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 Pascal (FPC 2.6.2) (judge verdict: Runtime Error)

var
  a:array[0..200000]of longint;
  f:array[0..100000000]of boolean;
  i,j,k,n,ans:longint;
Procedure qs(l,r:longint);
var
  i,j,t,mid:longint;
begin
  i:=l;j:=r;mid:=a[(l+r)div 2];
  repeat
    while a[i]<mid do inc(i);
    while a[j]>mid do dec(j);
    if i<=j then
      begin
        t:=a[i];a[i]:=a[j];a[j]:=t;
        inc(i);dec(j);
      end;
  until i>j;
  if l<j then qs(l,j);
  if i<r then qs(i,r);
end;
begin
  readln(n);
  j:=1;
  repeat
    f[j]:=true;
    j:=j*2;
  until j>1E9;
  k:=j;
  for i:=1 to n do
    read(a[i]);
  qs(1,n);
  for i:=1 to n do
    begin
      if a[i]<>0 then
        begin
          for j:=n downto i+1 do
            begin
              if (a[j]<>0)and((f[a[i]+a[j]])or(k=a[i]+a[j])) then
                begin
                  a[i]:=0;a[j]:=0;
                  inc(ans);
                end;
            end;
        end;
    end;
  write(ans);
end.