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 {

    private static void solve(InputReader in, OutputWriter out) {
        int n = in.nextInt();

        Map<Integer, Integer> cnts = new HashMap<>();
        int[] ar = new int[n];
        for (int i = 0; i < ar.length; i++) {
            ar[i] = in.nextInt();

            if (!cnts.containsKey(ar[i]))
                cnts.put(ar[i], 1);
            else
                cnts.put(ar[i], cnts.get(ar[i]) + 1);
        }

        int[] powers = new int[30];
        powers[0] = 2;
        for (int i = 1; i < powers.length; i++) {
            powers[i] = powers[i - 1] * 2;
        }

        long cnt = 0;
        for (int value : ar) {
            cnts.put(value, cnts.get(value) - 1);

            for (int j : powers) {
                int pair = j - value;

                if (cnts.containsKey(pair)) {
                    cnt += cnts.get(pair);
                }
            }
        }

        out.print(cnt);
    }

    private static void shuffleArray(int[] array) {
        int index;
        Random random = new Random();
        for (int i = array.length - 1; i > 0; i--) {
            index = random.nextInt(i + 1);
            if (index != i) {
                array[index] ^= array[i];
                array[i] ^= array[index];
                array[index] ^= array[i];
            }
        }
    }

    public static void main(String[] args) {
        InputReader in = new InputReader(System.in);
        OutputWriter out = new OutputWriter(System.out);
        solve(in, out);
        in.close();
        out.close();
    }

    private static class InputReader {
        private BufferedReader br;
        private StringTokenizer st;

        InputReader(InputStream is) {
            br = new BufferedReader(new InputStreamReader(is));
            st = null;
        }

        String nextLine() {
            String line = null;
            try {
                line = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return line;
        }

        String next() {
            while (st == null || !st.hasMoreTokens()) {
                String line = nextLine();
                if (line == null) return null;
                st = new StringTokenizer(line);
            }
            return st.nextToken();
        }

        byte nextByte() {
            return Byte.parseByte(next());
        }

        short nextShort() {
            return Short.parseShort(next());
        }

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

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }

        void close() {
            try {
                br.close();
            } catch (IOException e) {
                e.printStackTrace();
            }
        }
    }

    private static class OutputWriter {
        BufferedWriter bw;

        OutputWriter(OutputStream os) {
            bw = new BufferedWriter(new OutputStreamWriter(os));
        }

        void print(int i) {
            print(Integer.toString(i));
        }

        void println(int i) {
            println(Integer.toString(i));
        }

        void print(long l) {
            print(Long.toString(l));
        }

        void println(long l) {
            println(Long.toString(l));
        }

        void print(double d) {
            print(Double.toString(d));
        }

        void println(double d) {
            println(Double.toString(d));
        }

        void print(boolean b) {
            print(Boolean.toString(b));
        }

        void println(boolean b) {
            println(Boolean.toString(b));
        }

        void print(char c) {
            try {
                bw.write(c);
            } catch (IOException e) {
                e.printStackTrace();
            }
        }

        void println(char c) {
            println(Character.toString(c));
        }

        void print(String s) {
            try {
                bw.write(s);
            } catch (IOException e) {
                e.printStackTrace();
            }
        }

        void println(String s) {
            print(s);
            print('\n');
        }

        void close() {
            try {
                bw.close();
            } catch (IOException e) {
                e.printStackTrace();
            }
        }
    }
}
