<p>There is a rooted tree consisting of <code>n</code> nodes numbered <code>0</code> to <code>n - 1</code>. Each node&#39;s number denotes its <strong>unique genetic value</strong> (i.e. the genetic value of node <code>x</code> is <code>x</code>). The <strong>genetic difference</strong> between two genetic values is defined as the <strong>bitwise-</strong><strong>XOR</strong> of their values. You are given the integer array <code>parents</code>, where <code>parents[i]</code> is the parent for node <code>i</code>. If node <code>x</code> is the <strong>root</strong> of the tree, then <code>parents[x] == -1</code>.</p>

<p>You are also given the array <code>queries</code> where <code>queries[i] = [node<sub>i</sub>, val<sub>i</sub>]</code>. For each query <code>i</code>, find the <strong>maximum genetic difference</strong> between <code>val<sub>i</sub></code> and <code>p<sub>i</sub></code>, where <code>p<sub>i</sub></code> is the genetic value of any node that is on the path between <code>node<sub>i</sub></code> and the root (including <code>node<sub>i</sub></code> and the root). More formally, you want to maximize <code>val<sub>i</sub> XOR p<sub>i</sub></code>.</p>

<p>Return <em>an array </em><code>ans</code><em> where </em><code>ans[i]</code><em> is the answer to the </em><code>i<sup>th</sup></code><em> query</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/06/29/c1.png" style="width: 118px; height: 163px;" />
<pre>
<strong>Input:</strong> parents = [-1,0,1,1], queries = [[0,2],[3,2],[2,5]]
<strong>Output:</strong> [2,3,7]
<strong>Explanation: </strong>The queries are processed as follows:
- [0,2]: The node with the maximum genetic difference is 0, with a difference of 2 XOR 0 = 2.
- [3,2]: The node with the maximum genetic difference is 1, with a difference of 2 XOR 1 = 3.
- [2,5]: The node with the maximum genetic difference is 2, with a difference of 5 XOR 2 = 7.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/06/29/c2.png" style="width: 256px; height: 221px;" />
<pre>
<strong>Input:</strong> parents = [3,7,-1,2,0,7,0,2], queries = [[4,6],[1,15],[0,5]]
<strong>Output:</strong> [6,14,7]
<strong>Explanation: </strong>The queries are processed as follows:
- [4,6]: The node with the maximum genetic difference is 0, with a difference of 6 XOR 0 = 6.
- [1,15]: The node with the maximum genetic difference is 1, with a difference of 15 XOR 1 = 14.
- [0,5]: The node with the maximum genetic difference is 2, with a difference of 5 XOR 2 = 7.
</pre>

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

<ul>
	<li><code>2 &lt;= parents.length &lt;= 10<sup>5</sup></code></li>
	<li><code>0 &lt;= parents[i] &lt;= parents.length - 1</code> for every node <code>i</code> that is <strong>not</strong> the root.</li>
	<li><code>parents[root] == -1</code></li>
	<li><code>1 &lt;= queries.length &lt;= 3 * 10<sup>4</sup></code></li>
	<li><code>0 &lt;= node<sub>i</sub> &lt;= parents.length - 1</code></li>
	<li><code>0 &lt;= val<sub>i</sub> &lt;= 2 * 10<sup>5</sup></code></li>
</ul>

class Trie: 
    def __init__(self): 
        self.root = {}
        
    def insert(self, x): 
        node = self.root
        for i in range(18, -1, -1): 
            bit = (x >> i) & 1
            if bit not in node: node[bit] = {}
            node = node[bit]
        
    def search(self, x): 
        node = self.root
        max_xor = 0
        for i in range(18, -1, -1): 
            bit = (x >> i) & 1
            if 1^bit in node: 
                max_xor |= (1 << i)
                node = node[1^bit]
            else: 
                node = node[bit]
        return max_xor
        
    def remove(self, x): 
        node = self.root
        stack = []
        for i in range(18, -1, -1): 
            bit = (x >> i) & 1
            stack.append((node, bit))
            node = node[bit]
        for node, bit in reversed(stack):
            if len(node[bit]) == 0:
                del node[bit]
            else:
                break

class Solution:
    def maxGeneticDifference(self, parents: List[int], queries: List[List[int]]) -> List[int]:
        from collections import defaultdict
        
        mp = defaultdict(list)
        for i, (node, val) in enumerate(queries): 
            mp[node].append((val, i))
        
        tree, root = defaultdict(list), -1
        for i, x in enumerate(parents): 
            if x == -1: root = i
            else: tree[x].append(i)
        
        ans = [0] * len(queries)
        trie = Trie()
        
        def fn(x): 
            """Collect query results while traversing the tree."""
            trie.insert(x)
            for v, i in mp[x]: 
                ans[i] = trie.search(v)
            for xx in tree[x]: 
                fn(xx)
            trie.remove(x)
        
        fn(root)
        return ans
3743