Author:  M. Sporyshev  
Input file:  input.txt  Time limit:  1 sec  
Output file:  output.txt  Memory limit:  256 Mb 
Young game developer Alice has created a new game and sent it to friends for betatesting.
Young gamer Vasya wants to impress Alice by finishing the game completely.
At the final level Vasya fights the main boss — Binary King. At the beginning of the fight, Binary King generates a sequence K of N binary digits. After that, Vasya must present his own binary sequence V of the same length.
Vasya's sequence is scored as follows. For each position i, if V_{i} = 1 and K_{i} = 0, Vasya gains 1 point; if V_{i} = 0 and K_{i} = 1, Vasya loses 2 points.
Since Vasya plays at the hardest difficulty, each prefix of his sequence must contain at least as many zeroes as ones.
To win, Vasya must get maximum possible number of points.
Input file contains N characters 0 and 1 — King's sequence.
Output file must contain N characters 0 and 1 — Vasya's sequence scoring maximum number of points. If there are several optimal solutions, output any of them.
1 ≤ N ≤ 10^{5}
No.  Input file (input.txt ) 
Output file (output.txt ) 

1 


2 

