Smallest Fibonacci Greater or Equal

Given an integer \(N\), find the smallest Fibonacci number that is greater than or equal to \(N\). The Fibonacci sequence is defined as follows:

\(F(0)=0, F(1)=1\), and for \(n \geq 2\), \(F(n) = F(n-1) + F(n-2)\).

Your task is to compute \(F(k)\) such that \(F(k) \ge N\) and that for all \(j < k\), \(F(j) < N\). The input is provided via standard input and the output should be printed to standard output.

inputFormat

The input consists of a single integer \(N\) provided on one line via stdin.

Constraints: \(0 \leq N \leq 10^{18}\).

outputFormat

Output the smallest Fibonacci number that is greater than or equal to \(N\) on a single line to stdout.

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