Score : $600$ points

Problem Statement

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 $t$.

Constraints

• $1 \leq N \leq 2\times 10^5$
• $1 \leq A_i \leq 10^9$
• $A_i$ is an integer.

Input

Input is given from Standard Input in the following format:

$N$

$A_1$ $A_2$ $...$ $A_N$

Output

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

1

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

2