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.

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