1971D · Binary Cut

Problem: You are given a binary string$^{\dagger}$. Please find the minimum number of pieces you need to cut it into, so that the resulting pieces can be rearranged into a sorted binary string.

Note that:

• each character must lie in exactly one of the pieces;
• the pieces must be contiguous substrings of the original string;
• you must use all the pieces in the rearrangement.

$^{\dagger}$ A binary string is a string consisting of characters $\texttt{0}$ and $\texttt{1}$. A sorted binary string is a binary string such that all characters $\texttt{0}$ come before all characters $\texttt{1}$.

Input Format: The first line contains a single integer $t$ ($1 \leq t \leq 500$) — the number of test cases.

The only line of each test case contains a single string $s$ ($1 \leq |s| \leq 500$) consisting of characters $\texttt{0}$ and $\texttt{1}$, where $|s|$ denotes the length of the string $s$.

Output Format: For each test case, output a single integer — the minimum number of pieces needed to be able to rearrange the string into a sorted binary string.

Note: The first test case is pictured in the statement. It can be proven that you can't use fewer than $3$ pieces.

In the second and third test cases, the binary string is already sorted, so only $1$ piece is needed.

In the fourth test case, you need to make a single cut between the two characters and rearrange them to make the string $\texttt{01}$.