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)

import sys

def solve():
    N = int(sys.stdin.readline().rstrip())
    A = list(map(int,sys.stdin.readline().rstrip().split()))
    A = sorted(A, reverse=True)
    maxA = A[0]
    cntA = [0 for i in range(maxA+1)]
    for a in A:
        cntA[a] += 1

    ans = 0
    twos = 1 << 32
    for a in A:
        if a <= 2:
            return ans
        if cntA[a] == 0:
            continue
        cntA[a] -= 1
        #print('a =',a)
        while True:
            b = twos - a
            #print('b =',b)
            if b <= a:
                break
            twos //= 2
            if twos == 1:
                return ans
        if cntA[b] > 0:
            cntA[b] -= 1
            ans += 1
    return ans

print(solve())