Isabelle, Noelle, and Juliette acquired a pile of chocolate coins. They go to bed, leaving their dad to guard the coins. An hour later Juliette gets up, gives two chocolate coins from the pile to her dad as hush money, divides the remaining pile of coins evenly into three parts, takes one part, and goes back to bed. A little later, Noelle gets up, gives two chocolate coins to her dad as hush money, divides the remaining pile evenly into three parts, takes one part, and goes back to bed. A little later, Isabelle gets up and does the very same thing as her siblings. In the morning, when they count the remaining chocolate coins, there are 100 of them left. How many were in the pile originally?
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