<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 <a href="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 --&gt; Y</code>, then for the corresponding two nodes <code>x</code> and <code>y</code> in the copied list, <code>x.random --&gt; 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>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2019/12/18/e1.png" style="width: 700px; height: 142px;" />
<pre>
<strong>Input:</strong> head = [[7,null],[13,0],[11,4],[10,2],[1,0]]
<strong>Output:</strong> [[7,null],[13,0],[11,4],[10,2],[1,0]]
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2019/12/18/e2.png" style="width: 700px; height: 114px;" />
<pre>
<strong>Input:</strong> head = [[1,1],[2,1]]
<strong>Output:</strong> [[1,1],[2,1]]
</pre>

<p><strong class="example">Example 3:</strong></p>

<p><strong><img alt="" src="https://assets.leetcode.com/uploads/2019/12/18/e3.png" style="width: 700px; height: 122px;" /></strong></p>

<pre>
<strong>Input:</strong> head = [[3,null],[3,0],[3,null]]
<strong>Output:</strong> [[3,null],[3,0],[3,null]]
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>0 &lt;= n &lt;= 1000</code></li>
	<li><code>-10<sup>4</sup> &lt;= Node.val &lt;= 10<sup>4</sup></code></li>
	<li><code>Node.random</code> is <code>null</code> or is pointing to some node in the linked list.</li>
</ul>

"""
# Definition for a Node.
class Node:
    def __init__(self, x: int, next: 'Node' = None, random: 'Node' = None):
        self.val = int(x)
        self.next = next
        self.random = random
"""

class Solution:
    def copyRandomList(self, head: 'Optional[Node]') -> 'Optional[Node]':
        if not head:
            return head

        hashmap = {}
        node = head
        while node:
            hashmap[node] = Node(node.val, None, None)
            node = node.next
        
        node = head
        while node:
            if node.next:
                hashmap[node].next = hashmap[node.next]
            if node.random:
                hashmap[node].random = hashmap[node.random]

            node = node.next
        
        return hashmap[head]

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