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 PowersOfTwo implements Runnable {

    BufferedReader in;
    PrintWriter out;
    StringTokenizer tok = new StringTokenizer("");

    void init() throws FileNotFoundException {
        try {
            in = new BufferedReader(new FileReader("input.txt"));
            out = new PrintWriter("output.txt");
        } catch (Exception e) {
            String filename = "";
            if (filename.isEmpty()) {
                in = new BufferedReader(new InputStreamReader(System.in));
                out = new PrintWriter(System.out);
            } else {
                in = new BufferedReader(new FileReader(filename + ".in"));
                out = new PrintWriter(filename + ".out");
            }
        }
    }

    String readString() {
        while (!tok.hasMoreTokens()) {
            try {
                tok = new StringTokenizer(in.readLine(), " :");
            } catch (Exception e) {
                return null;
            }
        }
        return tok.nextToken();
    }

    int readInt() {
        return Integer.parseInt(readString());
    }

    long[] readLongArray(int size) {
        long[] res = new long[size];
        for (int i = 0; i < size; i++) {
            res[i] = readLong();
        }
        return res;
    }

    long readLong() {
        return Long.parseLong(readString());
    }

    double readDouble() {
        return Double.parseDouble(readString());
    }

    <T> List<T>[] createGraphList(int size) {
        List<T>[] list = new List[size];
        for (int i = 0; i < size; i++) {
            list[i] = new ArrayList<>();
        }
        return list;
    }

    class Graph {
        int[][] graph;
        List<Integer>[] temp;
        int n;

        Graph(int n) {
            this.n = n;
            graph = new int[n][];
            temp = createGraphList(n);
        }

        void add(int x, int y) {
            temp[x].add(y);
            temp[y].add(x);
        }

        void addDir(int x, int y) {
            temp[x].add(y);
        }

        void build() {
            for (int i = 0; i < n; i++) {
                graph[i] = new int[temp[i].size()];
                for (int j = 0; j < temp[i].size(); j++) graph[i][j] = temp[i].get(j);
            }
        }

        void buildWithUniq() {
            for (int i = 0; i < n; i++) {
                HashSet<Integer> uniqSet = new HashSet<>();
                uniqSet.addAll(temp[i]);
                graph[i] = new int[uniqSet.size()];
                int index = 0;
                for (int x : uniqSet) {
                    graph[i][index++] = x;
                }
            }
        }
    }

    public static void main(String[] args) {
        new Thread(null, new PowersOfTwo(), "", 1l * 200 * 1024 * 1024).start();
    }

    long timeBegin, timeEnd;

    void time() {
        timeEnd = System.currentTimeMillis();
        System.err.println("Time = " + (timeEnd - timeBegin));
    }

    long memoryTotal, memoryFree;

    void memory() {
        memoryFree = Runtime.getRuntime().freeMemory();
        System.err.println("Memory = " + ((memoryTotal - memoryFree) >> 10)
                + " KB");
    }

    public void run() {
        try {
            timeBegin = System.currentTimeMillis();
            memoryTotal = Runtime.getRuntime().freeMemory();
            init();
            solve();
            out.close();
            if (System.getProperty("ONLINE_JUDGE") == null) {
                time();
                memory();
            }
        } catch (Exception e) {
            e.printStackTrace();
            System.exit(-1);
        }
    }
    private void solve() {
        int n = readInt();
        if(n==0)
        	return ;
        long[] a = readLongArray(n);
        Map<Long,Long> hm=new HashMap<Long,Long>();  
        Long sum = (long) 0;
        Long count = (long) 0;
        for (int i=0;i<n;i++) {
            for(int j=0;j<31;j++)
            {
            	 Long l =(long) (1 << j);
            	 if(hm.get((l-a[i]))!=null)
            		 count+=hm.get(l-a[i]);
            	    
            	 
            }
            if(hm.get(a[i])==null)
            	hm.put(a[i],(long) 1);
            else
                hm.put(a[i],(hm.get(a[i]))+1);
          
        }
        out.println(count);
    }

}