Inspired by Otto...Funny back to the future

The Fibonacci sequence is defined with the recurrence relation \(f_{n} = f_{n-1} + f_{n-2}\) for \(n>2\) with initial terms \(f_1 = 1\), \(f_2 = 1\).

\[ (1 \cdot 1) + (1 \cdot 2) + (2 \cdot 3) + (3 \cdot 5) + \ldots + (f_{2012} \cdot f_{2013}) + (f_ {2013} \cdot f_{2014}) \]

If the value of the expression above equals \( f_n ^2 \), find the value of \(n\).

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