MIN-MEX Cut

题意翻译

定义一个 $01$ 串的 $\text{MEX}$ 这个串中没出现过的最小的数。 总共 $T$ 组询问，每次给定一个字符串 $s$，你可以将其分割为若干个子串 $t_1,t_2,\cdots,t_k$，使得 $\sum_{i=1}^{k}{\text{MEX}_{t_i}}$ 最小。求这个最小值。 $\sum|s|\leq 10^5$。

题目描述

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?

输入输出格式

输入格式

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 $ .

输出格式

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.

输入输出样例

输入样例 #1

6
01
1111
01100
101
0000
01010

输出样例 #1

1
0
2
1
1
2

说明

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 $ .