Educational Codeforces Round 15 B Powers of Two

思路：ai+aj=2^x，移过去就是aj=2^x-ai嘛，由于ai的范围到10^9，所以其实x不会超过31，所以枚举一下x就可以了

#include<bits/stdc++.h>
using namespace std;
const int maxn = 1e5+7;
#define LL long long
map<LL,int>vis;
LL ans = 0;
int main()
{
	int n=0;
	scanf("%d",&n);
    for(int i = 1;i<=n;i++)
	{
        LL t;scanf("%lld",&t);
		for(int j = 0;j<=31;j++)
			ans+=vis[(1LL<<j)-t];
		vis[t]++;
	}
	printf("%lld\n",ans);
}

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, ..., a_n. Find the number of pairs of indexes i, j (i < 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).

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, ..., a_n (1 ≤ a_i ≤ 10⁹).

Output

Print the number of pairs of indexes i, j (i < j) that a_i + a_j 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.