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.
def answer(n,A):
    count=0
    d={A[0]:1}
    for i in range(1,n):
        for j in range(1,32):
            if 2**j-A[i] in d:
                count+=d[2**j-A[i]]
        if A[i] in d:
            d[A[i]]+=1
        else:
            d[A[i]]=1
    
    return count
    

n=int(input())
arr=list(map(int,input().split()))
print(answer(n,arr))