<p>You are given the <code>root</code> of a binary tree with <strong>unique values</strong>.</p>

<p>In one operation, you can choose any two nodes <strong>at the same level</strong> and swap their values.</p>

<p>Return <em>the minimum number of operations needed to make the values at each level sorted in a <strong>strictly increasing order</strong></em>.</p>

<p>The <strong>level</strong> of a node is the number of edges along the path between it and the root node<em>.</em></p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img src="https://assets.leetcode.com/uploads/2022/09/18/image-20220918174006-2.png" style="width: 500px; height: 324px;" />
<pre>
<strong>Input:</strong> root = [1,4,3,7,6,8,5,null,null,null,null,9,null,10]
<strong>Output:</strong> 3
<strong>Explanation:</strong>
- Swap 4 and 3. The 2<sup>nd</sup> level becomes [3,4].
- Swap 7 and 5. The 3<sup>rd</sup> level becomes [5,6,8,7].
- Swap 8 and 7. The 3<sup>rd</sup> level becomes [5,6,7,8].
We used 3 operations so return 3.
It can be proven that 3 is the minimum number of operations needed.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img src="https://assets.leetcode.com/uploads/2022/09/18/image-20220918174026-3.png" style="width: 400px; height: 303px;" />
<pre>
<strong>Input:</strong> root = [1,3,2,7,6,5,4]
<strong>Output:</strong> 3
<strong>Explanation:</strong>
- Swap 3 and 2. The 2<sup>nd</sup> level becomes [2,3].
- Swap 7 and 4. The 3<sup>rd</sup> level becomes [4,6,5,7].
- Swap 6 and 5. The 3<sup>rd</sup> level becomes [4,5,6,7].
We used 3 operations so return 3.
It can be proven that 3 is the minimum number of operations needed.
</pre>

<p><strong class="example">Example 3:</strong></p>
<img src="https://assets.leetcode.com/uploads/2022/09/18/image-20220918174052-4.png" style="width: 400px; height: 274px;" />
<pre>
<strong>Input:</strong> root = [1,2,3,4,5,6]
<strong>Output:</strong> 0
<strong>Explanation:</strong> Each level is already sorted in increasing order so return 0.
</pre>

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

<ul>
	<li>The number of nodes in the tree is in the range <code>[1, 10<sup>5</sup>]</code>.</li>
	<li><code>1 &lt;= Node.val &lt;= 10<sup>5</sup></code></li>
	<li>All the values of the tree are <strong>unique</strong>.</li>
</ul>

class Solution:                                                             # Ex:  root = [1, 4,3, 7,6,8,5, None,None,11,None,9,None,10,None]
    def minimumOperations(self, root: TreeNode) -> int:                     #           _____1____
                                                                            #          /          \
        ans, queue, level = 0, [root],[]                                    #         4___         3___
                                                                            #        /    \       /    \
        while queue :                                                       #       7     _6     8     _5
                                                                            #            /      /     /
            for node in queue:                                              #           11     9     10
                    if node:  level.extend([node.left, node.right])         #
                                                                            #  level         idx             ans
            arr = [(v,i) for i,v in enumerate([c.val for c in level if c])] #  –––––        –––––           –––––
            idx = [i for _,i in sorted(arr)]                                #  [4,3]        [1,0]             1
                                                                            #  [7,6,8,5]    [2,1,3,0]         2
            for i in range(len(idx)):                                       #  [11,9,10]    [1,2,0]           2
                while (idx[i] != i):                                        #                               –––––
                    j = idx[i]                                              #                                 5   <--- ans
                    idx[i], idx[j] = idx[j], idx[i]
                    ans += 1

            queue, level = level, []
        
        return ans
47900