Mike, Nathan and Owen each had some marbles and decided to play a game
with their marbles.
In round 1, MIke lost \({1\over 2}{}{}\)of his marbles to Nathan.
In round 2, Nathan lost \({1\over 2}{}{}\)of his total number of marbles to Owen.
In round 3, Owen lost \( {1\over 2}{}{}\)of his total number of marbles to Mike.
In the end, Mike, Nathan and Owen ad 124, 88 and 68 marbles respectively.
How many marbles did Nathan have at first?