<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 solve(self, pairs, k):
        result = []
        for a, b in pairs:
            cur_delta = abs(a - b)
            min_ = min(a, b)
            max_ = max(a, b)
            max_delta = max(a, b, k - a, k - b)
            max_delta += 1
            
            result.append((cur_delta, max_delta))
        return result

    def cost(self, pairs_proc, k):
        result = 0
        for cur_delta, max_delta in pairs_proc:
            if cur_delta == k:
                continue
            elif k <= max_delta:
                result += 1
            else:
                result += 2
        return result

    def minChanges(self, nums: List[int], k: int) -> int:
        n = len(nums)
        pairs = [(nums[i], nums[-(i + 1)]) for i in range(n//2)]
        pairs_proc = self.solve(pairs, k)

        n_pairs = len(pairs_proc)
        count_sweet_spot = Counter([p[0] for p in pairs_proc])
        count_max_delta = Counter([p[1] for p in pairs_proc])

        max_delta_count = [0] * (k + 1)
        for i in range(1, k + 1):
            max_delta_count[i] = max_delta_count[i-1] + count_max_delta[i]

        result = math.inf
        for i in range(k + 1):
            cur_k_result = n_pairs
            cur_k_result -= count_sweet_spot[i]
            cur_k_result += max_delta_count[i]
            result = min(result, cur_k_result)

        """
        result_brute = math.inf
        for i in range(k):
            cost_i = self.cost(pairs_proc, i)
            #print(f'{i=}, {cost_i=}')
            result_brute = min(result_brute, cost_i)

        if result != result_brute:
            print('wtf')
        """

        return result
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