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.
l=lambda:map(int,raw_input().split())
n=input()
a=l()
T=[2**i for i in xrange(1,32)]
cnt=0
d={a[0]:1}
for i in xrange(1,n):
    for p in T:
        if p-a[i]>=1 and p-a[i] in d:
            cnt+=d[p-a[i]]
    d[a[i]]=d.get(a[i],0)+1
print cnt  