<p>Given an integer array <code>nums</code>, return <em>the maximum result of </em><code>nums[i] XOR nums[j]</code>, where <code>0 &lt;= i &lt;= j &lt; n</code>.</p>

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

<pre>
<strong>Input:</strong> nums = [3,10,5,25,2,8]
<strong>Output:</strong> 28
<strong>Explanation:</strong> The maximum result is 5 XOR 25 = 28.
</pre>

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

<pre>
<strong>Input:</strong> nums = [14,70,53,83,49,91,36,80,92,51,66,70]
<strong>Output:</strong> 127
</pre>

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

<ul>
	<li><code>1 &lt;= nums.length &lt;= 2 * 10<sup>5</sup></code></li>
	<li><code>0 &lt;= nums[i] &lt;= 2<sup>31</sup> - 1</code></li>
</ul>

class Solution:
    def findMaximumXOR(self, nums: List[int]) -> int:
        if len(nums) == 1:
            return 0
        
        max_size = len(format(max(nums), 'b'))
        binary_repr = [format(num, f'0{max_size}b') for num in nums]
        # binary_repr = [bin(num)[2:].zfill(max_size) for num in nums]

        def split(arr, col):
            zeros, ones = [], []
            for i in arr:
                if binary_repr[i][col] == '1':
                    ones.append(i)
                else:
                    zeros.append(i)
            return zeros, ones

        def solve(zeros, ones, col):
            if col == max_size:
                return nums[zeros[0]] ^ nums[ones[0]]
            
            if len(zeros) == 0 or len(ones) == 0:
                arr = max([zeros, ones], key=len)
                zeros, ones = split(arr, col)
                return solve(zeros, ones, col + 1)
            
            zz, zo = split(zeros, col)
            oz, oo = split(ones, col)

            res = float('-inf')

            if len(zo) > 0 and len(oz) > 0:
                res = max(res, solve(oz, zo, col + 1))

            if len(zz) > 0 and len(oo) > 0:
                res = max(res, solve(zz, oo, col + 1))

            if res == float('-inf'):
                return solve(zeros, ones, col + 1)
            
            return res

        return solve(list(range(len(nums))), [], 0)


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