AccurateLee

题意翻译

- 给你一个字符串 $s$，其中如果 $s_i=1$ 并且 $s_{i+1}=0$，我们可以删除其中一个，问经过 $\inf$ 次操作后字符串字典序最小的字符串。共有 $t$ 组数据。 - 数据范围：$1\le t\le 10^4$，$1\le n\le 10^5$。 - translate by qym2008

题目描述

Lee was cleaning his house for the party when he found a messy string under the carpets. Now he'd like to make it clean accurately and in a stylish way... The string $ s $ he found is a binary string of length $ n $ (i. e. string consists only of 0-s and 1-s). In one move he can choose two consecutive characters $ s_i $ and $ s_{i+1} $ , and if $ s_i $ is 1 and $ s_{i + 1} $ is 0, he can erase exactly one of them (he can choose which one to erase but he can't erase both characters simultaneously). The string shrinks after erasing. Lee can make an arbitrary number of moves (possibly zero) and he'd like to make the string $ s $ as clean as possible. He thinks for two different strings $ x $ and $ y $ , the shorter string is cleaner, and if they are the same length, then the lexicographically smaller string is cleaner. Now you should answer $ t $ test cases: for the $ i $ -th test case, print the cleanest possible string that Lee can get by doing some number of moves. Small reminder: if we have two strings $ x $ and $ y $ of the same length then $ x $ is lexicographically smaller than $ y $ if there is a position $ i $ such that $ x_1 = y_1 $ , $ x_2 = y_2 $ ,..., $ x_{i - 1} = y_{i - 1} $ and $ x_i < y_i $ .

输入输出格式

输入格式

The first line contains the integer $ t $ ( $ 1 \le t \le 10^4 $ ) — the number of test cases. Next $ 2t $ lines contain test cases — one per two lines. The first line of each test case contains the integer $ n $ ( $ 1 \le n \le 10^5 $ ) — the length of the string $ s $ . The second line contains the binary string $ s $ . The string $ s $ is a string of length $ n $ which consists only of zeroes and ones. It's guaranteed that sum of $ n $ over test cases doesn't exceed $ 10^5 $ .

输出格式

Print $ t $ answers — one per test case. The answer to the $ i $ -th test case is the cleanest string Lee can get after doing some number of moves (possibly zero).

输入输出样例

输入样例 #1

5
10
0001111111
4
0101
8
11001101
10
1110000000
1
1

输出样例 #1

0001111111
001
01
0
1

说明

In the first test case, Lee can't perform any moves. In the second test case, Lee should erase $ s_2 $ . In the third test case, Lee can make moves, for example, in the following order: 11001101 $ \rightarrow $ 1100101 $ \rightarrow $ 110101 $ \rightarrow $ 10101 $ \rightarrow $ 1101 $ \rightarrow $ 101 $ \rightarrow $ 01.