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())
a = list(map(int, input().strip().split()))
res = 0
countVal = {}
for i in range(n):
  pow2 = 1
  for j in range(30):
    pow2 *= 2
    if pow2 > a[i]:
      remain = pow2 - a[i]
      if remain in countVal:
        res += countVal[remain]
  if a[i] in countVal:
    countVal[a[i]] += 1
  else:
    countVal[a[i]] = 1
print(res)