<p>A <strong>good meal</strong> is a meal that contains <strong>exactly two different food items</strong> with a sum of deliciousness equal to a power of two.</p>

<p>You can pick <strong>any</strong> two different foods to make a good meal.</p>

<p>Given an array of integers <code>deliciousness</code> where <code>deliciousness[i]</code> is the deliciousness of the <code>i<sup>​​​​​​th</sup>​​​​</code>​​​​ item of food, return <em>the number of different <strong>good meals</strong> you can make from this list modulo</em> <code>10<sup>9</sup> + 7</code>.</p>

<p>Note that items with different indices are considered different even if they have the same deliciousness value.</p>

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

<pre>
<strong>Input:</strong> deliciousness = [1,3,5,7,9]
<strong>Output:</strong> 4
<strong>Explanation: </strong>The good meals are (1,3), (1,7), (3,5) and, (7,9).
Their respective sums are 4, 8, 8, and 16, all of which are powers of 2.
</pre>

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

<pre>
<strong>Input:</strong> deliciousness = [1,1,1,3,3,3,7]
<strong>Output:</strong> 15
<strong>Explanation: </strong>The good meals are (1,1) with 3 ways, (1,3) with 9 ways, and (1,7) with 3 ways.</pre>

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

<ul>
	<li><code>1 &lt;= deliciousness.length &lt;= 10<sup>5</sup></code></li>
	<li><code>0 &lt;= deliciousness[i] &lt;= 2<sup>20</sup></code></li>
</ul>

from collections import Counter

class Solution:
    def countPairs(self, deliciousness: List[int]) -> int:
        def isSqrt2(num):
            return num != 0 and num & (num - 1) == 0
        
        mod = 10 ** 9 + 7
        counts = Counter(deliciousness)
        vals = 0
        valid_powers = [1 << n for n in range(22)]
        print(valid_powers)
        for num, count in counts.items():

            for p2 in valid_powers:
                if p2 - num >= 0 and p2 - num in counts:
                    vals += count * (counts[p2 - num] - 1 if p2 - num == num else counts[p2 - num])




        # find all unique pairs in array such that their sum is equal to a power of 2
        # navie approach
        # pairs = []
        # vals = 0

        # for left in range(len(deliciousness)):
        #     for right in range(left + 1, len(deliciousness)):
        #         if isSqrt2(deliciousness[left] + deliciousness[right]):
        #             # pairs.append((deliciousness[left], deliciousness[right]))
        #             vals += 1
        
        return (vals // 2) % mod


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