<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>

class Solution:
    def minChanges(self, nums: List[int], k: int) -> int:
        D=Counter()
        arr, res = [], float("inf")

        for i in range(len(nums)//2):
            D[abs(nums[i]-nums[len(nums)-i-1])]+=1
        
        for diff,freq in D.items():
            arr.append([diff,freq])
        arr.sort(key=lambda x:x[1], reverse=True)

        for X,freq in arr[:50]:
            changes = 0

            for i in range(len(nums)//2):
                if abs(nums[i]-nums[len(nums)-i-1])==X:
                    continue
                a,b = (nums[i],nums[len(nums)-i-1])

                if 0 <= a - X <= k or 0 <= b + X <= k:
                    changes += 1
                elif 0 <= b - X <= k or 0 <= a + X <= k:
                    changes += 1
                else:
                    changes += 2

            res = min(res, changes)
            
        return res
30000