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())
s=0;k=0
a=list(map(int,input().split()))
d={}
for i in a:
    if i in d:
        d[i]+=1
    else:
        d[i]=1
for i in set(a):
    for j in range(32):
        if 1<<j == 2*i and i in d:
            s+=d[i]*(d[i]-1)//2
        elif (1<<j) - i in d:
            k+=d[i]*d[(1<<j) - i]
print(s+k//2)