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: Accepted)

import math
from collections import defaultdict
def larger_nibeki(i):
    return 2 ** len(format(i, 'b'))
N, *A = map(int, open(0).read().split())
A.sort(reverse=True)
C = defaultdict(int)
for a in A:
    C[a] += 1
ans = 0
for a in A:
    if C[a] == 0:
        continue
    C[a] -= 1
    partner = larger_nibeki(a) - a
    if C[partner] > 0:
        ans += 1
        C[partner] -= 1
print(ans)