<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>

import pprint

class Solution:
    def canSortArray(self, nums: List[int]) -> bool:
        
        set_bits = []
        for i in range(0, len(nums)):
            set_bits.append(self.countBits(nums[i]))

        pprint.pp(set_bits)

        prev_max = 0
        curr_max = nums[0]
        prev_bits = set_bits[0]
        for i in range(1, len(nums)):
            
            if prev_bits == set_bits[i]:
                if nums[i] < prev_max:
                    return False
                curr_max = nums[i] if nums[i] > curr_max else curr_max
            else:
                prev_max = curr_max
                curr_max = nums[i]
                prev_bits = set_bits[i]
                if nums[i] < prev_max:
                    return False

            

        return True

    def countBits(self, num: int) -> int:
        return sum(b == '1' for b in bin(num))
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