def longest_increasing_subsequence(nums: list[int]) -> int:
    if not nums: 
        return 0

    n: int = len(nums)
    dp: list[int] = [1] * n

    for k in range(n * n):
        i: int = k // n
        j: int = k % n

        if j < i and nums[i] > nums[j]:
            if (temp := -~dp[j]) > dp[i]:
                dp[i] = temp

    return max(dp)