CF1566B.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 $0 \lt 2$.

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?

二进制字符串是指仅由字符 $0$ 和 $1$ 组成的字符串。

定义一个二进制字符串的 $\operatorname{MEX}$ 为在 $0$、$1$、$2$ 中未出现在该字符串里的最小数字。例如，字符串 $001011$ 的 $\operatorname{MEX}$ 是 $2$，因为 $0$ 和 $1$ 均至少出现一次；而字符串 $1111$ 的 $\operatorname{MEX}$ 是 $0$，因为 $0$ 和 $2$ 均未出现，且 $0 < 2$。

给定一个二进制字符串 $s$。你需要将其切割成任意数量的子串，使得每个字符恰好属于其中一个子串（允许只切出一个子串——即整个字符串本身）。

若字符串 $a$ 可通过从字符串 $b$ 的开头删除若干个（可能为零个或全部）字符，并从结尾删除若干个（可能为零个或全部）字符而得到，则称 $a$ 是 $b$ 的子串。

所有子串的 $\operatorname{MEX}$ 值之和的最小可能值是多少？

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 $10^5$.

输入包含多个测试用例。第一行包含一个整数 $t$（$1 \le t \le 10^4$），表示测试用例的数量。随后是各测试用例的描述。

每个测试用例包含一个二进制字符串 $s$（$1 \le |s| \le 10^5$）。

保证所有测试用例中字符串 $s$ 的长度总和不超过 $10^5$。

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.

对于每个测试用例，输出一个整数——通过最优地切割字符串 $s$ 所能得到的所有子串的 $\operatorname{MEX}$ 值之和的最小值。

In the first test case the minimal sum is $\operatorname{MEX}(0) + \operatorname{MEX}(1) = 1 + 0 = 1$.

In the second test case the minimal sum is $\operatorname{MEX}(1111) = 0$.

In the third test case the minimal sum is $\operatorname{MEX}(01100) = 2$.

在第一个测试用例中，最小和为 $\operatorname{MEX}(0) + \operatorname{MEX}(1) = 1 + 0 = 1$。

在第二个测试用例中，最小和为 $\operatorname{MEX}(1111) = 0$。

在第三个测试用例中，最小和为 $\operatorname{MEX}(01100) = 2$。