from functools import cache
from collections import defaultdict


@cache
def is_palindrome(n: int) -> bool:
    ns = str(n)
    return ns == ns[::-1]


def euler_348():
    counts = defaultdict(int)

    for a in range(30000):
        for b in range(3000):
            x = a**2 + b**3
            if is_palindrome(x):
                counts[x] += 1
    rs = []
    for k, v in counts.items():
        if v == 4:
            rs.append(k)
    assert len(rs) == 5
    return sum(rs)


if __name__ == "__main__":
    solution = euler_348()
    print(f"e348.py: {solution}")
    assert(solution == 1004195061)