You are given the head of a linked list containing a sequence of integers separated by nodes with a value of $0$. The linked list begins and ends with nodes having Node.val equal to $0$.

For every pair of consecutive $0$ nodes, merge all intermediate nodes into a single node whose value is the sum of all the merged nodes. The resulting linked list must not contain any nodes with a value of $0$.

Return the head of the modified linked list.

Constraints:

• The number of nodes in the list is in the range $[3, 2 imes 10^5]$.

• $0 \leq$ Node.val $\leq 1000$

• There are no two consecutive nodes with Node.val $= 0$.

• The beginning and end of the linked list have Node.val $= 0$.

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.