CF1005C.Summarize to the Power of Two

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.

一个序列 $a_1, a_2, \dots, a_n$ 被称为好序列，当且仅当对其中每个元素 $a_i$，均存在另一个元素 $a_j$（满足 $i \ne j$），使得 $a_i + a_j$ 是 2 的幂（即形如 $2^d$，其中 $d$ 为非负整数）。

例如，以下序列是好序列：

• $[5, 3, 11]$（例如，对 $a_1 = 5$，可取 $a_2 = 3$；注意它们的和是 2 的幂。类似地，对 $a_2$ 和 $a_3$ 也都能找到满足条件的配对），
• $[1, 1, 1, 1023]$，
• $[7, 39, 89, 25, 89]$，
• $[]$。

注意：根据定义，空序列（长度为 $0$）是好序列。

例如，以下序列不是好序列：

• $[16]$（对 $a_1 = 16$，无法找到另一个元素 $a_j$，使其与 $a_1$ 的和为 2 的幂），
• $[4, 16]$（对 $a_1 = 4$，无法找到另一个元素 $a_j$，使其与 $a_1$ 的和为 2 的幂），
• $[1, 3, 2, 8, 8, 8]$（对 $a_3 = 2$，无法找到另一个元素 $a_j$，使其与 $a_3$ 的和为 2 的幂）。

现给你一个序列 $a_1, a_2, \dots, a_n$。最少需要删除多少个元素，才能使它变成好序列？你可以删除任意一组元素。

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 $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 10^9$).

第一行包含整数 $n$（$1 \le n \le 120000$）—— 给定序列的长度。

第二行包含整数序列 $a_1, a_2, \dots, a_n$（$1 \le a_i \le 10^9$）。

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.

输出使给定序列变为“好序列”所需删除的最少元素个数。有可能需要删除全部 $n$ 个元素，使其变为空序列，从而得到一个“好序列”。

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.

在第一个例子中，只需删除一个元素 $a_4=5$。剩余元素构成序列 $[4, 7, 1, 4, 9]$，该序列是“好”的。