<p>You are given an integer array <code>nums</code> containing <strong>distinct</strong> numbers, and you can perform the following operations <strong>until the array is empty</strong>:</p>

<ul>
	<li>If the first element has the <strong>smallest</strong> value, remove it</li>
	<li>Otherwise, put the first element at the <strong>end</strong> of the array.</li>
</ul>

<p>Return <em>an integer denoting the number of operations it takes to make </em><code>nums</code><em> empty.</em></p>

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

<pre>
<strong>Input:</strong> nums = [3,4,-1]
<strong>Output:</strong> 5
</pre>

<table style="border: 2px solid black; border-collapse: collapse;">
	<thead>
		<tr>
			<th style="border: 2px solid black; padding: 5px;">Operation</th>
			<th style="border: 2px solid black; padding: 5px;">Array</th>
		</tr>
	</thead>
	<tbody>
		<tr>
			<td style="border: 2px solid black; padding: 5px;">1</td>
			<td style="border: 2px solid black; padding: 5px;">[4, -1, 3]</td>
		</tr>
		<tr>
			<td style="border: 2px solid black; padding: 5px;">2</td>
			<td style="border: 2px solid black; padding: 5px;">[-1, 3, 4]</td>
		</tr>
		<tr>
			<td style="border: 2px solid black; padding: 5px;">3</td>
			<td style="border: 2px solid black; padding: 5px;">[3, 4]</td>
		</tr>
		<tr>
			<td style="border: 2px solid black; padding: 5px;">4</td>
			<td style="border: 2px solid black; padding: 5px;">[4]</td>
		</tr>
		<tr>
			<td style="border: 2px solid black; padding: 5px;">5</td>
			<td style="border: 2px solid black; padding: 5px;">[]</td>
		</tr>
	</tbody>
</table>

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

<pre>
<strong>Input:</strong> nums = [1,2,4,3]
<strong>Output:</strong> 5
</pre>

<table style="border: 2px solid black; border-collapse: collapse;">
	<thead>
		<tr>
			<th style="border: 2px solid black; padding: 5px;">Operation</th>
			<th style="border: 2px solid black; padding: 5px;">Array</th>
		</tr>
	</thead>
	<tbody>
		<tr>
			<td style="border: 2px solid black; padding: 5px;">1</td>
			<td style="border: 2px solid black; padding: 5px;">[2, 4, 3]</td>
		</tr>
		<tr>
			<td style="border: 2px solid black; padding: 5px;">2</td>
			<td style="border: 2px solid black; padding: 5px;">[4, 3]</td>
		</tr>
		<tr>
			<td style="border: 2px solid black; padding: 5px;">3</td>
			<td style="border: 2px solid black; padding: 5px;">[3, 4]</td>
		</tr>
		<tr>
			<td style="border: 2px solid black; padding: 5px;">4</td>
			<td style="border: 2px solid black; padding: 5px;">[4]</td>
		</tr>
		<tr>
			<td style="border: 2px solid black; padding: 5px;">5</td>
			<td style="border: 2px solid black; padding: 5px;">[]</td>
		</tr>
	</tbody>
</table>

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

<pre>
<strong>Input:</strong> nums = [1,2,3]
<strong>Output:</strong> 3
</pre>

<table style="border: 2px solid black; border-collapse: collapse;">
	<thead>
		<tr>
			<th style="border: 2px solid black; padding: 5px;">Operation</th>
			<th style="border: 2px solid black; padding: 5px;">Array</th>
		</tr>
	</thead>
	<tbody>
		<tr>
			<td style="border: 2px solid black; padding: 5px;">1</td>
			<td style="border: 2px solid black; padding: 5px;">[2, 3]</td>
		</tr>
		<tr>
			<td style="border: 2px solid black; padding: 5px;">2</td>
			<td style="border: 2px solid black; padding: 5px;">[3]</td>
		</tr>
		<tr>
			<td style="border: 2px solid black; padding: 5px;">3</td>
			<td style="border: 2px solid black; padding: 5px;">[]</td>
		</tr>
	</tbody>
</table>

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

<ul>
	<li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>
	<li><code>-10<sup>9&nbsp;</sup>&lt;= nums[i] &lt;= 10<sup>9</sup></code></li>
	<li>All values in <code>nums</code> are <strong>distinct</strong>.</li>
</ul>

class Solution:
    def countOperationsToEmptyArray(self, nums: List[int]) -> int:
        pos = {}
        for i, x in enumerate(nums):
            pos[x] = i

        n = len(nums)
        # print(f"{n=}")
        # print(f"{nums=}")
        tree = [0] * (4*n+1)

        def init(node: int = 1, left: int = 0, right: int = n-1):
            if left == right:
                tree[node] = 1
                return
            mid = (left + right) // 2
            init(2*node, left, mid)
            init(2*node+1, mid+1, right)
            tree[node] = tree[2*node] + tree[2*node+1]
        
        init()
        # print(f"init {tree=}")

        def update(i: int, node: int = 1, left: int = 0, right: int = n-1):
            if left >= right:
                tree[node] = 0
                return
            mid = (left + right) // 2
            if i <= mid:
                update(i, 2*node, left, mid)
            else:
                update(i, 2*node+1, mid+1, right)
            tree[node] = tree[2*node] + tree[2*node+1]
        
        def query(qLeft: int, qRight: int, node: int = 1, left: int = 0, right: int = n-1):
            if qRight < 0: return 0
            if right < qLeft or qRight < left:
                return 0
            if qLeft <= left and right <= qRight:
                return tree[node]
            mid = (left + right) // 2
            return query(qLeft, qRight, 2*node, left, mid) + query(qLeft, qRight, 2*node+1, mid+1, right)
        
        counter = 0
        start = 0
        for i in sorted(nums):
            j = pos[i]
            if start <= j:
                counter += query(start, j-1)
            else:
                counter += query(start, n-1) + query(0, j-1)
            update(j)
            start = j
            # print(f"finished {i=}; now {start=}, {counter=}")
            # print(f"{tree=}")
        return counter + n
2598