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.)

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.

Constraints

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

Sample Input 1

3
XXX
YYY

Sample Output 1

XY

• If you swap nothing, the only common subsequence of XXX and YYY is the empty string.
• If you swap the 1-st characters, the common subsequences of YXX and XYY are the empty string, X, and Y.
• If you swap the 2-nd characters, the common subsequences of XYX and YXY are the empty string, X, Y, XY, and YX.
• If you swap the 3-rd characters, the common subsequences of XXY and YYX are the empty string, X and Y.

Doing two or more swaps is equivalent to one of the above after swapping S and T themselves.
Thus, the longest strings that can be a common subsequence are XY and YX. The lexicographically smaller of them, XY, is the answer.

Sample Input 2

1
X
Y

Sample Output 2

The answer may be the empty string.

Sample Input 3

4
XXYX
YYYY

Sample Output 3

XYY

XYY will be a common subsequence after, for instance, swapping just the 2-nd characters.
Any string that is longer or has the same length and is lexicographically smaller will not be a common subsequence after any combination of swaps, so this is the answer.

见题面 Input 部分

见题面 Output 部分