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 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 the sequence of integers: 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.

Sample Input:

```
1
2
4
22
1000000000
```

Sample Output:

```
1
2
5
21
1134903170
```