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#F1140. Powers of Two

    ID: 1146 传统题 2000ms 256MiB 尝试: 0 已通过: 0 难度: 4 上传者: 标签>枚举数据结构模拟数学算法思想编程与模拟进阶难度共享题库Codeforces英文题面题目来源题面语言

Powers of Two

题目描述

B. Powers of Two
time limit per test
3 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given n integers a1,a2,...,an. Find the number of pairs of indexes i,j (i<j) that ai+aj is a power of 2 (i. e. some integer x exists so that ai+aj=2x).

Input

The first line contains the single positive integer n (1≤n≤105) − the number of integers.

The second line contains n positive integers a1,a2,...,an (1≤ai≤109).

Output

Print the number of pairs of indexes i,j (i<j) that ai+aj is a power of 2.

Examples
Input
4
7 3 2 1
Output
2
Input
3
1 1 1
Output
3
Note

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<j) include in answer.

题目来源：fps-www.educg.net-codeforce-1-2833.xml.zip；FPS 共享题包，题包内第 609 题。保留原作者与原赛事署名。