问题 O: Fibonacci System

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 1s in adjacent positions. One can prove that if you have number N = anan-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 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.

The input contains a single integer N (0<=N<=10^15).

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

21

10