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.*;
import java.io.*;
public class Solution {
	static FastScanner scr=new FastScanner();
//	static Scanner scr=new Scanner(System.in);
	static PrintStream out=new PrintStream(System.out);
	static StringBuilder sb=new StringBuilder();
	
	
	
	
	static class pair{
		int x;int y;
		pair(int x,int y){ 
			this.x=x;this.y=y;
			
		}
	}
	static class triplet{
		int x;
		long y;
		int z;
		triplet(int x,long y,int z){
			this.x=x;
			this.y=y;
			this.z=z;
		}
	}
	static class FastScanner {
		 BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st=new StringTokenizer("");
	 	String next() {
	 		while (!st.hasMoreTokens())
	 			try {
	 				st=new StringTokenizer(br.readLine());
	 			} catch (IOException e) {
	 				e.printStackTrace();
	 			}
	 			return st.nextToken();
		} long gcd(long a,long b){
			if(b==0) {
				return a;
			}
				
			return gcd(b,a%b);
		}
	 	int[]  sort(int a[]) {
			 
	        int multiplier = 1, len = a.length, max = Integer.MIN_VALUE;
	        int b[] = new int[len];
	        int bucket[];
	        for (int i = 0; i < len; i++) if (max < a[i]) max = a[i];
	        while (max / multiplier > 0) {
	            bucket = new int[10];
	            for (int i = 0; i < len; i++) bucket[(a[i] / multiplier) % 10]++;
	            for (int i = 1; i < 10; i++) bucket[i] += (bucket[i - 1]);
	            for (int i = len - 1; i >= 0; i--) b[--bucket[(a[i] / multiplier) % 10]] = a[i];
	            for (int i = 0; i < len; i++) a[i] = b[i];
	            multiplier *= 10;
	        }
	        return a;
	    }
	 	 long modPow(long base,long exp) {
			if(exp==0) {
				return 1;
			}
			if(exp%2==0) {
				long res=(modPow(base,exp/2));
				return (res*res);
			}
			return (base*modPow(base,exp-1));
		}
		int []reverse(int a[]){
			int b[]=new int[a.length];
			int index=0;
			for(int i=a.length-1;i>=0;i--) {
				b[index]=a[i];
			}
			return b;
		}
		int nextInt() {
			return Integer.parseInt(next());
		}
		int[] readArray(int n) {
			int[] a=new int[n];
			for (int i=0; i<n; i++) a[i]=nextInt();
			return a;
		}
		long[] readLongArray(int n) {
			long  [] a=new long  [n];
			for (int i=0; i<n; i++) a[i]=nextLong();
			return a;
		}
		long nextLong() {
			return Long.parseLong(next());
		}
	}
	
	static void print(Object ele) {
		sb.append(ele).append(" ");
	}
	static void println(Object ele) {
		sb.append(ele).append('\n');
		
	}
	static void println() {
		sb.append('\n');
	}
//	static long LCM(long a,long b) {
//		return a*b/(scr.gcd(a, b));
//	}
//	static long n, m, k, l, q, count, sum, temp, ans;
//	static long []a;
//	static long b[];
//	static  char c[];
//	static char t[];
//	static boolean visited[][];
	
	static int count[];
	static void solve() {
		
		int n = scr.nextInt();
		int []a=new int[n];
		int power[]=new int[30+1];
		
		power[0]=1;
		for(int i=1;i<=30;i++) {
			power[i]=power[i-1]*2;
		}
		HashMap<Integer,Long>hm=new HashMap<>();
		
		for(int i=0;i<n;i++){
			a[i]=scr.nextInt();
			
			hm.put(a[i],hm.getOrDefault(a[i], (long)0)+1);
		}
		
		long cnt=0;
		HashSet<String>hs=new HashSet<>();
		for(Map.Entry<Integer,Long>m: hm.entrySet()) {
			int ele = m.getKey();
			for(int j=0;j<=30;j++) {
				int add = power[j]-ele;
				String s="";
				s+=add;
				s+=".";
				s+=ele;
				
				String s1="";
				s1+=ele;
				s1+=".";
				s1+=add;
				
				if(hm.containsKey(add) && hs.contains(s1)==false && hs.contains(s)==false) {
					
					
					if(ele!=add) {
						cnt += (long)(hm.get(ele)*(long)hm.get(add));
					}else {
						if(hm.get(ele)==1) {
							continue;
						}else {
							cnt+=get(hm.get(ele));
						}
					}
					hs.add(s1);
					hs.add(s);
				}
			}
		}
		out.println(cnt);
	}  
	static long get(long n) {
		if(n==1) {
			return n;
		}
		return (n-1)*(n)/2;
	}
	static int  MAX = Integer.MAX_VALUE;
	static int  MIN = Integer.MIN_VALUE;
	public static void main(String []args) {
//		int t=scr.nextInt();
//		while(t-->0) {
//			solve();
//		}
		solve();
	}
}
 