# Mutation from 'input.py'
import os
import sys
from typing import Any, Callable, Dict, List, Optional, Tuple

import numpy as np

import geniz


def expand_around_center(s: str, left: int, right: int) -> str:
    """Helper function to expand around a center and return the palindrome."""
    while left >= 0 and right < len(s) and (s[left] == s[right]):
        left -= 1
        right += 1
    return s[left + 1:right]

@geniz.CodeAgent()
def make_palindrome(s: str) -> str:
    """Find and return the shortest palindrome beginning with the given string."""
    if s == s[::-1]:
        return s + s
    for i in range(len(s)):
        palindrome = expand_around_center(s, i, i)
        palindrome2 = expand_around_center(s, i, i + 1)
        if len(palindrome) < len(palindrome2):
            result = s + palindrome[::-1]
        else:
            result = s + palindrome + palindrome[::-1]
        if is_valid_palindrome(result):
            return result
    raise ValueError('No palindrome could be adequately formed.')

def is_valid_palindrome(s: str) -> bool:
    """Helper to check if the constructed string s is a palindrome"""
    return s == s[::-1]
if __name__ == '__main__':
    print(make_palindrome(''))
    print(make_palindrome('cat'))
    print(make_palindrome('cata'))
    assert expand_around_center('a', 0, 1) == ''
    assert expand_around_center('a', 0, 0) == 'a'
    assert expand_around_center('ab', 0, 1) == 'b'
    assert expand_around_center('racecar', 0, 7) == 'racecar'
    assert expand_around_center('hello', 0, 4) == 'olleh'
    assert not expand_around_center('apple', 0, 2)
    assert is_valid_palindrome('aba') and (not is_valid_palindrome('abac'))
    assert is_valid_palindrome(make_palindrome('ab'))
