<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:
        good_meals = 0
        freq = Counter(deliciousness)
        good_meals_pair = set()

        for i in range(0,22):
            for meal in deliciousness:
                if pow(2,i) - meal >= 0 and pow(2,i) - meal in freq:
                    min_val = min(meal, pow(2,i) - meal)
                    max_val = max(meal, pow(2,i) - meal)
                    good_meals_pair.add((min_val, max_val))

        print(good_meals_pair)

        for meal_pair in good_meals_pair:
            m1, m2 = meal_pair
            n = m1 + m2
            # check if n is a power of two
            if ((n & (n-1) == 0) and n != 0):
                if m1 == m2:
                    good_meals += (freq[m1] * (freq[m1] - 1))//2
                else:
                    good_meals += freq[m1] * freq[m2]

        
        return good_meals % (pow(10,9) + 7)


        
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