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: Runtime Error)

import math
a=int(input())
o = []
e = []
x = list(map(int, input().split()))
for i in x:
    if i%2 ==0:e.append(i)
    else:o.append(i)
e.sort()
o.sort()
e[::-1]
o[::-1]
def cal(k):
    r=0
    l = len(k)
    if l <2:return 0
    else:
        for i in range(l):
            for j in range(i,l):
                lo = math.log2(k[i] + k[j])
                #print(lo,int(lo))
                if lo == int(lo):
                    r+=1
                    break
    return r
print(cal(o)+cal(e))