how to merge the files of DNA sequences?

newperler has asked for the wisdom of the Perl Monks concerning the following question:

I have 2 fasta files with each storing DNA sequences under different individual names respectively. eg.

>John     >John
atgc      gggg
>Tom      >Tom
atgg      ccgg
...       ...
(file1)   (file2)
[download]

Now I need to merge the sequences from the 2 files under every same name and output as a new file. eg.

>John     
atgcgggg
>Tom
atggccgg
...
(newfile)
[download]

I would like to use hash to store the names and sequences then push them into new hashes. Since I am really a newbie, so could anyone tell me how to merge the values of 2 hashes? thanks a lot!

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