Split Array into Consecutive Subsequences

lcpy gen -n 659   # by problem number
lcpy gen -s split_array_into_consecutive_subsequences   # by problem name

Input: nums = [1,2,3,3,4,5]
Output: true
Explanation: nums can be split into the following subsequences:
[1,2,3,3,4,5] --> 1, 2, 3
[1,2,3,3,4,5] --> 3, 4, 5

Input: nums = [1,2,3,3,4,4,5,5]
Output: true
Explanation: nums can be split into the following subsequences:
[1,2,3,3,4,4,5,5] --> 1, 2, 3, 4, 5
[1,2,3,3,4,4,5,5] --> 3, 4, 5

Input: nums = [1,2,3,4,4,5]
Output: false
Explanation: It is impossible to split nums into consecutive increasing subsequences of length 3 or more.

import heapq


class Solution:
    # Time: O(n log n)
    # Space: O(n)
    def is_possible(self, nums: list[int]) -> bool:
        chains: list[tuple[int, int]] = []
        for num in nums:
            while chains and chains[0][0] < num - 1:
                if heapq.heappop(chains)[1] < 3:
                    return False
            if chains and chains[0][0] == num - 1:
                _, length = heapq.heappop(chains)
                heapq.heappush(chains, (num, length + 1))
            else:
                heapq.heappush(chains, (num, 1))
        return all(length >= 3 for _, length in chains)