Problem p02113 - Generation 3

Orig Description

Problem C: Palindrome
Problem
Taro has N strings of length L each. He loves palindromes, so he wants to choose some of the N strings, arrange them in any order he likes, and make the longest palindrome possible.
Find the longest palindrome that Taro can make. If there are multiple palindromes of the same length, output the lexicographically smallest one. If it is impossible to make a palindrome no matter how he chooses and arranges strings, output an empty line.
Input
The input is given in the following format:
N L
s1
s2
.
.
.
sN
The first line contains two integers N and L which are the number of strings and the length of the strings, respectively. The following N lines contain the strings that Taro has.
Constraints
The input satisfies the following constraints:
1 ≤ N ≤ 1000
1 ≤ L ≤ 30
si consists of lowercase English letters.
Output
Output the lexicographically smallest longest palindrome that can be made. If it is impossible to make a palindrome, output an empty line.
Sample Input 1
4 2
oi
io
rr
rr
Sample Output 1
iorrrroi
Sample Input 2
5 1
a
b
c
a
c
Sample Output 2
acbca
Sample Input 3
3 3
uki
uku
uke
Sample Output 3
uku

Extracted Specification

An integer N (1 ≤ N ≤ 1000), representing some quantity.
An integer L (1 ≤ L ≤ 30), representing another quantity.
N strings, each of length L, consisting of lowercase English letters.

### Example Input:

```
4 2
oi
io
rr
rr
```

### Function Signature:
Write a function f(N, L, strings) that takes in the input.
```python
def f(N: int, L: int, strings: List[str]):
    '''
    N: an integer
    L: an integer
    strings: a list of strings
    '''
```

Test Case Generator

To generate test cases for the problem "Palindrome", we need to create random inputs that satisfy the given constraints. Here's a Python function to generate such test cases:

```python
import random
import string

def generate_random_string(length):
    return ''.join(random.choices(string.ascii_lowercase, k=length))

def tcgen():
    N = random.randint(1, 1000)
    L = random.randint(1, 30)
    
    strings = [generate_random_string(L) for _ in range(N)]
    
    return N, L, strings

# Example usage
N, L, strings = tcgen()
print(N, L)
for s in strings:
    print(s)
```

### Explanation:
1. **generate_random_string(length)**: This helper function generates a random string of lowercase English letters of the specified length `L`.
2. **tcgen()**: This function generates the required test case.
   - It first selects random values for `N` (number of strings) and `L` (length of each string) within the given constraints.
   - It then generates `N` random strings each of length `L` using the `generate_random_string` function.
   - Finally, it returns `N`, `L`, and the list of strings.

### Example Output
Running the `tcgen()` function will give an output like this:

```
983 17
abcdeabcdeabcde
fghijfghijfghij
...
```

This output will be a randomly generated test case that you can use to test the solution to the problem. You can generate as many test cases as needed by calling the `tcgen()` function multiple times.

Extract Arguments

def extract_arguments(fh):
    N, L = map(int, fh.readline().strip().split())
    strings = [fh.readline().strip() for _ in range(N)]
    return N, L, strings