Reversibly Cyclic Strings

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요약

문자열 s의 모든 진부분 문자열 t에 대해 t의 뒤집은 문자열이 s의 어떤 회전에서 부분 문자열로 나타나는지 판정합니다.

문제

A string $t$ is a Cyclic Substring of a string $s$ if there is some rotation of $s$ such that $t$ is a substring of that rotation of $s$ .

For example, if $s$ is fatcat, then atc and atf are both Cyclic Substrings of $s$ . However, act is not a Cyclic Substring of $s$ .

A string $s$ is Internally Reversibly Cyclic if, for every proper substring $t$ of $s$ , the reverse of $t$ is a Cyclic Substring of $s$ .

Given a string, determine if it is Internally Reversibly Cyclic.

The single line of input contains a string $s$ ( $1 \le |s| \le 1{,}000$ , $s \in \\{\texttt{a}-\texttt{z}\\}^\*$ )

Output a single integer, which is $1$ if $s$ is Internally Reversibly Cyclic, $0$ otherwise.