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: Time Limit Exceeded)

import bisect
import math

N = int(input())
A = list(map(int, input().split()))
A.sort()

ans = 0
used = [0] * N
for i in range(N - 1, 0, -1):
    if used[i] == 0:
        A_i = A[i]
        comp = 2 ** math.ceil(math.log(A_i + 1, 2)) - A_i
        j = bisect.bisect_left(A, comp, 0, i - 1)
        while True:
            if A[j] == comp:
                if used[j] == 0:
                    ans += 1
                    used[j] = 1
                    break
                else:
                    if j + 1 < i:
                        j += 1
                    else:
                        break
            else:
                break

print(ans)