<p>You are given a <strong>0-indexed</strong> integer array <code>nums</code>. A pair of integers <code>x</code> and <code>y</code> is called a <strong>strong</strong> pair if it satisfies the condition:</p>

<ul>
	<li><code>|x - y| &lt;= min(x, y)</code></li>
</ul>

<p>You need to select two integers from <code>nums</code> such that they form a strong pair and their bitwise <code>XOR</code> is the <strong>maximum</strong> among all strong pairs in the array.</p>

<p>Return <em>the <strong>maximum</strong> </em><code>XOR</code><em> value out of all possible strong pairs in the array</em> <code>nums</code>.</p>

<p><strong>Note</strong> that you can pick the same integer twice to form a pair.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,2,3,4,5]
<strong>Output:</strong> 7
<strong>Explanation:</strong> There are 11 strong pairs in the array <code>nums</code>: (1, 1), (1, 2), (2, 2), (2, 3), (2, 4), (3, 3), (3, 4), (3, 5), (4, 4), (4, 5) and (5, 5).
The maximum XOR possible from these pairs is 3 XOR 4 = 7.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [10,100]
<strong>Output:</strong> 0
<strong>Explanation:</strong> There are 2 strong pairs in the array nums: (10, 10) and (100, 100).
The maximum XOR possible from these pairs is 10 XOR 10 = 0 since the pair (100, 100) also gives 100 XOR 100 = 0.
</pre>

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

<pre>
<strong>Input:</strong> nums = [500,520,2500,3000]
<strong>Output:</strong> 1020
<strong>Explanation:</strong> There are 6 strong pairs in the array nums: (500, 500), (500, 520), (520, 520), (2500, 2500), (2500, 3000) and (3000, 3000).
The maximum XOR possible from these pairs is 500 XOR 520 = 1020 since the only other non-zero XOR value is 2500 XOR 3000 = 636.
</pre>

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

<ul>
	<li><code>1 &lt;= nums.length &lt;= 5 * 10<sup>4</sup></code></li>
	<li><code>1 &lt;= nums[i] &lt;= 2<sup>20</sup> - 1</code></li>
</ul>

class TrieNode:
    def __init__(self):
        self.child={}
        self.is_end = False
        self.sco = 0
class Solution:
    def __init__(self):
        self.root = TrieNode()

    def insert(self,word):
        node = self.root
        for i in word:
            if i not in node.child:
                node.child[i] = TrieNode()
            node = node.child[i]
        node.sco+=1
        node.is_end = True
        
    def search(self,word):
        node = self.root
        cur = 0
        for i in word:
            j='1' if i=='0' else '0'
            if j in node.child:
                cur = cur<<1 | 1
                node = node.child[j]
            else:
                cur = cur<<1 
                node = node.child[i]
        return cur
    
    def delete(self,word):
        
        def helper(node,word,l):
            if l==len(word):
                if node.is_end:
                    node.sco-=1
                    if node.sco==0:
                        node.is_end = False
                    return len(node.child)==0 and node.sco==0
                return False
            
            if word[l] not in node.child:
                return False
            can_del = helper(node.child[word[l]],word,l+1)
            if can_del:
                del node.child[word[l]]
                return len(node.child)==0 and not node.is_end
            return False
        
        helper(self.root,word,0)


    def maximumStrongPairXor(self, nums: List[int]) -> int:
        m=0
        l,r = 0,0
        nums = sorted(nums)
        for i in range(len(nums)):
            b = "{:032b}".format(nums[i])
            while (nums[r]>2*nums[l]) and l<r:
                p = "{:032b}".format(nums[l])
                self.delete(p)
                l+=1
            if self.root.child:
                m = max(m,self.search(b))
            self.insert(b)
            r+=1
        return m
81800