"""
The arithmetic sequence, 1487,4817,8147, in which each of the terms increases by 3330,
is unusual in two ways: (i) each of the three terms are prime, and, (ii) each of the
4-digit numbers are permutations of one another.

There are no arithmetic sequences made up of three 1-, 2-, or 3-digit primes, exhibiting this property,
but there is one other 4-digit increasing sequence.

What 12-digit number do you form by concatenating the three terms in this sequence?
"""

import time
from logging import root
from pathlib import Path


def timer(func):
    def wrapper(*args, **kwargs):
        start_time = time.time()
        result = func(*args, **kwargs)
        end_time = time.time()
        elapsed_time = end_time - start_time
        print(f"{func.__name__} time: {elapsed_time:.6f} seconds")
        return result

    return wrapper


@timer
def solve_ultra_optimized(n: int = 4) -> list[str]:
    limit = 10**n
    mini_limit = 10 ** (n - 1) + 1
    # ========== 1. Bitset 筛法（内存高效） ==========
    is_prime = bytearray(b"\x01") * limit
    is_prime[0] = is_prime[1] = 0

    # 埃氏筛，使用切片赋值加速
    for i in range(2, int(limit**0.5) + 1):
        if is_prime[i]:
            start = i * i
            is_prime[start:limit:i] = b"\x00" * ((limit - start - 1) // i + 1)

    # ========== 2. 按数字签名分组 ==========
    groups = {}
    for p in range(mini_limit, limit, 2):  # 只遍历奇数，4位质数必为奇数
        if is_prime[p]:
            key = "".join(sorted(str(p)))
            groups.setdefault(key, []).append(p)

    # ========== 3. 组内搜索（利用模18剪枝） ==========
    res = []
    for key, group in groups.items():
        if len(group) < 3:
            continue

        group.sort()
        group_set = set(group)  # 用于O(1)成员检查

        n = len(group)
        for i in range(n):
            a = group[i]
            for j in range(i + 1, n):
                b = group[j]
                d = b - a

                # 核心数学优化：公差必须是18的倍数
                # 原因：(1) 排列数字和相同 => 模9同余 => d%9==0
                #      (2) 质数>2都是奇数 => 奇+偶=奇 => d%2==0
                if d % 18 != 0:
                    continue

                c = b + d

                # 边界检查（利用group有序性提前终止）
                if c >= limit:
                    break

                # Bitset O(1) 质数检查
                if not is_prime[c]:
                    continue

                # 确认第三项在组内（数字签名匹配）
                if c in group_set:
                    res.append(f"{a}-{b}-{c}:{d}")

    return res


if __name__ == "__main__":
    try:
        n = int(input("Search digits (default is 4-digit): ") or "4")
    except ValueError:
        n = 4
    res = solve_ultra_optimized(n)
    if lr := len(res) > 10:
        head = 10
        print(
            f"Too much data, only showing the first ten rows. Other data saved in result_{n}_digit.txt."
        )
        root_path = Path(__file__).parent
        with open(f"{root_path}/result_{n}_digit.txt", "w", encoding="utf-8") as f:
            f.write("\n".join(res))
    else:
        head = lr
    for x in res[:head]:
        print(x)