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())
arr=list(map(int,input().split()))
p=[]
cnt=0
i=2
while i<10000000007:
    p.append(i)
    i*=2
d={}
for i in arr:
    if i not in d:
        d[i]=0
    d[i]+=1
cnt=0
for i in arr:
    d[i]-=1
    for j in p:
        v = j-i
        if v in d:
            cnt += d[v]
print(cnt)
