Problem:
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.

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

Solution in Lua (5.3.2) (judge verdict: Accepted)

local n=io.read("n")
local a,a_map={},{}
for i=1,n do
    local x=io.read("n")
    a[i]=x
    a_map[x]=(a_map[x] or 0)+1
end
table.sort(a)

local counter=0
for i=n,2,-1 do
    local p=1
    while a[i]>=p do
        p=p*2
    end
    if a_map[a[i]] and a_map[a[i]]>0 then
        a_map[a[i]]=a_map[a[i]]-1
        if a_map[p-a[i]] and a_map[p-a[i]]>0 then
            a_map[p-a[i]]=a_map[p-a[i]]-1
            counter=counter+1
        end
    end
end
print(counter)