Consider that they will likely not hire the new person no matter how much notice you give because they don't want to pay (or have the budget) the salary twice. I have never seen anyone who gave a longer than normal notice actually have a replacement on board before they left. If you need a month to get everything ready for your replacement, go for it, but don't assume you will have someone there in time to actually train them unless they are using a current emplyee in your place.
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