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Dmitry Gozman Contest 1. Petrozavodsk training camp. Winter 2007

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I. Ones and Zeroes

Time limit: 1.0 second
Memory limit: 64 MB
Consider two binary sequences A and B of length n each. Let us call these sequences compatible if A XOR B = A + B where XOR is the element-wise exclusive OR operation.
Given an integer n and a pair of binary sequences p and q, find the pair of compatible binary sequences a and b which comes first after the pair (p, q). Pair (a, b) is said to be lexicographically less that (c, d) if a is lexicographically less than c, or a and c are equal and b is lexicographically less than d. If there is no pair of compatible binary sequences lexicographically greater than (p, q), output the lexicographically first compatible pair.

Input

There is a single integer n (1 ≤ n ≤ 100000) on the first line of the input. The sequence p is given on the second line, and the sequence q is on the third one. There are no spaces or other delimiters inside the sequences; however, there could be trailing whitespace on these two lines.

Output

Output the sequences a and b on the first two lines of the output, correspondingly. Use the same format as the input.

Samples

inputoutput
1  
0 
0 
0
1
2   
01 
10 
10
00
Problem Author: Dmitry Gozman
Problem Source: Dmitry Gozman Contest 1, Petrozavodsk training camp, January 2007
To submit the solution for this problem go to the Problem set: 1530. Ones and Zeroes