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())
array=[int(i) for i in input().split()]
ans=0
for j in range(32):
    num=2**j
    diction=dict()
    for i in array:
        if i in diction:
            ans+=diction[i]
        if num-i>0:
            if num-i in diction:
                diction[num-i]+=1
            else:
                diction[num-i]=1
print(ans)
