Infinite Pattern Matching

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문제 설명

예제2

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 $A$ , $1 \le \left\lvert A \right\rvert \le 55$ .

출력

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