A14544 | MIN-MEX Cut

A binary string is a string that consists of characters $0$ and $1$ .

Let $\operatorname{MEX}$ of a binary string be the smallest digit among $0$ , $1$ , or $2$ that does not occur in the string. For example, $\operatorname{MEX}$ of $001011$ is $2$ , because $0$ and $1$ occur in the string at least once, $\operatorname{MEX}$ of $1111$ is $0$ , because $0$ and $2$ do not occur in the string and $0 < 2$ .

A binary string $s$ is given. You should cut it into any number of substrings such that each character is in exactly one substring. It is possible to cut the string into a single substring — the whole string.

A string $a$ is a substring of a string $b$ if $a$ can be obtained from $b$ by deletion of several (possibly, zero or all) characters from the beginning and several (possibly, zero or all) characters from the end.

What is the minimal sum of $\operatorname{MEX}$ of all substrings pieces can be?

The input consists of multiple test cases. The first line contains a single integer $t$ ( $1 \le t \le 10^4$ ) — the number of test cases. Description of the test cases follows.

Each test case contains a single binary string $s$ ( $1 \le |s| \le 10^5$ ).

It's guaranteed that the sum of lengths of $s$ over all test cases does not exceed $10^5$ .

For each test case print a single integer — the minimal sum of $\operatorname{MEX}$ of all substrings that it is possible to get by cutting $s$ optimally.