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题面翻译

给一个长度为$n$的序列$a$

从中选取$a_i,a_j$,使$a_i+a_j=2^x,(x\in N^* ,i<j)$

求序列中有多少对这样的数

$P.S$：

样例1：有$(1,4),(2,4)$两对数

题目描述

You are given $n$ integers $a_{1},a_{2},...,a_{n}$ . Find the number of pairs of indexes $i,j$ ( i&lt;j ) that $a_{i}+a_{j}$ is a power of $2$ (i. e. some integer $x$ exists so that $a_{i}+a_{j}=2^{x}$ ).

输入格式

The first line contains the single positive integer $n$ ( $1<=n<=10^{5}$ ) — the number of integers.

The second line contains $n$ positive integers $a_{1},a_{2},...,a_{n}$ ( $1<=a_{i}<=10^{9}$ ).

输出格式

Print the number of pairs of indexes $i,j$ ( i&lt;j ) that $a_{i}+a_{j}$ is a power of $2$ .

样例 #1

样例输入 #1

4
7 3 2 1

样例输出 #1

2

样例 #2

样例输入 #2

3
1 1 1

样例输出 #2

3

提示

In the first example the following pairs of indexes include in answer: $(1,4)$ and $(2,4)$ .

In the second example all pairs of indexes $(i,j)$ (where i&lt;j ) include in answer.