<p>You are given an array <code>nums</code>​​​ and an integer <code>k</code>​​​​​. The <font face="monospace">XOR</font> of a segment <code>[left, right]</code> where <code>left &lt;= right</code> is the <code>XOR</code> of all the elements with indices between <code>left</code> and <code>right</code>, inclusive: <code>nums[left] XOR nums[left+1] XOR ... XOR nums[right]</code>.</p>

<p>Return <em>the minimum number of elements to change in the array </em>such that the <code>XOR</code> of all segments of size <code>k</code>​​​​​​ is equal to zero.</p>

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

<pre>
<strong>Input:</strong> nums = [1,2,0,3,0], k = 1
<strong>Output:</strong> 3
<strong>Explanation: </strong>Modify the array from [<u><strong>1</strong></u>,<u><strong>2</strong></u>,0,<u><strong>3</strong></u>,0] to from [<u><strong>0</strong></u>,<u><strong>0</strong></u>,0,<u><strong>0</strong></u>,0].
</pre>

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

<pre>
<strong>Input:</strong> nums = [3,4,5,2,1,7,3,4,7], k = 3
<strong>Output:</strong> 3
<strong>Explanation: </strong>Modify the array from [3,4,<strong><u>5</u></strong>,<strong><u>2</u></strong>,<strong><u>1</u></strong>,7,3,4,7] to [3,4,<strong><u>7</u></strong>,<strong><u>3</u></strong>,<strong><u>4</u></strong>,7,3,4,7].
</pre>

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

<pre>
<strong>Input:</strong> nums = [1,2,4,1,2,5,1,2,6], k = 3
<strong>Output:</strong> 3
<strong>Explanation: </strong>Modify the array from [1,2,<strong><u>4,</u></strong>1,2,<strong><u>5</u></strong>,1,2,<strong><u>6</u></strong>] to [1,2,<strong><u>3</u></strong>,1,2,<strong><u>3</u></strong>,1,2,<strong><u>3</u></strong>].</pre>

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

<ul>
	<li><code>1 &lt;= k &lt;= nums.length &lt;= 2000</code></li>
	<li><code>​​​​​​0 &lt;= nums[i] &lt; 2<sup>10</sup></code></li>
</ul>

from collections import defaultdict
from typing import List

class Solution:
    def minChanges(self, input_array: List[int], num_groups: int) -> int:
        # The maximum XOR value for 10 bits is 1024 (2^10)
        x = 1 << 10
        
        # Create a list of dictionaries to count occurrences in each segment
        segment_counts = [defaultdict(int) for _ in range(num_groups)]
        # This array holds the size of each segment
        segment_sizes = [0] * num_groups
        
        # Loop through the array and count occurrences
        for idx, elem in enumerate(input_array):
            segment_counts[idx % num_groups][elem] += 1
            segment_sizes[idx % num_groups] += 1
        
        # change_counts[i] will hold the minimum number of changes needed for XOR of the new array equal to i
        change_counts = [float('inf')] * x
        change_counts[0] = 0
        
        # Iterate over the segments
        for group_index in range(num_groups):
            new_change_counts = [min(change_counts) + segment_sizes[group_index]] * x
            
            for xor_value in range(x):
                for number, count in segment_counts[group_index].items():
                    # Update the number of changes needed for each XOR value
                    new_change_counts[xor_value] = min(new_change_counts[xor_value], 
                                                         change_counts[xor_value ^ number] + 
                                                         segment_sizes[group_index] - count)
            
            change_counts = new_change_counts
        
        # The answer is the minimum number of changes needed to have XOR of the new array equal to 0
        return change_counts[0]

# Example usage:
solution_instance = Solution()
print(solution_instance.minChanges([1, 2, 3], 2))  # Example call

3524