A Kaboobly Dooist discovers an infinite pool of coins with \($1\), \($2\) and \($5\) coins distributed uniformly in it.

He takes a coin at random from the pool and puts it in his bag.

He does so until the sum of the values of all coins in his bag is equal to or more than \($200\).

If the expected number of \($1\) coins in the bag is \(n\), what is the value of \( \left\lfloor n\right\rfloor \)?

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