A sequence $a_1, a_2, \dots, a_n$ is called good if, for each element $a_i$, there exists an element $a_j$ ($i \ne j$) such that $a_i+a_j$ is a power of two (that is, $2^d$ for some non-negative integer $d$).

For example, the following sequences are good:
 -  $[5, 3, 11]$ (for example, for $a_1=5$ we can choose $a_2=3$. Note that their sum is a power of two. Similarly, such an element can be found for $a_2$ and $a_3$), -  $[1, 1, 1, 1023]$, -  $[7, 39, 89, 25, 89]$, -  $[]$. 
Note that, by definition, an empty sequence (with a length of $0$) is good.

For example, the following sequences are not good:
 -  $[16]$ (for $a_1=16$, it is impossible to find another element $a_j$ such that their sum is a power of two), -  $[4, 16]$ (for $a_1=4$, it is impossible to find another element $a_j$ such that their sum is a power of two), -  $[1, 3, 2, 8, 8, 8]$ (for $a_3=2$, it is impossible to find another element $a_j$ such that their sum is a power of two). 
You are given a sequence $a_1, a_2, \dots, a_n$. What is the minimum number of elements you need to remove to make it good? You can delete an arbitrary set of elements.
The first line contains the integer $n$ ($1 \le n \le 120000$) — the length of the given sequence.

The second line contains the sequence of integers $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 10^9$).
6
4 7 1 5 4 9
1
5
1 2 3 4 5
2
1
16
1
4
1 1 1 1023
0
10
2 10 9 1 10 4 7 8 5 4
5
2
1 1
0
2
1 6
2
6
1 7 7 7 7 7
0
3
1 2 3
1
3
1 3 3
0
2
3 3
2
2
3 1
0
3
1 2 2
1
2
2 2
0
2
2 1
2
3
1 1 3
0
3
1 3 2
1
3
1 1 2
1
1
1
1
n = int(input())
liss = [int(x) for x in input().split()]
from collections import Counter as CO
count_map = CO(liss)

def solve():
    if n ==1:
        return 1
    result = 0

    for ai in liss:
        stay = 0
        for j in range(32):
            ss= (1 << j)
            if ((ss-ai)>0 and ((ss-ai)in count_map and ((ss-ai != ai) or count_map[ss-ai]>1))):
                stay =1
                break

        if stay == 0:
            result+=1
    return result

print(solve())





