<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>

import math
class Solution:
    def insertGreatestCommonDivisors(self,head):
        if not head or not head.next:
            return head
        a = []
        while head:
            a.append(head.val)
            head = head.next
        m = self.make_arr(a)
        tail = start = ListNode(0)
        for i in m :
            tail.next = ListNode(i)
            tail = tail.next
        return start.next
            

    def greatest_factor(self, r, t):
        d = set()
        e = set()
        for i in range(1, int(math.ceil(r ** 0.5))+1):
            if r % i == 0:
                d.add(i)
                d.add(r // i)
        for l in range(1, int(math.ceil(t ** 0.5))+1):
            if t % l == 0:
                e.add(l)
                e.add(t // l)
        d = sorted(d)
        d.reverse()
        # print(d,e, int(math.ceil(16**0.5)+1))
        for k in d:
            if k in e:
                return k
        return 1

    def make_arr(self,a):
        b = []
        for i in range(len(a)-1):
            b.append(a[i])
            if a[i] % a[i+1] == 0:
                b.append(a[i+1])
            elif a[i+1] % a[i] == 0:
                b.append(a[i])
            else:
                c = self.greatest_factor(a[i],a[i+1])
                b.append(c)
        b.append(a[-1])
        return b


s = Solution()
print(s.make_arr([18, 6, 10, 3,6,666]))
180