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.HashMap;
import java.util.Scanner;
public class main1 {
public static void main(String[]args){
Scanner in = new Scanner(System.in);
int a = in.nextInt();
HashMap<Long,Long> m = new HashMap<Long,Long>();
long r=0;
for(int i=0;i<a;i++){
long x = in.nextLong();
long y=1;
while(y<x){y=y*2;}
while(y<2000000000){
long c=y-x;
y=y*2;
if(m.get(c)!=null){
r+=m.get(c);
}
}
if(m.get(x)==null){
m.put(x,1l);
}
else{
m.put(x,m.get(x)+1);
}
}
System.out.print(r);
}
}