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 = list(map(int,input().split()))
a.sort(reverse=True)

b = [2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 
     131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 
     67108864, 134217728, 268435456, 536870912]

sum = 0
i = 0
u = [0 for i in range(len(a))]
while True:

    t = 0
    for bb in b :
        if bb > a[i]:
            t = bb - a[i]
            break
    
    try:
        idx = a.index(t)
        if u[idx] != 1:            
            sum += 1
            u[idx] = 1
    except Exception as e:
        pass
    
    i = i + 1
    if i >= len(a)-1:
        break

print(sum)