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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.StringTokenizer;

import static java.lang.Integer.parseInt;

public class B_Powers_of_Two {
    static int n,ar[],pw2[];
    static HashMap<Integer, ArrayList<Integer>> map;
    public static void main(String[] args) throws IOException {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer tk;
        n = parseInt(in.readLine());
        pw2 = new int[31];
        map = new HashMap<>();
        ar = new int[n];
        tk = new StringTokenizer(in.readLine());
        for (int i = 0; i < n; i++) {
            ar[i] = parseInt(tk.nextToken());
            if(!map.containsKey(ar[i])){
                map.put(ar[i],new ArrayList<>());
                map.get(ar[i]).add(i);
                continue;
            }
            map.get(ar[i]).add(i);
        }
        long ans = 0;
        for (int i = 0; i < 31; i++) {
            pw2[i] = 1 << i;
        }
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < 31; j++) {
                if(map.containsKey(pw2[j] - ar[i])){
                    ans += search(i,map.get(pw2[j] - ar[i]));
                }
            }
        }
        System.out.println(ans);
    }

    static int search(int key,ArrayList<Integer> list){
        int l = 0,h = list.size() - 1,mid;
        int idx = list.size();
        while (l <= h){
            mid = (l + h) / 2;
            if(list.get(mid) > key){
                idx = mid;
                h = mid - 1;
            }
            else
                l = mid + 1;
        }
        return list.size() - idx;
    }
}
