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)

from math import log2, ceil
from bisect import bisect_left, bisect_right

N = int(input())
a = list(map(int, input().split()))
a = sorted(a)
b = [True for _ in range(N)]

ans = 0
for i in list(range(N))[::-1]:
    if not b[i]: continue
    t = a[i]
    flg = False
    for j in list(range(ceil(log2(t)), int(log2(t * 2)) + 1))[::-1]:
        pair = 2 ** j - t
        left = bisect_left(a, pair)
        right = bisect_right(a, pair)
        # print(t, pair, a, b, left, right)
        if left == right:
            if left < N and left != i:
                if a[left] == pair and b[left]:
                    b[left] = False
                    b[i] = False
                    ans += 1
                    flg = True
                    break
        else:
            k = right - 1
            k = min(right - 1, N - 1)
            while k >= max(0, left):
                if a[k] == pair and b[k] and k != i:
                    b[k] = False
                    b[i] = False
                    ans += 1
                    flg = True
                    break
                k -= 1
            if flg:
                break

print(ans)