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 class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Solver solver = new Solver();
        solver.solve(in, out);
        out.close();
    }
    static class Solver {
        public void solve(InputReader in, PrintWriter out) {
            int n = in.nextInt();
            long tot = 0;
            Map<Integer, Integer> map = new HashMap<>();
            for (int i = 0; i < n; ++i) {
                int a = in.nextInt();
                for (int j = 1; j < 31; ++j) {
                    int tmp = (1 << j) - a;
                    if (tmp > 0 && map.containsKey(tmp)) {
                        tot += map.get(tmp);
                    }
                }
                map.put(a, map.containsKey(a) ? map.get(a) + 1 : 1);
            }
            out.println(tot);
        }
    }
    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;
        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }
        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreElements()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }
        public String nextLine() {
            String s = "";
            try {
                s = reader.readLine();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
            return s;
        }
        public int nextInt() {
            return Integer.parseInt(next());
        }
        public long nextLong() {
            return Long.parseLong(next());
        }
        public double nextDouble() {
            return Double.parseDouble(next());
        }
    }
}