Fibonacci Numeral System Representation

You are given a positive integer (n). In this problem, the Fibonacci numeral system is defined uniquely by the sequence (F = [2, 3, 5, 8, \ldots]). The element (F_i) is the ((i+1))-th Fibonacci number in this sequence (i.e. (F_1 = 2, F_2 = 3, F_3 = 5, \ldots)).

Your task is to determine if the given number (n) is one of the Fibonacci numbers in this sequence. If it is, output its positional representation (i.e. if (n = F_i), then output (i+1) as a string). If not, print the message:

Not a valid input according to the unique Fibonacci numeral system.

Note: The input is given via standard input (stdin) and the output should be printed to standard output (stdout).

inputFormat

A single integer (n) is provided via stdin.

outputFormat

Print the positional representation if (n) is a Fibonacci number in the sequence (F = [2, 3, 5, 8, \ldots]). Otherwise, print:

Not a valid input according to the unique Fibonacci numeral system.## sample

2

1