<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:
        # Idea....
        # we know from constarints taht our power of two can only be from 2^0 to 2^20
        # so we can start by knowing that we only need to compute that many two powers

        # our next step is to know that we need to look over each step in the array
        # A delicious meal is a power of two, so lets try all pwoers of two 
        # see if we can do the power of two, minus our current number, then is that number 
        # already in our dict? If it is, we can say we have another delicious meal. 
        # Once we've checked all powers of two for a particular element, we add that 
        # element to our dictionary so that future elements can use it. 
        mod = 1000000007
        nmeals = 0
        n = len(deliciousness)
        keep = dict()
        i = 0
        for each in deliciousness:
            power = 1
            # We use i as a counter to general the powers of two in range
            for i in range(22):
                if keep.get(power - each):
                    nmeals += keep[power - each]
                    nmeals %= mod
                power *= 2
            if keep.get(each):
                keep[each] += 1
            else:
                keep[each] = 1
        return nmeals
             
        
1293