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 $2$.