pick a non-void adjacent substring of s that contains an equivalent number of 0's and 1's;    flip all characters in the substring, that is, supplant all 0's with 1's, as well as the other way around;    turn around the substring.    For instance, think

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
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pick a non-void adjacent substring of s that contains an equivalent number of 0's and 1's; 

 

flip all characters in the substring, that is, supplant all 0's with 1's, as well as the other way around; 

 

turn around the substring. 

 

For instance, think about s = 00111011, and the accompanying activity: 

 

Pick the initial six characters as the substring to follow up on: 00111011. Note that the number of 0's and 1's are equivalent, so this is a lawful decision. Picking substrings 0, 110, or the whole string would not be imaginable. 

 

Flip all characters in the substring: 11000111. 

 

Invert the substring: 10001111. 

 

Find the lexicographically littlest string that can be gotten from s after nothing or more tasks. 

 

Input 

 

The primary line contains a solitary integer T (1≤T≤5⋅105) — the number of experiments. Every one of the accompanying T lines contains a solitary non-void string — the input string s for the separate experiment. 

 

All strings comprise of characters 0 and 1, and their all out length doesn't surpass 5⋅105. 

 

Output 

 

For each experiment, on a different line print the lexicographically littlest string that can be gotten from s after nothing or more tasks.

 

 

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