<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 Solution:
    def maximumStrongPairXor(self, nums: List[int]) -> int:
        nums.sort()
        a=[bin(i)[2:] for i in nums]
        s=0
        for i in a:
            s=max(s,len(i))
        a=[i.zfill(s) for i in a]
        trie={}
        for i in a:
            c=trie
            for j in i:
                c[j]=c.get(j,{})
                c=c[j]
        ans=0
        for i in range(len(a)):
            n=s
            cur=""
            c=trie
            for j in a[i]:
                fl=0
                if(j=="1"):
                    if("0" in c):
                        l=int(cur+"0"*n,2)
                        r=min(int(cur+'0'+'1'*(n-1),2),2*nums[i])
                        if(l<=r and l>=nums[i]):
                            p=bisect.bisect_left(nums,l)
                            q=bisect.bisect_right(nums,r)
                            if(p!=q):
                                fl=1
                                cur+='0'
                                n-=1
                                c=c["0"]
                else:
                    if("1" in c):
                        l=int(cur+"1"+"0"*(n-1),2)
                        r=min(int(cur+'1'*(n),2),2*nums[i])
                        if(l<=r):
                            p=bisect.bisect_left(nums,l)
                            q=bisect.bisect_right(nums,r)
                            if(p!=q):
                                fl=1
                                cur+='1'
                                n-=1
                                c=c["1"]
                if(fl==0):
                    cur+=j
                    n-=1
                    c=c[j]
            op=int(cur,2)
            # print(nums[i],op)
            if(abs(nums[i]-op)<=min(nums[i],op)):
                ans=max(ans,nums[i]^int(cur,2))
        return ans
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