Euler's count of circle pieces
The function \( R(n) \) denotes the maximum number of areas which can be formed within the circle when all chords between \( n \) distinct points on a circle are drawn.
In the figures above we see that \( R(2) = 2, R(3) = 4 \) and \( R(4) = 8 \).
Find the smallest value of \( R(n) \geq 1000 \).
Note: The \( n \) points lie on the circle in such a way that the 'maximum' number of areas are formed.