Problem C
Lonely Strings

String art and image by SimpleVibesStudio (Etsy); Used with permission

A binary string has either even parity or odd parity, depending on whether it contains an even or an odd number of $1$’s, respectively. Now suppose a binary string, $S$, has been partitioned into $m \geq 2$ nonempty substrings, $S = S_1 S_2 \ldots S_ m$. The neighbours of any substring $S_ i$ are the substrings immediately adjacent to it, so every substring has two neighbours, except $S_1$, which has only a right neighbour, and $S_ m$, which has only a left neighbour. We say that a substring is lonely if it has no neighbour with the same parity as itself.

Given a binary string, $S$, in how many ways can $S$ be partitioned into two or more nonempty substrings so that no substring is lonely?

Input

The input consists of a single binary string, i.e., a string composed entirely of characters from $\{ \texttt{0}, \texttt{1}\} $. The length of this string is between $2$ and $2\, 000$, inclusive.

Output

Let $w$ be the number of ways $S$ can be partitioned into two or more nonempty substrings so that no substring is lonely. If $w$ is greater than $100$, print a single line containing $w$; since $w$ may be large, reduce it mod $(10^9 + 33)$.

If $w$ is at most $100$, first print a line containing $w$. Then print $w$ lines containing the partitions of the input string, one per line. Represent each partition as a string of characters from $\{ \texttt{0}, \texttt{1}, \texttt{/} \} $, using / as a separator between adjacent substrings. Order these $w$ strings lexicographically (with the ASCII/Unicode rule that ‘/’ is before ‘0’, which in turn is before ‘1’). See the first two sample outputs for examples.

01010

5
0/101/0
0/1010
01/010
010/10
0101/0

0000

7
0/0/0/0
0/0/00
0/00/0
0/000
00/0/0
00/00
000/0

00000000

127