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())
A = [int(i) for i in input().split()]
A.sort(reverse=True)
t = 0
while(A[0] + A[1] > 2**t):
    t += 1
mark = [0 for i in range(len(A))]
ct = 0
for i in range(len(A)):
    while(2**(t-1) > A[i]):
        t -= 1
    if mark[i] == 1:
        continue
    if 2**t - A[i] in A[i+1:]:
        j = A.index(2**t - A[i])
        mark[i] = 1
        mark[j] = 1
        ct += 1

print(ct)