<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:
        check = [0] * (k + 1)
        n = len(nums)
        m = {}
        for i in range(0, len(nums)//2):
            cind = n - 1 - i
            val = nums[i]
            cval = nums[cind]
            if cval < val:
                val, cval = cval, val
            diff = cval - val
            # print(diff)
            m[diff] = m.get(diff, 0) + 1
            # val is always <= cval
            currmax = max(cval - 0, k - val)
            check[currmax] += 1

        precheck = []
        # print(check)
        sofar = 0
        for x in check:
            sofar += x
            precheck.append(sofar)

        tarr = []
        for key in m:
            tarr.append([m[key], key])
        tarr.sort(reverse=True)
        print(tarr)

        res = n

        for a, b in tarr:
            temp = 0
            if b > 0:
                temp += precheck[b-1]
            ccnt = m.get(b, 0)
            temp += n// 2 - ccnt
            res = min(res, temp)

        return res
32000