<p>Given the head of a linked list <code>head</code>, in which each node contains an integer value.</p>

<p>Between every pair of adjacent nodes, insert a new node with a value equal to the <strong>greatest common divisor</strong> of them.</p>

<p>Return <em>the linked list after insertion</em>.</p>

<p>The <strong>greatest common divisor</strong> of two numbers is the largest positive integer that evenly divides both numbers.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2023/07/18/ex1_copy.png" style="width: 641px; height: 181px;" />
<pre>
<strong>Input:</strong> head = [18,6,10,3]
<strong>Output:</strong> [18,6,6,2,10,1,3]
<strong>Explanation:</strong> The 1<sup>st</sup> diagram denotes the initial linked list and the 2<sup>nd</sup> diagram denotes the linked list after inserting the new nodes (nodes in blue are the inserted nodes).
- We insert the greatest common divisor of 18 and 6 = 6 between the 1<sup>st</sup> and the 2<sup>nd</sup> nodes.
- We insert the greatest common divisor of 6 and 10 = 2 between the 2<sup>nd</sup> and the 3<sup>rd</sup> nodes.
- We insert the greatest common divisor of 10 and 3 = 1 between the 3<sup>rd</sup> and the 4<sup>th</sup> nodes.
There are no more adjacent nodes, so we return the linked list.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2023/07/18/ex2_copy1.png" style="width: 51px; height: 191px;" />
<pre>
<strong>Input:</strong> head = [7]
<strong>Output:</strong> [7]
<strong>Explanation:</strong> The 1<sup>st</sup> diagram denotes the initial linked list and the 2<sup>nd</sup> diagram denotes the linked list after inserting the new nodes.
There are no pairs of adjacent nodes, so we return the initial linked list.
</pre>

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

<ul>
	<li>The number of nodes in the list is in the range <code>[1, 5000]</code>.</li>
	<li><code>1 &lt;= Node.val &lt;= 1000</code></li>
</ul>

# Definition for singly-linked list.
# class ListNode:
#     def __init__(self, val=0, next=None):
#         self.val = val
#         self.next = next
class Solution:
    def insertGreatestCommonDivisors(self, head: Optional[ListNode]) -> Optional[ListNode]:
        def gcd(a ,b):
            c = min(a,b)
            for i in range(c,0,-1):
                if a%i==0 and b%i==0:
                    return i
        curr = head
        while curr and curr.next:
            r = gcd(curr.val, curr.next.val)
            newN = ListNode(r)
            newN.next = curr.next
            curr.next = newN
            curr = curr.next.next
        return head
        
18400