Problem Statement

You are given strings $S$ and $T$ of length $N$ consisting of X and Y. For each $i = 1, 2, \dots, N$, you can swap the $i$-th character of $S$ and the $i$-th character of $T$ or choose not to do it. There are $2^N$ pairs of strings that can result from this process, including duplicates. Find the longest string that is a common subsequence (not necessarily contiguous) of one of such pairs. If there are multiple such strings, find the lexicographically smallest of them.

What is a common subsequence? A subsequence of string $S$ is a string obtained by deleting zero or more characters from $S$ and concatenating the remaining characters without changing the order. A common subsequence of strings $S$ and $T$ is a string that is a subsequence of both $S$ and $T$. (See also Sample Output 1.)

Constraints

• $1 \leq N \leq 50$
• Each of $S$ and $T$ is a string of length $N$ consisting of X and Y.

Input

The input is given from Standard Input in the following format:

N
S
T

Output

Print the lexicographically smallest of the longest strings that can be a common subsequence of the resulting pair of strings.