<p>Given an integer array <code>nums</code>, partition it into two (contiguous) subarrays <code>left</code> and <code>right</code> so that:</p>

<ul>
	<li>Every element in <code>left</code> is less than or equal to every element in <code>right</code>.</li>
	<li><code>left</code> and <code>right</code> are non-empty.</li>
	<li><code>left</code> has the smallest possible size.</li>
</ul>

<p>Return <em>the length of </em><code>left</code><em> after such a partitioning</em>.</p>

<p>Test cases are generated such that partitioning exists.</p>

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

<pre>
<strong>Input:</strong> nums = [5,0,3,8,6]
<strong>Output:</strong> 3
<strong>Explanation:</strong> left = [5,0,3], right = [8,6]
</pre>

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

<pre>
<strong>Input:</strong> nums = [1,1,1,0,6,12]
<strong>Output:</strong> 4
<strong>Explanation:</strong> left = [1,1,1,0], right = [6,12]
</pre>

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

<ul>
	<li><code>2 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>
	<li><code>0 &lt;= nums[i] &lt;= 10<sup>6</sup></code></li>
	<li>There is at least one valid answer for the given input.</li>
</ul>

class Solution:
    def partitionDisjoint(self, nums: List[int]) -> int:
        left, right = [], [(num, i) for i, num in enumerate(nums)]
        heapq.heapify(right)
        left_max, left_max_idx = heapq.heappop(right)
        left_len = 1
        while left_max_idx != left_len - 1 or left_max > right[0][0]:
            count = left_max_idx - left_len + 1
            for i in range(count):
                #get the smallest from the right
                smallest, idx = heapq.heappop(right)
                left.append(smallest)
                left_max = max(left_max, smallest)
                left_max_idx = max(left_max_idx, idx)
                left_len += 1
        return left_max_idx + 1
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