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)

N = input()
b= input().split(" ")

i = 0
gu_num =[]
ki_num = []
list_ni =[1, 2, 4, 8, 16, 32, 64, 128, 256, 512,
1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288,
1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912]
while i<=int(N)-1:
    if int(b[i])%2==0:
        gu_num.append(int(b[i]))
    else:
        ki_num.append(int(b[i]))
    i +=1

ki_kaisu =0
i=0
while i < len(ki_num):
    k=i+1
    while  k<len(ki_num):
        goukei = ki_num[i]+ki_num[k]
        judge= goukei in list_ni
        if judge==True:
            ki_kaisu += 1
        k +=1
    i += 1


gu_kaisu =0
i=0
while i < len(gu_num):
    k=i+1
    while  k<len(gu_num):
        goukei = ki_num[i]+gu_num[k]
        judge= goukei in list_ni
        if judge==True:
            gu_kaisu += 1
        k +=1
    i += 1



print(ki_kaisu+gu_kaisu)