Problem:
Score : 600 points

Problem Statement

Takahashi has N balls with positive integers written on them. The integer written on the i-th ball is A_i.
He would like to form some number of pairs such that the sum of the integers written on each pair of balls is a power of 2.
Note that a ball cannot belong to multiple pairs.
Find the maximum possible number of pairs that can be formed.

Here, a positive integer is said to be a power of 2 when it can be written as 2^t using some non-negative integer t.

Constraints

1 \leq N \leq 2\times 10^5

1 \leq A_i \leq 10^9

A_i is an integer.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

Print the maximum possible number of pairs such that the sum of the integers written on each pair of balls is a power of 2.

Sample Input 1

3
1 2 3

Sample Output 1

1

We can form one pair whose sum of the written numbers is 4 by pairing the first and third balls.
Note that we cannot pair the second ball with itself.

Sample Input 2

5
3 11 14 5 13

Sample Output 2

2

Solution in Python (3.4.3) (judge verdict: Wrong Answer)

N = int(input().strip())
A = list(map(int, input().strip().split()))
remain_a = [0 for _ in range(max(A) + 1)]
for a in A:
  remain_a[a] += 1
pair_d = {}
for i in range(len(A)):
  for j in range(i+1, len(A)):
    a = A[i] + A[j]
    if a & 1<<(len(bin(a))-3) == a:
      if A[i] not in pair_d:
        pair_d[A[i]] = [A[j]]
      else:
        pair_d[A[i]].append(A[j])

twop = 0
for i, jlist in sorted(pair_d.items(), key=lambda x: len(x[1])):
  for j in sorted(jlist, key=lambda x: remain_a[x]):
    if remain_a[i] > 0 and remain_a[j] > 0:
      twop += 1
      remain_a[i] -= 1
      remain_a[j] -= 1

print(twop)