GCD and MST

You are given an array $$$a$$$ of $$$n$$$ ($$$n \geq 2$$$) positive integers and an integer $$$p$$$. Consider an undirected weighted graph of $$$n$$$ vertices numbered from $$$1$$$ to $$$n$$$ for which the edges between the vertices $$$i$$$ and $$$j$$$ ($$$i<j$$$) are added in the following manner:

• If $$$gcd(a_i, a_{i+1}, a_{i+2}, \dots, a_{j}) = min(a_i, a_{i+1}, a_{i+2}, \dots, a_j)$$$, then there is an edge of weight $$$min(a_i, a_{i+1}, a_{i+2}, \dots, a_j)$$$ between $$$i$$$ and $$$j$$$.
• If $$$i+1=j$$$, then there is an edge of weight $$$p$$$ between $$$i$$$ and $$$j$$$.

Here $$$gcd(x, y, \ldots)$$$ denotes the greatest common divisor (GCD) of integers $$$x$$$, $$$y$$$, ....

Note that there could be multiple edges between $$$i$$$ and $$$j$$$ if both of the above conditions are true, and if both the conditions fail for $$$i$$$ and $$$j$$$, then there is no edge between these vertices.

The goal is to find the weight of the minimum spanning tree of this graph.