<p>A linked list of length <code>n</code> is given such that each node contains an additional random pointer, which could point to any node in the list, or <code>null</code>.</p>
<p>Construct a <ahref="https://en.wikipedia.org/wiki/Object_copying#Deep_copy"target="_blank"><strong>deep copy</strong></a> of the list. The deep copy should consist of exactly <code>n</code><strong>brand new</strong> nodes, where each new node has its value set to the value of its corresponding original node. Both the <code>next</code> and <code>random</code> pointer of the new nodes should point to new nodes in the copied list such that the pointers in the original list and copied list represent the same list state. <strong>None of the pointers in the new list should point to nodes in the original list</strong>.</p>
<p>For example, if there are two nodes <code>X</code> and <code>Y</code> in the original list, where <code>X.random --> Y</code>, then for the corresponding two nodes <code>x</code> and <code>y</code> in the copied list, <code>x.random --> y</code>.</p>
<p>Return <em>the head of the copied linked list</em>.</p>
<p>The linked list is represented in the input/output as a list of <code>n</code> nodes. Each node is represented as a pair of <code>[val, random_index]</code> where:</p>
<ul>
<li><code>val</code>: an integer representing <code>Node.val</code></li>
<li><code>random_index</code>: the index of the node (range from <code>0</code> to <code>n-1</code>) that the <code>random</code> pointer points to, or <code>null</code> if it does not point to any node.</li>
</ul>
<p>Your code will <strong>only</strong> be given the <code>head</code> of the original linked list.</p>