<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>

class Solution:
    def countPairs(self, deliciousness: List[int]) -> int:
        """
        brute force:
        iterate over each element of array i, then try to the number of delcious meal you can make with it arr[i:]
        runtime (n**2)

        improved:
        given the constraints 0 <= deliciousness[i] <= 2**20 there's are 22 delicious numbers (validVal)
        we can sort the array and use a two pointer approach.
        use the twoSum approach where the target is each value in deliciousVals
        do some preprocessing with a hashmap counter, key = deliciousness and value the number of values with that deliciousness
        runtime: O(22 * n)
        """
        deliciousnessCnt = Counter(deliciousness)
        mod = 10 ** 9 + 7
        ans = 0
        for i in range(22):
            target = 2 ** i
            used = set()
            for ingredient, count in deliciousnessCnt.items():
                    if ingredient > target or ingredient in used:
                        continue
                    otherIngredient = target - ingredient
                    # n chose 2
                    goodMeals = 0
                    if otherIngredient == ingredient:
                        goodMeals = (count * (count-1)) // 2
                    else:
                        otherCnt = deliciousnessCnt.get(otherIngredient, 0)
                        goodMeals = otherCnt * count
                    
                    used.add(ingredient)
                    used.add(otherIngredient)
                    ans = (ans + goodMeals) % mod
                    
        return ans
26500