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.

input()
arr = list(map(int, input().split()))

def sumK(arr, k):
  m = {} # a + b = k
  total = 0

  for number in arr:
    if number in m:
      total += m[number]
    #   m[number] += 1
    # else:
    compl = k - number
    m[compl] = m.get(compl, 0) + 1

  return total
 
k = 1
ans = 0
while k <= 2*10**9:
  ans += sumK(arr, k)
  k *= 2

print(ans)
