Problem Statement

Takahashi has $N$ balls with positive integers written on them. The integer written on the $i$-th ball is Ai​. 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 2t using some non-negative integer $t$.

Constraints

• 1≤N≤2×105
• 1≤Ai​≤109
• Ai​ is an integer.

Sample Input 1

3
1 2 3

Sample Output 1

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.

Sample Input 2

5
3 11 14 5 13

Sample Output 2

2