# Summarize to the Power of Two

## 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.