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.
//package codeforces.div2;

import java.util.HashMap;
import java.util.Scanner;

public class PowersofTwo {

    static public void print(long arr[]) {

        long count = 0;

        HashMap<Long,Integer> map = new HashMap<>();
        for(int i = 0; i < arr.length; i++) {

        }
        //int count = 0;

            for(int j = 0; j < arr.length; j++) {
                for(int i = 0; i < 32; i++) {

                    long val = (long)Math.pow(2, i);
                if(map.containsKey(val - arr[j])) {
                   count = count + map.get(val - arr[j]);
                    }

            }
                map.put(arr[j], map.getOrDefault(arr[j], 0) + 1);
         }
        System.out.println(count);
    }
    public static void main(String []args) {

        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int i = 0;
        long arr[] = new long[n];
        while ( i < arr.length) {
            arr[i++] = sc.nextLong();
        }
        print(arr);
    }
}
