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.io.*;
import java.util.*;
public final class power_of_two
{
    static BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
	static FastScanner sc=new FastScanner(br);
    static PrintWriter out=new PrintWriter(System.out);
	static Map<Long,Integer> m1=new HashMap<Long,Integer>();
	
	static void put(long num)
	{
		if(m1.get(num)==null)
		{
			m1.put(num,1);
		}
		else
		{
			m1.put(num,m1.get(num)+1);
		}
	}
	
	public static void main(String args[]) throws Exception
	{
		int n=sc.nextInt();long[] a=new long[n];long res=0;
		for(int i=0;i<n;i++)
		{
			a[i]=sc.nextInt();
		}
		long[] pow=new long[35];pow[0]=1;
		for(int i=1;i<35;i++)
		{
			pow[i]=(pow[i-1]*2L);
		}
		for(int i=0;i<n;i++)
		{
			for(int j=1;j<35;j++)	
			{
				if(pow[j]<=a[i])
				{
					continue;
				}
				long curr=pow[j]-a[i];
				if(m1.get(curr)!=null)
				{
					res=res+m1.get(curr);
				}
			}
			put(a[i]);
		}
		out.println(res);out.close();
	}
}
class FastScanner
{
    BufferedReader in;
    StringTokenizer st;

    public FastScanner(BufferedReader in) {
        this.in = in;
    }
	
    public String nextToken() throws Exception {
        while (st == null || !st.hasMoreTokens()) {
            st = new StringTokenizer(in.readLine());
        }
        return st.nextToken();
    }
	
	public String next() throws Exception {
		return nextToken().toString();
	}
	
    public int nextInt() throws Exception {
        return Integer.parseInt(nextToken());
    }

    public long nextLong() throws Exception {
        return Long.parseLong(nextToken());
    }

    public double nextDouble() throws Exception {
        return Double.parseDouble(nextToken());
    }
}