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.util.*;
    import java.io.*;
 
     public class CodeForces {
        
        
        public static void main(String[] args) throws IOException {
            Reader.init(System.in);
            PrintWriter writer = new PrintWriter(System.out);
            
            int freq[] = new int[(int)1e6+1];
            
            int n = Reader.nextInt();
            
            for (int i = 0; i < n; i++) {
                int x = calc(Reader.nextInt());
                
                freq[x]++;
            }
            
            long ans = 0;
            for (int i = 0; i < freq.length; i++) {
                ans += (1l*freq[i] * (freq[i]-1)) / 2;
            }
            
            writer.println(ans);
            writer.close();
        }
        
        static int calc(int x){
            if(x == 0)
                return x;
            
            
            if((x&1) == 1)
                return calc(x/2) + 1;
            return calc(x/2);
        }
    }
    
    class  Edge implements Comparable<Edge>{
 
        int to;
        int from;
        int cost;
        
        Edge(int a, int b, int c){
            from = a;
            to = b;
            cost = c;
        }
 
        @Override
        public int compareTo(Edge t) {
            return t.cost - cost;
        }
    }
 
 
class Pair {
    int x, y;

    public Pair(int x, int y) {
        this.x = x;
        this.y = y;
    }
        
            
    public Pair clone(){
        return new Pair(x, y);
    }

    @Override
    public String toString() {
        return this.x + ", " + this.y;
    }

    @Override
    public boolean equals(Object obj) {
        Pair other = (Pair)obj;
        
        return this.x == other.x && this.y == other.y;
    }

    @Override
    public int hashCode() {
        return (x*y) % ((int)1e9 + 7);
    }

    
}
 
 
    class Reader {
 
        static BufferedReader reader;
        static StringTokenizer tokenizer;
 
        public static int pars(String x) {
            int num = 0;
            int i = 0;
            if (x.charAt(0) == '-') {
                i = 1;
            }
            for (; i < x.length(); i++) {
                num = num * 10 + (x.charAt(i) - '0');
            }
 
            if (x.charAt(0) == '-') {
                return -num;
            }
 
            return num;
        }
 
        static void init(InputStream input) {
            reader = new BufferedReader(
                    new InputStreamReader(input));
            tokenizer = new StringTokenizer("");
        }
 
        static void init(FileReader input) {
            reader = new BufferedReader(input);
            tokenizer = new StringTokenizer("");
        }
 
        static String next() throws IOException {
            while (!tokenizer.hasMoreTokens()) {
                tokenizer = new StringTokenizer(
                        reader.readLine());
            }
            return tokenizer.nextToken();
        }
 
        static int nextInt() throws IOException {
            return pars(next());
        }
 
        static long nextLong() throws IOException {
            return Long.parseLong(next());
        }
 
        static double nextDouble() throws IOException {
            return Double.parseDouble(next());
        }
    }