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 Julia (0.5.0) (judge verdict: Wrong Answer)

parseInt(x) = parse(Int, x)
parseMap(x::Array{SubString{String},1}) = map(parseInt, x)
function bsearch(a,x);l,r=0,length(a)+1;while r-l>1;m=(r+l)>>1;if a[m]<=x;l=m;else;r=m;end;end;l;end

function main()
    n = readline() |> parseInt
    a = readline() |> split |> parseMap |> sort
    d = Dict{Int,Int}()
    for i in 1:n
        if haskey(d,a[i])
            d[a[i]]+=1
        else
            d[a[i]]=1
        end
    end
    x = 0
    for i in n:-1:1
        r = 0
        while 2^r<=a[i]
            r+=1
        end
        t = bsearch(a,2^r-a[i])
        if 0<t<=n
            if a[t]+a[i]==2^r
             if d[a[t]]>0&&d[a[i]]>0
                 x+=1
                 d[a[t]]-=1
                 d[a[i]]-=1
             end
            end
         end
     end

    println(x)
end

main()