Consider the **Fibonacci** sequence, defined as follows:

```
Fibonacci(1) = 1
Fibonacci(2) = 1
Fibonacci(n) = Fibonacci(n - 2) + Fibonacci(n - 1)
```

The first two Fibonacci numbers are **1, 1**. The following elements are computed by adding the prior two.

The first 6 Fibonacci numbers are: **1, 1, 2, 3, 5, 8**.

Let **F** be the \(46^\text{th}\) Fibonacci number. What are the *last* 3 digits of **F**?

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