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.HashMap;
import java.util.StringTokenizer;

/**
 * Created by constanzafierro on 29-07-16.
 */
public class PowersOfTwo {
    static int n;
    static long[] numbers, powersOfTwo;
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        n = Integer.parseInt(br.readLine());
        StringTokenizer st = new StringTokenizer(br.readLine());
        numbers = new long[n];
        HashMap<Long, Long> pairs = new HashMap<>();
        for (int i = 0; i < n; i++) {
            numbers[i] = Integer.parseInt(st.nextToken());
            pairs.put(numbers[i], 0L);
        }
        powersOfTwo = new long[32];
        powersOfTwo[0] = 1;
        for (int i = 1; i < 32; i++) {
            powersOfTwo[i] = powersOfTwo[i-1]*2;
        }
        long ans = 0;
        for (int i = n-1; i >= 0; i--) {
            int j = 31;
            long searched = 1;
            while (searched > 0){
                searched = powersOfTwo[j] - numbers[i];
                if (pairs.get(searched) != null) ans += pairs.get(searched);
                j--;
            }
            long times = pairs.get(numbers[i])+1;
            pairs.put(numbers[i], times);
        }
        System.out.println(ans);
    }
}
