Score : $600$ points
Takahashi has $N$ balls with positive integers written on them. The integer written on the $i$-th ball is $A_i$. He would like to form some number of pairs such that the sum of the integers written on each pair of balls is a power of $2$. Note that a ball cannot belong to multiple pairs. Find the maximum possible number of pairs that can be formed.
Here, a positive integer is said to be a power of $2$ when it can be written as $2^t$ using some non-negative integer $t$.
Input is given from Standard Input in the following format:
$N$ $A_1$ $A_2$ $...$ $A_N$
Print the maximum possible number of pairs such that the sum of the integers written on each pair of balls is a power of $2$.
3 1 2 3
We can form one pair whose sum of the written numbers is $4$ by pairing the first and third balls. Note that we cannot pair the second ball with itself.
5 3 11 14 5 13