You are given n integers a1, a2, ..., an. Find the number of pairs of indexes i, j (i < j) that ai + aj is a power of 2 (i. e. some integer x exists so that ai + aj = 2x).

Input

The first line contains the single positive integer n (1 ≤ n ≤ 105) — the number of integers.

The second line contains n positive integers a1, a2, ..., an (1 ≤ ai ≤ 109).

Output

Print the number of pairs of indexes i, j (i < j) that ai + aj is a power of 2.

Examples

Input

4
7 3 2 1


Output

2


Input

3
1 1 1


Output

3

Note

In the first example the following pairs of indexes include in answer: (1, 4) and (2, 4).

In the second example all pairs of indexes (i, j) (where i < j) include in answer.
import com.sun.prism.shader.Solid_TextureYV12_AlphaTest_Loader;
import org.omg.Messaging.SYNC_WITH_TRANSPORT;
import org.omg.Messaging.SyncScopeHelper;

import java.math.BigInteger;
import java.util.*;
import java.io.*;
public class Main {
          public static void main(String[] args) throws IOException {
            // TODO Auto-generated method stub
            Scanner S = new Scanner(System.in);
            int n=S.nextInt();
              Map<Long,ArrayList<Integer>>all=new HashMap<>();
              long num=0;
              for (int i = 0; i < n; i++) {
                  num=S.nextLong();
                  if(!all.containsKey(num)){
                      all.put(num,new ArrayList<>());
                  }
                  all.get(num).add(1);
              }
              long ans=0;
              long req=0;
              long help=0;
              for (Long ii:all.keySet()) {
                  for (int k = 0; k <=31; k++) {
                      req=(long)Math.pow(2,k);
                      if(ii>req)continue;
                      if(all.containsKey(req-ii)&&(req-ii)!=ii){ans+=(((all.get(req-ii).size()*all.get(ii).size())));}
                      else if(all.containsKey(req-ii)&&(req-ii)==ii){help=all.get(ii).size()-1;if(help==-1)continue;ans+=(((help)*(help+1))/2);}
                      }
                      all.get(ii).clear();

              }
              System.out.println(ans);
        }
}



