Powers of Two
time limit per test
3 secondsmemory limit per test
256 megabytesinput
standard inputoutput
standard outputYou 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 xexists 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.
#include <iostream> #include <cstring> #include <cstdio> #include <algorithm> #include <queue> #include <vector> #include <iomanip> #include <math.h> #include <map> using namespace std; #define FIN freopen("input.txt","r",stdin); #define INF 0x3f3f3f3f #define lson l,m,rt<<1 #define rson m+1,r,rt<<1|1 typedef long long LL; int a[100005]; int main() { //FIN int n; LL ans; map<int,int> m; while(~scanf("%d",&n)) { ans=0; for(int i=1; i<=n; i++) scanf("%d",&a[i]); m.clear(); for(int i=1; i<=n; i++) { for(LL j=1; j<=2e9; j+=j) { ans+=m[j-a[i]]; } m[a[i]]++; } cout<<ans<<endl; return 0; } }