There are a few different rounding methods. The most common one rounds up/down from 5. Another one rounds up/down depending on the number being even or odd (this has to do with statistical bias). Here we'll implement a yet another type of rounding -- rounding a number to the closest whole integer in the Fibonacci sequence. *If two elements in the sequence are equally far away,* **round up**.

The Fibonacci sequence is defined as:

- F(0) = 0
- F(1) = 1
- F(n) = F(n-1) + F(n-2)

Which produces a sequence of: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ...

The input file **DATA2.txt** will contain 5 lines, integers 0 <= N <= 1,000,000,000.

The output file **OUT2.txt** will contain 5 lines, each a corresponding integer rounded to the closest number from the Fibonacci sequence.

1 2 4 22 1000000000

1 2 5 21 1134903170