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.
from bisect import bisect_left as bi
n=int(input())
a=list(map(int,input().split()))
a.sort()
cnt={}
for i in range(n):
    cnt[a[i]]=0
for i in range(n):
    cnt[a[i]]+=1

b=[2**(i+1) for i in range(31)]
c=0
for i in range(n):
    for j in range(31):
        d=bi(a,b[j]-a[i])
        if d!=n:
            if a[d]==b[j]-a[i]:
                c=c+cnt[a[d]]
                if a[d]==a[i]:
                    c=c-1
print(c//2)