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)

import math
from collections import deque
N=int(input())
a=list(map(int,input().split()))
dq=deque(sorted(a))
ans=0
while len(dq)>1:#1になった時点で終わり。
    head=dq.pop()
    for n in range(head):
        if head<=2**n:
            t=n
            break
    if 2**(t-1)==head:
    #これは、2,4,8とか2のべき乗だけが引っかかる条件
        second=dq.pop()
        if head==second:
        #2のべきでも、きちんと2個存在するならおｋ
            ans+=1
        else:
            dq.append(second)
    else:
        #inが遅すぎるかもしれない。ちょっと高速化
        #上で被りうる奴は排除できている。
        for j in range(len(dq)):
            if 2**t-head==dq[j]:
                ans+=1
                dq.remove(dq[j])
                break
            elif 2**t-head<dq[j]:
                continue
            else:
                break
                #可能性なしがわかったらすぐ切る！！
print(ans)
#removeって探して削除なので遅い。popに変更してみよう
#forにしたことでインデックスも取得できるので。

#加えた工夫
# dequeにしてremoveをO(1)にした
# log2の計算をforにした