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 java.util.*;
import java.io.*;
public class PowersofTwo
{
	
	
	/************************ SOLUTION STARTS HERE ***********************/
	
	
	
	private static void solve(FastScanner s1, PrintWriter out){
		
		final int MAX = 32;
		int pows[] = new int[MAX];
		for(int i=0;i<MAX;i++)
			pows[i] = 1 << i;
		
		HashMap<Integer,Integer> freq = new HashMap<>();
		int N = s1.nextInt();
		int arr[] = s1.nextIntArray(N);
		for(int a:arr)
			freq.put(a, freq.getOrDefault(a, 0) + 1);
		
		long cnt = 0;
		
		for(int a:arr){
			for(int pow:pows){
				int rem = pow - a;
				int f = freq.getOrDefault(rem, 0);
				cnt += (rem == a) ? f - 1 : f;
			}
		}
		cnt /= 2L;
		
		out.println(cnt);
	}
	
	
	
	/************************ SOLUTION ENDS HERE ************************/
	
	
	
	
	
	/************************ TEMPLATE STARTS HERE *********************/
	
	public static void main(String []args) throws IOException {
		FastScanner in  = new FastScanner(System.in);
		PrintWriter out = 
				new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)), false); 
		solve(in, out);
		in.close();
		out.close();
	}    
	
	static class FastScanner{
		BufferedReader reader;
		StringTokenizer st;
		FastScanner(InputStream stream){reader=new BufferedReader(new InputStreamReader(stream));st=null;}	
		String next()
		{while(st == null || !st.hasMoreTokens()){try{String line = reader.readLine();if(line == null){return null;}		    
		st = new StringTokenizer(line);}catch (Exception e){throw new RuntimeException();}}return st.nextToken();}
		String nextLine()  {String s=null;try{s=reader.readLine();}catch(IOException e){e.printStackTrace();}return s;}	    	  	
		int    nextInt()   {return Integer.parseInt(next());}
		long   nextLong()  {return Long.parseLong(next());}		
		double nextDouble(){return Double.parseDouble(next());}
		char   nextChar()  {return next().charAt(0);}
		int[]  nextIntArray(int n)         {int[] arr= new int[n];   int i=0;while(i<n){arr[i++]=nextInt();}  return arr;}
		long[] nextLongArray(int n)        {long[]arr= new long[n];  int i=0;while(i<n){arr[i++]=nextLong();} return arr;}	
		int[]  nextIntArrayOneBased(int n) {int[] arr= new int[n+1]; int i=1;while(i<=n){arr[i++]=nextInt();} return arr;}	    	
		long[] nextLongArrayOneBased(int n){long[]arr= new long[n+1];int i=1;while(i<=n){arr[i++]=nextLong();}return arr;}	    	
		void   close(){try{reader.close();}catch(IOException e){e.printStackTrace();}}				
	}
	
	/************************ TEMPLATE ENDS HERE ************************/
}