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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

## 貪欲
# 大きい数xとすると、2べきになるyは一意に定まる
# x < x + y < = 2*x
import sys
from collections import defaultdict
sys.setrecursionlimit(10**7)

N = int(input())
As = sorted(list(map(int, input().split())),reverse=True)
d = defaultdict(int)
for a in As:
    d[a] += 1
cnt = 0
for a in As:
    n = 0
    while 2**n < a:
        n += 1
    p = 2**n - a 
    if d[p] > 0:
        d[p] -= 1
        cnt += 1
    d[a] -= 1
print(cnt)