<p>You are given an integer array <code>nums</code> that is <strong>sorted in non-decreasing order</strong>.</p>

<p>Determine if it is possible to split <code>nums</code> into <strong>one or more subsequences</strong> such that <strong>both</strong> of the following conditions are true:</p>

<ul>
	<li>Each subsequence is a <strong>consecutive increasing sequence</strong> (i.e. each integer is <strong>exactly one</strong> more than the previous integer).</li>
	<li>All subsequences have a length of <code>3</code><strong> or more</strong>.</li>
</ul>

<p>Return <code>true</code><em> if you can split </em><code>nums</code><em> according to the above conditions, or </em><code>false</code><em> otherwise</em>.</p>

<p>A <strong>subsequence</strong> of an array is a new array that is formed from the original array by deleting some (can be none) of the elements without disturbing the relative positions of the remaining elements. (i.e., <code>[1,3,5]</code> is a subsequence of <code>[<u>1</u>,2,<u>3</u>,4,<u>5</u>]</code> while <code>[1,3,2]</code> is not).</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,2,3,3,4,5]
<strong>Output:</strong> true
<strong>Explanation:</strong> nums can be split into the following subsequences:
[<strong><u>1</u></strong>,<strong><u>2</u></strong>,<strong><u>3</u></strong>,3,4,5] --&gt; 1, 2, 3
[1,2,3,<strong><u>3</u></strong>,<strong><u>4</u></strong>,<strong><u>5</u></strong>] --&gt; 3, 4, 5
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,2,3,3,4,4,5,5]
<strong>Output:</strong> true
<strong>Explanation:</strong> nums can be split into the following subsequences:
[<strong><u>1</u></strong>,<strong><u>2</u></strong>,<strong><u>3</u></strong>,3,<strong><u>4</u></strong>,4,<strong><u>5</u></strong>,5] --&gt; 1, 2, 3, 4, 5
[1,2,3,<strong><u>3</u></strong>,4,<strong><u>4</u></strong>,5,<strong><u>5</u></strong>] --&gt; 3, 4, 5
</pre>

<p><strong class="example">Example 3:</strong></p>

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

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= nums.length &lt;= 10<sup>4</sup></code></li>
	<li><code>-1000 &lt;= nums[i] &lt;= 1000</code></li>
	<li><code>nums</code> is sorted in <strong>non-decreasing</strong> order.</li>
</ul>

class Solution:
    def isPossible(self, nums: List[int]) -> bool:
        
        n = len(nums)
        ending_with = defaultdict(list)

        for v in nums:

            if v - 1 not in ending_with or not ending_with[v - 1]:
                heapq.heappush(ending_with[v], 1)
            else:
                new_len = 1 + heapq.heappop(ending_with[v - 1])
                heapq.heappush(ending_with[v], new_len)

        # print(ending_with)

        for k, v in ending_with.items():
            
            if not v:
                continue

            if v[0] < 3:
                # print(k, v)
                return False
        
        return True
17800