<p>You are given a <strong>2D</strong> integer array <code>coordinates</code> and an integer <code>k</code>, where <code>coordinates[i] = [x<sub>i</sub>, y<sub>i</sub>]</code> are the coordinates of the <code>i<sup>th</sup></code> point in a 2D plane.</p>

<p>We define the <strong>distance</strong> between two points <code>(x<sub>1</sub>, y<sub>1</sub>)</code> and <code>(x<sub>2</sub>, y<sub>2</sub>)</code> as <code>(x1 XOR x2) + (y1 XOR y2)</code> where <code>XOR</code> is the bitwise <code>XOR</code> operation.</p>

<p>Return <em>the number of pairs </em><code>(i, j)</code><em> such that </em><code>i &lt; j</code><em> and the distance between points </em><code>i</code><em> and </em><code>j</code><em> is equal to </em><code>k</code>.</p>

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

<pre>
<strong>Input:</strong> coordinates = [[1,2],[4,2],[1,3],[5,2]], k = 5
<strong>Output:</strong> 2
<strong>Explanation:</strong> We can choose the following pairs:
- (0,1): Because we have (1 XOR 4) + (2 XOR 2) = 5.
- (2,3): Because we have (1 XOR 5) + (3 XOR 2) = 5.
</pre>

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

<pre>
<strong>Input:</strong> coordinates = [[1,3],[1,3],[1,3],[1,3],[1,3]], k = 0
<strong>Output:</strong> 10
<strong>Explanation:</strong> Any two chosen pairs will have a distance of 0. There are 10 ways to choose two pairs.
</pre>

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

<ul>
	<li><code>2 &lt;= coordinates.length &lt;= 50000</code></li>
	<li><code>0 &lt;= x<sub>i</sub>, y<sub>i</sub> &lt;= 10<sup>6</sup></code></li>
	<li><code>0 &lt;= k &lt;= 100</code></li>
</ul>

from collections import defaultdict

class Solution:
    def countPairs(self, coordinates, k):
        # Initialize a dictionary to store the frequency of each coordinate
        coord_freq = defaultdict(int)
        
        # Initialize a variable to store the number of valid pairs
        valid_pairs = 0
        
        # Iterate through each coordinate
        for x, y in coordinates:
            # Iterate through all possible values of x1 and y1 that could result in the desired distance k
            for i in range(k + 1):
                x1 = x ^ i
                y1 = y ^ (k - i)
                # Increment the count of valid pairs by the frequency of the coordinate (x1, y1)
                valid_pairs += coord_freq[(x1, y1)]
            
            # Increment the frequency of the current coordinate
            coord_freq[(x, y)] += 1
        
        return valid_pairs

# Example usage:
solution = Solution()
coordinates = [[1,2],[4,2],[1,3],[5,2]]
k = 5
print(solution.countPairs(coordinates, k))  # Output: 2

coordinates = [[1,3],[1,3],[1,3],[1,3],[1,3]]
k = 0
print(solution.countPairs(coordinates, k))  # Output: 10
664300