Problem Description

Given two strings $s$ and $t$ consisting of lowercase English letters, and an integer $L$, consider generating a string of length $L$ by arranging $s$ and $t$ in any order, using each string one or more times. You can use the same string multiple times.

For example, when $s =$ at, $t =$ code, and $L = 6$, you can generate strings like atatat, atcode, and codeat.

Among the strings of length $L$ generated in this way, find the lexicographically smallest one. Note that in the given cases, it is always possible to generate a string of length $L$.

Input Format

The input is given from the standard input in the following format:

$L$ $s$ $t$

Output Format

Output the lexicographically smallest string of length $L$ that can be generated as described in the problem statement.

Sample Input and Output

Sample Input #1

6
at
code

Sample Output #1

atatat

Sample Input #2

8
coding
festival

Sample Output #2

festival

Sample Input #3

8
same
same

Sample Output #3

samesame

Sample Input #4

10
coin
age

Sample Output #4

ageagecoin

Notes/Hints

Constraints

• $1 \leq L \leq 2 \times 10^5$
• $1 \leq |s|, |t| \leq L$
• $s$ and $t$ consist of lowercase English letters.
• It is possible to generate a string of length $L$ from $s$ and $t$ as described in the problem statement.

Sample Explanation 1

This input corresponds to the example given in the problem statement.

Sample Explanation 2

One of the strings $s$ or $t$ might be completely useless in generating a string of length $L$.

Sample Explanation 3

It is possible that $s = t$.

见题面 Input 部分

见题面 Output 部分