19046번 - Infinite Pattern Matching 다국어

문제

Consider the infinite binary string $I$ formed by concatenating the binary representations of all the strictly positive integers in increasing order: $I = $ "11011100...".

You are given a binary string $A$. Your task is to find the smallest integer $L$ such that $A$ is a suffix of $I[1 \ldots L]$.

입력

The only line of input contains the binary string $A,ドル 1ドル \le \left\lvert A \right\rvert \le 55$.

출력

Print a single line with a single integer: the number $L$.

제한

힌트