2001 Pascal Problem 20

Square ABCD has an area of 4. E is the midpoint of AB. Similarly, F, G, H, and I are the midpoints of DE, CF, DG, and CH, respectively. The area of \triangle IDC is

\textbf{(A)}\ \frac{1}{4}\quad \textbf{(B)}\ \frac{1}{8}\quad \textbf{(C)}\ \frac{1}{16}\quad \textbf{(D)}\ \frac{1}{32}\quad \textbf{(E)}\ \frac{1}{64}

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Full credit to this problem is given to the CEMC, you may view all Pascal contests here.