<p>You are given a <strong>0-indexed</strong> array of <strong>positive</strong> integers <code>nums</code>.</p>

<p>In one <strong>operation</strong>, you can swap any two <strong>adjacent</strong> elements if they have the <strong>same</strong> number of <span data-keyword="set-bit">set bits</span>. You are allowed to do this operation <strong>any</strong> number of times (<strong>including zero</strong>).</p>

<p>Return <code>true</code> <em>if you can sort the array, else return </em><code>false</code>.</p>

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

<pre>
<strong>Input:</strong> nums = [8,4,2,30,15]
<strong>Output:</strong> true
<strong>Explanation:</strong> Let&#39;s look at the binary representation of every element. The numbers 2, 4, and 8 have one set bit each with binary representation &quot;10&quot;, &quot;100&quot;, and &quot;1000&quot; respectively. The numbers 15 and 30 have four set bits each with binary representation &quot;1111&quot; and &quot;11110&quot;.
We can sort the array using 4 operations:
- Swap nums[0] with nums[1]. This operation is valid because 8 and 4 have one set bit each. The array becomes [4,8,2,30,15].
- Swap nums[1] with nums[2]. This operation is valid because 8 and 2 have one set bit each. The array becomes [4,2,8,30,15].
- Swap nums[0] with nums[1]. This operation is valid because 4 and 2 have one set bit each. The array becomes [2,4,8,30,15].
- Swap nums[3] with nums[4]. This operation is valid because 30 and 15 have four set bits each. The array becomes [2,4,8,15,30].
The array has become sorted, hence we return true.
Note that there may be other sequences of operations which also sort the array.
</pre>

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

<pre>
<strong>Input:</strong> nums = [1,2,3,4,5]
<strong>Output:</strong> true
<strong>Explanation:</strong> The array is already sorted, hence we return true.
</pre>

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

<pre>
<strong>Input:</strong> nums = [3,16,8,4,2]
<strong>Output:</strong> false
<strong>Explanation:</strong> It can be shown that it is not possible to sort the input array using any number of operations.
</pre>

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

<ul>
	<li><code>1 &lt;= nums.length &lt;= 100</code></li>
	<li><code>1 &lt;= nums[i] &lt;= 2<sup>8</sup></code></li>
</ul>

class Solution:
    def canSortArray(self, nums: List[int]) -> bool:
        def min_in_range(lst, start, end):
            # Ensure start and end are within bounds
            start = max(start, 0)
            end = min(end, len(lst))
            
            # Use enumerate to find the minimum value and its index within the specified range
            min_val, min_idx_in_sublist = min(
                (lst[i], i) for i in range(start, end)
            )
    
            return min_val, min_idx_in_sublist

        n = len(nums)
        
        for i in range(n - 1):
            min_val, min_index = min_in_range(nums, i, n)
            
            # Swap elements if necessary
            while min_index != i:
                # Compare bit counts and swap if they match
                if nums[min_index].bit_count() == nums[min_index - 1].bit_count():
                    nums[min_index], nums[min_index - 1] = nums[min_index - 1], nums[min_index]
                    min_index -= 1
                else:
                    return False
        
        return True

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