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().strip())
d={}
for i in input().strip().split():
  x=int(i)
  if x in d:
    d[x]+=1
  else:
    d[x]=1
ans=0
for i in d.keys():
  for j in range(1,31):
    x=2**j-i
    if x<i:
      continue
    elif x==i:
      ans+=(d[i]*(d[i]-1))//2
    elif x>i and x in d:
      ans+=d[i]*d[x]
print(ans)