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.util.*;

public class Main {

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        Map<Integer, Integer> map = new HashMap<>();
        int n = in.nextInt(), arr[] = new int[n];
        for (int i = 0; i < n; i++) {
            arr[i] = in.nextInt();
            if (map.containsKey(arr[i])) {
                map.replace(arr[i], map.get(arr[i]) + 1);
            } else {
                map.put(arr[i], 1);
            }
        }//for
        int power2[] = new int[32];
        for (int i = 0; i < 32; i++) {
            power2[i] = (int) Math.pow(2, i);
        }
        long cnt = 0;
        for (int i = 0; i < n; i++) {
            for (int j = 1; j < 32; j++) {
                if (power2[j] > arr[i]) {
                    int x = power2[j] - arr[i];
                    if (map.containsKey(x)) {
                        cnt = cnt + (long) map.get(x);
                        if (x == arr[i]) {
                            cnt--;
                        }
                    }
                }
            }//forpower
        }//fori
        System.out.println(cnt / 2);
    }//psvm
}//class
