mail app for icloud email

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http://androidforums.com – Finally got my sgs3 ..moved from iPhone after 7 yrs!! So obviously trying to learn android. The stock email app works fine for my gmail..but for my iCloud email account it doesn't support push. I need the email delivered instantly to my inbox similar to gmail or Microsoft exchange. Tried other alternates like k9 mail. It seem to work ok for iCloud but the interface is not very nice. Other programs like mail.com or aquamail etc has problems such as having the sent emails storied on the server Esther than a separate sent folder Can u guys recommend something that will work for both gma (General)