D. Binary Cut
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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

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

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.

Example
Input
6
11010
00000000
1
10
0001111
0110
Output
3
1
1
2
1
2
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 $$$\texttt{01}$$$.