Dima got into number sequences. Now he's got sequence a1, a2, ..., an, consisting of n positive integers. Also, Dima has got a function f(x), which can be defined with the following recurrence:

  * f(0) = 0; 
  * f(2·x) = f(x); 
  * f(2·x + 1) = f(x) + 1. 



Dima wonders, how many pairs of indexes (i, j) (1 ≤ i < j ≤ n) are there, such that f(ai) = f(aj). Help him, count the number of such pairs. 

Input

The first line contains integer n (1 ≤ n ≤ 105). The second line contains n positive integers a1, a2, ..., an (1 ≤ ai ≤ 109).

The numbers in the lines are separated by single spaces.

Output

In a single line print the answer to the problem.

Please, don't use the %lld specifier to read or write 64-bit integers in C++. It is preferred to use the cin, cout streams or the %I64d specifier.

Examples

Input

3
1 2 4


Output

3


Input

3
5 3 1


Output

1

Note

In the first sample any pair (i, j) will do, so the answer is 3.

In the second sample only pair (1, 2) will do.
import java.io.*;
import java.util.*;

public class Main {

    static BufferedReader br;
    static PrintWriter out;
    static StringTokenizer st;

    static void solve() throws Exception {
        int n = nextInt();
        int MAX = 1000000000;
        Long[] a = new Long[n];
        Map<Long, Integer> map = new HashMap<Long, Integer>();
        for(int i = 0; i < n; i++){
            a[i] = (long)nextInt();
            map.put(a[i], i);
        }
        int cnt = 0;
        boolean[] used = new boolean[n];
        for(int i = 0; i < n; i++){
            if(used[i]){
                continue;
            }
            long item = a[i];
            int lc = 0;
            if(item % 2 != 0 && item != 1){
                item = a[i] - 1;
                for(;item <= MAX;){
                    item *= 2;
                    if(map.containsKey(item)){
                        int indx = map.get(item);
                        if(!used[indx] && i <= indx){
                            used[indx] = true;
                            lc++;
                        }
                    }
                }
                item = a[i] - 1;
                for(;item > 0;){
                    item /= 2;
                    if(map.containsKey(item)){
                        int indx = map.get(item);
                        if(!used[indx] &&i <= indx){
                            used[indx] = true;
                            lc++;
                        }
                    }
                }
            }else{
                item = a[i];
                for(;item <= MAX;){
                    item *= 2;
                    if(map.containsKey(item)){
                        int indx = map.get(item);
                        if(!used[indx] &&i <= indx){
                            used[indx] = true;
                            lc++;
                        }
                    }
                }
                item = a[i];
                for(;item > 0;){
                    item /= 2;
                    if(map.containsKey(item)){
                        int indx = map.get(item);
                        if(!used[indx] &&i <= indx){
                            used[indx] = true;
                            lc++;
                        }
                    }
                }
            }
            cnt += lc * (lc + 1) / 2 ;
        }
        System.out.println(cnt);
    }

    static int nextInt() throws IOException {
        return Integer.parseInt(next());
    }

    static long nextLong() throws IOException {
        return Long.parseLong(next());
    }

    static double nextDouble() throws IOException {
        return Double.parseDouble(next());
    }

    static String next() throws IOException {
        while (st == null || !st.hasMoreTokens()) {
            String line = br.readLine();
            if (line == null) {
                return null;
            }
            st = new StringTokenizer(line);
        }
        return st.nextToken();
    }

    public static void main(String[] args) {
        try {
            File file = new File(".in");
            InputStream input = System.in;
            OutputStream output = System.out;
            if (file.canRead()) {
                input = new FileInputStream(file);
                output = new FileOutputStream(".out");
            }
            br = new BufferedReader(new InputStreamReader(input));
            out = new PrintWriter(new PrintStream(output));
            solve();
            out.close();
            br.close();
        } catch (Throwable t) {
            t.printStackTrace();
        }
    }
}