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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.util.HashMap;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        EPowersOfTwo solver = new EPowersOfTwo();
        solver.solve(1, in, out);
        out.close();
    }

    static class EPowersOfTwo {
        int n;
        int[] arr;

        public void readInput(Scanner sc) {
            n = sc.nextInt();
            arr = new int[n];
            for (int i = 0; i < n; i++)
                arr[i] = sc.nextInt();
        }

        public void solve(int testNumber, Scanner sc, PrintWriter pw) {
            readInput(sc);
            HashMap<Integer, Integer> map = new HashMap<>();
            long ans = 0;
            for (int i = 0; i < n; i++) {
                for (int j = 1; j < 31; j++) {
                    ans += map.getOrDefault((1 << j) - arr[i], 0);
                }
                map.put(arr[i], map.getOrDefault(arr[i], 0) + 1);
            }
            pw.println(ans);
        }

    }

    static class Scanner {
        StringTokenizer st;
        BufferedReader br;

        public Scanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

        public String next() {
            try {
                while (st == null || !st.hasMoreTokens())
                    st = new StringTokenizer(br.readLine());
                return st.nextToken();
            } catch (Exception e) {
                throw new RuntimeException(e);
            }
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

    }
}


 				 	     	    			   		 	  		