Five brothers stayed in the house with their mother. One day, their mother brought home some mangos.

Alex woke up first. As he was hungry, he ate \( \frac{1}{6} \) of the mangoes, and headed out.

Brian woke up next. As he was hungry, he ate \( \frac{1}{5} \) of what was left, and headed out.

Charles woke up next. As he was hungry, he ate \( \frac{1}{4} \) of what was left, and headed out.

Danny woke up next. As he was hungry, he ate \( \frac{1}{3} \) of what was left, and headed out.

Euler woke up next. As he was hungry, he ate \( \frac{1}{2} \) of what was left, and headed out.

Their mother came home and saw 3 mangoes in the basket. How many mangoes were there initially?

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