Large Fibonacci Numbers Part 3

\[ \left ( F(10^1) \bmod 1 \right ) + \left ( F(10^2) \bmod 2 \right ) + \left ( F(10^3) \bmod 3 \right ) + \left ( F(10^4) \bmod 4 \right ) \]

Let \(F(n)\) denote the nth Fibonacci number. What is the value of the expression above?

To clarify: \(F(0) = 0, F(1) = F(2) = 1 \) are the initials terms of the Fibonacci sequence.

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