<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> </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> </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 <= Node.val <= 1000</code></li> </ul>