DWITE Online Computer Programming Contest, December 2009, Problem 2

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 a sequence of: ~0, 1, 1, 2, 3, 5, 8, 13, 21, 34, \dots~

The input will contain 5 lines, integers ~0 \le N \le 1\,000\,000\,000~.

The output 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

Problem Resource: DWITE