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 = tuple(map(int, input().split()))

ans = 0
pwtwo = [2**i for i in range(1, 31)]
pn = [0 for _ in range(n)]
ok = []
for i in range(n):
    for j in range(i+1, n):
        if (a[i]+a[j]) in pwtwo:
            ok.append((i, j))
            pn[i] += 1
            pn[j] += 1

while sum(x >= 2 for x in pn):
    if 1 in pn:
        i = pn.index(1)
        for j in range(n):
            if i in ok[j]:
                p, q = ok[j]
                pn[p] = 0
                pn[q] = 0
                break
        ans += 1
    else:
        ans += sum(x >= 2 for x in pn) // 2
        break

ans += sum(x >= 1 for x in pn) // 2

print(ans)