Problem Statement

Given is a string $S$ consisting of 0 and 1. Find the number of strings, modulo $998244353$, that can result from applying the following operation on $S$ zero or more times:

• Remove the two characters at the beginning of $S$, erase one of them, and reinsert the other somewhere in $S$. This operation can be applied only when $S$ has two or more characters.

Constraints

• $1 \leq |S| \leq 300$
• $S$ consists of 0 and 1.

Input

Input is given from Standard Input in the following format:

S

Output

Print the number of strings, modulo $998244353$, that can result from applying the operation on $S$ zero or more times.