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.StringTokenizer;
import java.util.TreeMap;

public class PowersOfTwo {
    public static TreeMap<Integer, Integer> tm = new TreeMap<>();

    public static long matches(int x) {
        int ans = 0;

        int sum = 2;
        for (int i = 1; i <= 30; i++) {
            int y = sum - x;
            if (tm.containsKey(y))
                ans += tm.get(y);
            sum <<= 1;
        }
        return ans;
    }

    public static void addToTreeMap(int x) {
        int freq = 0;
        if (tm.containsKey(x))
            freq = tm.get(x);

        tm.put(x, freq + 1);
    }

    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

        int n = Integer.parseInt(br.readLine());

        long ans = 0;

        StringTokenizer st = new StringTokenizer(br.readLine());


        for (int i = 0; i < n; i++) {
            int a = Integer.parseInt(st.nextToken());
            ans += matches(a);
            addToTreeMap(a);
        }

        System.out.println(ans);
    }
}