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: Time Limit Exceeded)

import math
N=int(input())
A=list(map(int,input().split()))
Ae1=[]
Ao1=[]
for i in range(N):
    if A[i]%2==0:
        Ae1.append(A[i])
    else:
        Ao1.append(A[i])
if Ao1!=[]:
    s=0
    Ao=sorted(Ao1,reverse=True)
    i=0
    while i<=len(Ao)-1:
        a=int(math.log2(Ao[i]))
        try:
            Ao.pop(Ao[i+1:].index(2**(a+1)-Ao[i])+i+1)
            s+=1
            i+=1
        except:
            i+=1
else:
    s=0
if Ae1!=[]:
    t=0
    Ae=sorted(Ae1,reverse=True)
    j=0
    while j<=len(Ae)-1:
        b=int(math.log2(Ae[j]))
        try:
            Ae.pop(Ae[j+1:].index(2**(b+1)-Ae[j])+j+1)
            t+=1
            j+=1
        except:
            j+=1
else:
    t=0
print(s+t)