<p>Given a <strong>(0-indexed)</strong> integer array <code>nums</code> and two integers <code>low</code> and <code>high</code>, return <em>the number of <strong>nice pairs</strong></em>.</p>

<p>A <strong>nice pair</strong> is a pair <code>(i, j)</code> where <code>0 &lt;= i &lt; j &lt; nums.length</code> and <code>low &lt;= (nums[i] XOR nums[j]) &lt;= high</code>.</p>

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

<pre>
<strong>Input:</strong> nums = [1,4,2,7], low = 2, high = 6
<strong>Output:</strong> 6
<strong>Explanation:</strong> All nice pairs (i, j) are as follows:
    - (0, 1): nums[0] XOR nums[1] = 5 
    - (0, 2): nums[0] XOR nums[2] = 3
    - (0, 3): nums[0] XOR nums[3] = 6
    - (1, 2): nums[1] XOR nums[2] = 6
    - (1, 3): nums[1] XOR nums[3] = 3
    - (2, 3): nums[2] XOR nums[3] = 5
</pre>

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

<pre>
<strong>Input:</strong> nums = [9,8,4,2,1], low = 5, high = 14
<strong>Output:</strong> 8
<strong>Explanation:</strong> All nice pairs (i, j) are as follows:
​​​​​    - (0, 2): nums[0] XOR nums[2] = 13
&nbsp;   - (0, 3): nums[0] XOR nums[3] = 11
&nbsp;   - (0, 4): nums[0] XOR nums[4] = 8
&nbsp;   - (1, 2): nums[1] XOR nums[2] = 12
&nbsp;   - (1, 3): nums[1] XOR nums[3] = 10
&nbsp;   - (1, 4): nums[1] XOR nums[4] = 9
&nbsp;   - (2, 3): nums[2] XOR nums[3] = 6
&nbsp;   - (2, 4): nums[2] XOR nums[4] = 5</pre>

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

<ul>
	<li><code>1 &lt;= nums.length &lt;= 2 * 10<sup>4</sup></code></li>
	<li><code>1 &lt;= nums[i] &lt;= 2 * 10<sup>4</sup></code></li>
	<li><code>1 &lt;= low &lt;= high &lt;= 2 * 10<sup>4</sup></code></li>
</ul>
class Solution:

    def helper(self, nums, range_val):
        map1 = defaultdict(int)
        map2 = defaultdict(int)

        # Create frequency map for nums
        for num in nums:
            map1[num] = map1.get(num, 0) + 1

        res = 0
        while range_val > 0:
            for key in list(map1.keys()):
                val = map1[key]
                map2[key >> 1] = map2.get(key >> 1, 0) + val
                if (range_val & 1) > 0:
                    res += val * map1.get((range_val - 1) ^ key, 0)

            # Prepare for the next iteration
            map1 = map2
            map2 = {}
            range_val >>= 1

        return res // 2

    def countPairs(self, nums: List[int], low: int, high: int) -> int:

        return self.helper(nums, high + 1) - self.helper(nums, low)

20000