<p>You are given an integer array <code>nums</code> of length <code>n</code> and an integer <code>numSlots</code> such that <code>2 * numSlots &gt;= n</code>. There are <code>numSlots</code> slots numbered from <code>1</code> to <code>numSlots</code>.</p>

<p>You have to place all <code>n</code> integers into the slots such that each slot contains at <strong>most</strong> two numbers. The <strong>AND sum</strong> of a given placement is the sum of the <strong>bitwise</strong> <code>AND</code> of every number with its respective slot number.</p>

<ul>
	<li>For example, the <strong>AND sum</strong> of placing the numbers <code>[1, 3]</code> into slot <u><code>1</code></u> and <code>[4, 6]</code> into slot <u><code>2</code></u> is equal to <code>(1 AND <u>1</u>) + (3 AND <u>1</u>) + (4 AND <u>2</u>) + (6 AND <u>2</u>) = 1 + 1 + 0 + 2 = 4</code>.</li>
</ul>

<p>Return <em>the maximum possible <strong>AND sum</strong> of </em><code>nums</code><em> given </em><code>numSlots</code><em> slots.</em></p>

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

<pre>
<strong>Input:</strong> nums = [1,2,3,4,5,6], numSlots = 3
<strong>Output:</strong> 9
<strong>Explanation:</strong> One possible placement is [1, 4] into slot <u>1</u>, [2, 6] into slot <u>2</u>, and [3, 5] into slot <u>3</u>. 
This gives the maximum AND sum of (1 AND <u>1</u>) + (4 AND <u>1</u>) + (2 AND <u>2</u>) + (6 AND <u>2</u>) + (3 AND <u>3</u>) + (5 AND <u>3</u>) = 1 + 0 + 2 + 2 + 3 + 1 = 9.
</pre>

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

<pre>
<strong>Input:</strong> nums = [1,3,10,4,7,1], numSlots = 9
<strong>Output:</strong> 24
<strong>Explanation:</strong> One possible placement is [1, 1] into slot <u>1</u>, [3] into slot <u>3</u>, [4] into slot <u>4</u>, [7] into slot <u>7</u>, and [10] into slot <u>9</u>.
This gives the maximum AND sum of (1 AND <u>1</u>) + (1 AND <u>1</u>) + (3 AND <u>3</u>) + (4 AND <u>4</u>) + (7 AND <u>7</u>) + (10 AND <u>9</u>) = 1 + 1 + 3 + 4 + 7 + 8 = 24.
Note that slots 2, 5, 6, and 8 are empty which is permitted.
</pre>

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

<ul>
	<li><code>n == nums.length</code></li>
	<li><code>1 &lt;= numSlots &lt;= 9</code></li>
	<li><code>1 &lt;= n &lt;= 2 * numSlots</code></li>
	<li><code>1 &lt;= nums[i] &lt;= 15</code></li>
</ul>

class Solution:
    def maximumANDSum(self, nums, numSlots):
        n = len(nums)
        numSlots *= 2  # Since each slot can hold 2 numbers
        
        # Initialize dp array
        dp = [[-1] * (1 << numSlots) for _ in range(n + 1)]
        dp[0][0] = 0  # Base case: no numbers, sum is 0
        
        # Function to check if a slot is available
        def is_available(mask, slot):
            return mask & (1 << slot) == 0
        
        # Function to place a number in a slot
        def place(mask, slot):
            return mask | (1 << slot)
        
        # Iterate over each number
        for i in range(1, n + 1):
            num = nums[i - 1]
            for mask in range(1 << numSlots):
                if dp[i - 1][mask] == -1:
                    continue
                for slot in range(numSlots):
                    if is_available(mask, slot):
                        new_mask = place(mask, slot)
                        dp[i][new_mask] = max(dp[i][new_mask], dp[i - 1][mask] + (num & (slot // 2 + 1)))
        
        # The answer is the maximum value in the last row of dp
        return max(dp[n])

# Example usage:
solution = Solution()
nums = [1, 2, 3, 4, 5, 6]
numSlots = 3
print(solution.maximumANDSum(nums, numSlots))  # Output: 9
55400