CF193E.Fibonacci Number

John Doe has a list of all Fibonacci numbers modulo 1013. This list is infinite, it starts with numbers 0 and 1. Each number in the list, apart from the first two, is a sum of previous two modulo 1013. That is, John's list is made from the Fibonacci numbers' list by replacing each number there by the remainder when divided by 1013.

John got interested in number f (0 ≤ f < 1013) and now wants to find its first occurrence in the list given above. Help John and find the number of the first occurence of number f in the list or otherwise state that number f does not occur in the list.

The numeration in John's list starts from zero. There, the 0-th position is the number 0, the 1-st position is the number 1, the 2-nd position is the number 1, the 3-rd position is the number 2, the 4-th position is the number 3 and so on. Thus, the beginning of the list looks like this: 0, 1, 1, 2, 3, 5, 8, 13, 21, ...

约翰·多伊（John Doe）有一个所有斐波那契数对 $1013$ 取模后构成的列表。该列表是无限长的，起始于数字 $0$ 和 $1$。列表中除前两个数外，每个数均为其前两个数之和对 $1013$ 取模的结果。换言之，约翰的列表是通过对标准斐波那契数列中的每个数除以 $1013$ 后取余数而得到的。

约翰对某个数 $f$（其中 $0 \leq f < 1013$）产生了兴趣，现在他希望找出该数在上述列表中首次出现的位置。请帮助约翰找出数 $f$ 在该列表中首次出现的下标；若 $f$ 并未出现在列表中，则说明该数不存在于列表中。

约翰的列表下标从零开始计数：第 $0$ 位是数字 $0$，第 $1$ 位是数字 $1$，第 $2$ 位是数字 $1$，第 $3$ 位是数字 $2$，第 $4$ 位是数字 $3$，依此类推。因此，该列表开头部分为：$0,\,1,\,1,\,2,\,3,\,5,\,8,\,13,\,21,\,\dots$

The first line contains the single integer f (0 ≤ f < 1013) — the number, which position in the list we should find.

Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.

第一行包含一个整数 $f$（$0 ≤ f < 10^{13}$）—— 我们需要在列表中查找该数的位置。

请注意，在 C++ 中不要使用 %lld 说明符来读取或写入 64 位整数。推荐使用 cin、cout 流，或 %I64d 说明符。

Print a single number — the number of the first occurrence of the given number in John's list. If this number doesn't occur in John's list, print -1.

输出一个数字——给定数字在约翰列表中首次出现的位置编号。如果该数字未在约翰的列表中出现，则输出 -1。