<p>You are given the <code>head</code> of a linked list.</p>

<p>The nodes in the linked list are <strong>sequentially</strong> assigned to <strong>non-empty</strong> groups whose lengths form the sequence of the natural numbers (<code>1, 2, 3, 4, ...</code>). The <strong>length</strong> of a group is the number of nodes assigned to it. In other words,</p>

<ul>
	<li>The <code>1<sup>st</sup></code> node is assigned to the first group.</li>
	<li>The <code>2<sup>nd</sup></code> and the <code>3<sup>rd</sup></code> nodes are assigned to the second group.</li>
	<li>The <code>4<sup>th</sup></code>, <code>5<sup>th</sup></code>, and <code>6<sup>th</sup></code> nodes are assigned to the third group, and so on.</li>
</ul>

<p>Note that the length of the last group may be less than or equal to <code>1 + the length of the second to last group</code>.</p>

<p><strong>Reverse</strong> the nodes in each group with an <strong>even</strong> length, and return <em>the</em> <code>head</code> <em>of the modified linked list</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/10/25/eg1.png" style="width: 699px; height: 124px;" />
<pre>
<strong>Input:</strong> head = [5,2,6,3,9,1,7,3,8,4]
<strong>Output:</strong> [5,6,2,3,9,1,4,8,3,7]
<strong>Explanation:</strong>
- The length of the first group is 1, which is odd, hence no reversal occurs.
- The length of the second group is 2, which is even, hence the nodes are reversed.
- The length of the third group is 3, which is odd, hence no reversal occurs.
- The length of the last group is 4, which is even, hence the nodes are reversed.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/10/25/eg2.png" style="width: 284px; height: 114px;" />
<pre>
<strong>Input:</strong> head = [1,1,0,6]
<strong>Output:</strong> [1,0,1,6]
<strong>Explanation:</strong>
- The length of the first group is 1. No reversal occurs.
- The length of the second group is 2. The nodes are reversed.
- The length of the last group is 1. No reversal occurs.
</pre>

<p><strong class="example">Example 3:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/11/17/ex3.png" style="width: 348px; height: 114px;" />
<pre>
<strong>Input:</strong> head = [1,1,0,6,5]
<strong>Output:</strong> [1,0,1,5,6]
<strong>Explanation:</strong>
- The length of the first group is 1. No reversal occurs.
- The length of the second group is 2. The nodes are reversed.
- The length of the last group is 2. The nodes are reversed.
</pre>

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

<ul>
	<li>The number of nodes in the list is in the range <code>[1, 10<sup>5</sup>]</code>.</li>
	<li><code>0 &lt;= Node.val &lt;= 10<sup>5</sup></code></li>
</ul>

class Solution:
    def reverseEvenLengthGroups(self, head: ListNode) -> ListNode:

        node, nums, ans = head, [], []
        T = lambda x: x*(x+1)//2
        flip = lambda x: x if len(x)%2 else x[::-1]         #  Example: head = 1->5->4->2->6->3->0->8

        while node:                                         #    nums = [1,5,4,2,6,3,0,8]
            nums.append(node.val)
            node = node.next

        for i in range(ceil(-0.5+sqrt(0.25+2*len(nums)))):  #     ans = [[1], [5,4], [2,6,3], [0,8]]
            ans.append(nums[T(i):T(i+1)])

        ans = chain(*map(flip,ans))                         #     ans = chain(*[[1], [4,5], [2,6,3], [8,0]])
                                                            #         = chain([1], [4,5], [2,6,3], [8,0])
                                                            #         = [1, 4,5, 2,6,3, 8,0]

        node = head                                         #    head = 1->4->5->2->6->3->8->0
        for a in ans:
            node.val  = a
            node = node.next

        return head
44000