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.

n=int(input())
l=list(map(int,input().split()))
d={}
k=0
for i in range(n) :
    
    for j in range(1,32) :
        m=2**j
        f=-1
        try :
            d[m-l[i]]
            f=0
        except KeyError :
            pass
        if f==0  :
            k+=d[m-l[i]]
    f=-1
    try :
        d[l[i]]
        f=0
    except KeyError :
        pass
    if f==0 :
        d[l[i]]+=1
    else :
        d[l[i]]=1
print(k)
            
