斐波那契 [A] - 問題

#6043. 斐波那契 [A]

統計

この問題は以下のコンテストで使用されています：

Potyczki Algorytmiczne 2015, Runda 2

AI Translation — This statement was translated using AI and may contain inaccuracies. Please refer to the original statement if in doubt.

斐波那契数列定义如下： $F_0 = 0, F_1 = 1, F_m = F_{m-1} + F_{m-2}$，其中 $m \ge 2$。

你的任务是找到一个整数 $k$，使得 $F_k$ 的十进制表示（不含前导零）以给定的数字序列结尾。

输入格式

输入仅一行，包含一个由 $n$ 个数字组成的字符串 $c_1c_2 \dots c_n$ ($1 \le n \le 18, 0 \le c_i \le 9$)。

输出格式

如果存在至少一个整数 $k$ ($0 \le k < 10^{100}$)，使得 $F_k$ 的十进制表示以数字序列 $c_1c_2 \dots c_n$ 结尾，则输出任意一个这样的 $k$。否则，输出 NIE。

样例

输入 1

输出 1

输入 2

输出 2

NIE

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