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(raw_input())
d={}
for i in raw_input().split():
    if int(i) in d:
        d[int(i)]+=1
    else:
        d[int(i)]=1       
mylist=[]
ans=0  
for a in range(1,31):
    mylist.append(2**a)
 
for a in d:
    for b in mylist:
        if b-a in d:
            if b-a!=a:
                ans+=d[b-a]*d[a]
            else:
                ans+=(d[a]-1)*(d[a])
            
print ans//2