<p>You are given an integer array <code>nums</code> of size <code>n</code> where <code>n</code> is <strong>even</strong>, and an integer <code>k</code>.</p>

<p>You can perform some changes on the array, where in one change you can replace <strong>any</strong> element in the array with <strong>any</strong> integer in the range from <code>0</code> to <code>k</code>.</p>

<p>You need to perform some changes (possibly none) such that the final array satisfies the following condition:</p>

<ul>
	<li>There exists an integer <code>X</code> such that <code>abs(a[i] - a[n - i - 1]) = X</code> for all <code>(0 &lt;= i &lt; n)</code>.</li>
</ul>

<p>Return the <strong>minimum</strong> number of changes required to satisfy the above condition.</p>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">nums = [1,0,1,2,4,3], k = 4</span></p>

<p><strong>Output:</strong> <span class="example-io">2</span></p>

<p><strong>Explanation:</strong><br />
We can perform the following changes:</p>

<ul>
	<li>Replace <code>nums[1]</code> by 2. The resulting array is <code>nums = [1,<u><strong>2</strong></u>,1,2,4,3]</code>.</li>
	<li>Replace <code>nums[3]</code> by 3. The resulting array is <code>nums = [1,2,1,<u><strong>3</strong></u>,4,3]</code>.</li>
</ul>

<p>The integer <code>X</code> will be 2.</p>
</div>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">nums = [0,1,2,3,3,6,5,4], k = 6</span></p>

<p><strong>Output:</strong> <span class="example-io">2</span></p>

<p><strong>Explanation:</strong><br />
We can perform the following operations:</p>

<ul>
	<li>Replace <code>nums[3]</code> by 0. The resulting array is <code>nums = [0,1,2,<u><strong>0</strong></u>,3,6,5,4]</code>.</li>
	<li>Replace <code>nums[4]</code> by 4. The resulting array is <code>nums = [0,1,2,0,<strong><u>4</u></strong>,6,5,4]</code>.</li>
</ul>

<p>The integer <code>X</code> will be 4.</p>
</div>

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

<ul>
	<li><code>2 &lt;= n == nums.length &lt;= 10<sup>5</sup></code></li>
	<li><code>n</code> is even.</li>
	<li><code>0 &lt;= nums[i] &lt;= k &lt;= 10<sup>5</sup></code></li>
</ul>

import sys
class Solution:
    def minChanges(self, nums: List[int], k: int) -> int:
        hash2 = dict()
        firstHalf = nums[:len(nums)//2]
        nums = nums[len(nums)//2:]
        nums.reverse()
        for i in range(len(nums)):
            index = abs(nums[i] - firstHalf[i])
            try:
                hash2[index][0] += 1
                hash2[index][2].append(i)
            except:
                hash2[index] = [1,index,[i]]
        why = hash2.values()
        ok = max(why)
        yes = [y if y[0] == ok[0] else [(10**5)+3,k+1,[1]] for y in why]
        extra = 0
        amount = 0
        while True:
            extra = 0
            o = min(yes)
            banned = []
            amount = len(nums) - o[0]
            if o[1] <= math.ceil(k/2):
                break
            else:
                banned = [x for x in range(o[1]-1, k - o[1], -1)]
                for i in range(len(nums)):
                    if not i in o[2]:
                        if nums[i] in banned and firstHalf[i] in banned:
                            extra += 1
                why = [x if x[0] < o[0] else [-1] for x in why]
                if max(why)[0] == -1:
                    break
                if o[0] - extra >= max(why)[0]:
                    break
                else:
                    yes = [y if y[0] == max(why)[0] else [k+1,k+1,[1]] for y in why]
        return amount + extra
        
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