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: Time Limit Exceeded)

var
  a:array[1..200000]of longint;
  f:array[1..200000]of boolean;
  n,s,i,j,ans:longint;
function sp(a,b:longint):boolean;
var c:longint;
begin
  c:=a+b;
  while c mod 2 = 0 do c:=c div 2;
  if c = 1 then sp:=true else sp := false
end;
begin
  readln(n);
  for i:=1 to n do begin
    read(a[i]);
    f[i]:=true
  end;
  for i:=2 to n do
  for j:=n downto i  do
    if a[j]>a[j-1] then begin
      s:=a[j];
      a[j]:=a[j-1];
      a[j-1]:=s
    end;
  for i:=1 to n-1 do
  for j:=i+1 to n do
  if sp(a[i],a[j])and f[i]and f[j] then begin
    ans:=ans+1;
    f[i]:=false;
    f[j]:=false
    end;
  write(ans)
end.