# Summarize to the Power of Two

## 题意翻译

给出一个长度为 $n$ 的序列 $a$，求最少删除多少个数使 $\forall i$，$\exists j\ne i,a_i+a_j$ 为 $2$ 的幂次方。

## 题目描述

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.

## 输入输出格式

### 输入格式

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 $ ).

### 输出格式

Print the minimum number of elements needed to be removed from the given sequence in order to make it good. It is possible that you need to delete all $ n $ elements, make it empty, and thus get a good sequence.

## 输入输出样例

### 输入样例 #1

```
6
4 7 1 5 4 9
```

### 输出样例 #1

```
1
```

### 输入样例 #2

```
5
1 2 3 4 5
```

### 输出样例 #2

```
2
```

### 输入样例 #3

```
1
16
```

### 输出样例 #3

```
1
```

### 输入样例 #4

```
4
1 1 1 1023
```

### 输出样例 #4

```
0
```

## 说明

In the first example, it is enough to delete one element $ a_4=5 $ . The remaining elements form the sequence $ [4, 7, 1, 4, 9] $ , which is good.