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 com.pb.codeforces.practice;

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

public class CF702B {
	
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int n = in.nextInt();
		HashMap<Long, Integer> fs = new HashMap<>();
		long ans = 0;
		for(int i=0;i<n;i++) {
			long v = in.nextInt();
			for(long b=1;b< 1L << 40;b <<= 1)
				ans += fs.getOrDefault(b-v, 0);
			fs.put(v, fs.getOrDefault(v, 0)+1);
		}
		System.out.println(ans);
	}
}
