input you supplied. And no, the delete command only deletes the specified element from the hash, not the whole hash (that would be undef -- see the delete documentation for more).