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 File {
    public static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException e) {
                    e.printStackTrace();
                }
            }

            return st.nextToken();
        }

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

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

        double nextDouble() {
            return Double.parseDouble(next());
        }
    }
	
    public static void main(String[] args) {
        FastScanner sc = new FastScanner();
        PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out));
		
		
		
		
		int n = sc.nextInt();
		
		Map<Integer, Integer> map = new HashMap<>();
		
		// f(7) = 1 + f(3)
		//      = 1 + 1 + f(1)
		//      = 1 + 1 + 1 + f(0) = 3
		
		// f(5) = 1 + f(2)
		//      = 1 + f(1)
		//      = 1 + 1 + f(0) = 2
		
		// f(3) = 1 + f(1)
		//      = 1 + 1 + f(0) = 2
		
		long pairs = 0;
		
		for (int i = 0; i < n; i++) {
			int a = sc.nextInt();
			int total = 0;
			
			while (a > 0) {
				if (a % 2 == 0) {
					a /= 2;
				}
				else {
					total += 1;
					a /= 2;
				}
			}
			
			pairs += map.getOrDefault(total, 0);
			map.put(total, map.getOrDefault(total, 0) + 1);
		}
		
		
		out.println(pairs);
		
		
		
        out.close();
    }
}













