<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 BIT():
    def __init__(self, n):
        self.n = n
        self.tree = [0] * (n + 1)

    def sum(self, i):
        ans = 0
        i += 1
        while i > 0:
            ans += self.tree[i]
            i -= (i & (-i))
        return ans

    def update(self, i, value):
        i += 1
        while i <= self.n:
            self.tree[i] += value
            i += (i & (-i))

class Solution:
    def countOperationsToEmptyArray(self, nums) -> int:
        mp=defaultdict(int)
        for id,i in enumerate(nums):
            mp[i]=id
        n=len(nums)
        bt=BIT(n)
        for i in range(n):
            bt.update(i,1)
        last=-1
        ans=0
        for i in sorted(nums):
            li=0
            bt.update(mp[i],-1)
            if last==-1:
                ans+=bt.sum(mp[i])+1
                last=mp[i]
            elif last<mp[i]:
                ans+=bt.sum(mp[i])-bt.sum(last)+1
                last=mp[i]
            elif last>mp[i]:
                li=bt.sum(n-1)-bt.sum(last)
                ans+=bt.sum(mp[i])+li+1
                last=mp[i]
                
        return ans

1980