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A large jug contains 2018 nickels and 2019 dimes. Next to the jug is a large pile of dimes (treat it as an unlimited number of dimes). The following procedure is to be performed repeatedly until a single coin remains in the jug.
Two coins are chosen at random from the jug:
i. If both coins are dimes, one is put back and the other is discarded.
ii. If both coins are nickels, both are discarded and a dime from the pile is added to the jug.
iii. If one coin is a dime and the other is a nickel, the nickel is put back and the dime is discarded.
Will the last coin remaining in the jug be a nickel or a dime?
*You must include an explanation to support your answer*