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: Runtime Error)

#AGC030 B - Powers of two
import collections
import math
N=int(input())
A=list(map(int,input().split()))
A.sort(reverse=True)
cnter=collections.Counter(A)
ans=0
for a in A:
    inv=2**(int(math.log2(a))+1)
    if cnter[a]==0:
        continue
    if cnter[a]>=2 and a==inv//2:a
        cnter[a]=cnter[a]-2
        ans=ans+1
        continue
    if inv-a in cnter:
        cnter[inv-a]=cnter[inv-a]-1
        ans=ans+1
print(ans)