Problem F. Fibonacci System ≡

 Author: ACM ICPC NEERC 2008 Jury Time limit: 2 sec Input file: fibonacci.in Memory limit: 256 Mb Output file: fibonacci.out

Statement

Author: Anton Maydell Text: Andrew Lopatin Tests: Anton Maydell

Little John studies numeral systems. After learning all about fixed-base systems, he became interested in more unusual cases. Among those cases he found a Fibonacci system, which represents all natural numbers in an unique way using only two digits: zero and one. But unlike usual binary scale of notation, in the Fibonacci system you are not allowed to place two \t{1}s in adjacent positions.

One can prove that if you have number N = an an − 1… a1F in Fibonacci system, its value is equal to N = an ⋅ Fn + an − 1 ⋅ Fn − 1 + …  + a1 ⋅ F1, where Fk is a usual Fibonacci sequence defined by F0 = F1 = 1, Fi = Fi − 1 + Fi − 2.

For example, first few natural numbers have the following unique representations in Fibonacci system:

1 = 1F, 2 = 10F, 3 = 100F, 4 = 101F, 5 = 1000F, 6 = 1001F, 7 = 1010F,

John wrote a very long string (consider it infinite) consisting of consecutive representations of natural numbers in Fibonacci system. For example, the first few digits of this string are 110100101100010011010...

He is very interested, how many times the digit \t{1} occurs in the N-th prefix of the string. Remember that the N-th prefix of the string is just a string consisting of its first N characters.

Write a program which determines how many times the digit 1 occurs in N-th prefix of John's string.

Input file format

The input file contains a single integer N (0≤ N≤ 1015).

Output file format

Output a single integer — the number of 1s in N-th prefix of John's string.

Sample tests

No. Input file (fibonacci.in) Output file (fibonacci.out)
1
21
10

0.118s 0.030s 15