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.BufferedReader;
import java.io.File;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.math.BigInteger;
import java.util.StringTokenizer;

public class B {
	static int dp [] = new int[10000001];
	static int tc [] = new int[31];
	public static void main(String [] args){
		FastScanner in = new FastScanner(System.in);
		dp[0]=0;
		dp[1]=1;
		int n = in.nextInt();
		for(int i = 0 ; i < n ; i++){
			tc[build(in.nextInt())]++;
		}
		BigInteger ans = BigInteger.ZERO; 
		for(int i = 0 ; i < tc.length; i++){
			if(tc[i]>1){
				ans = ans.add(Combine(tc[i]));
			}
		}
		System.out.println(ans);
	}
	public static int build(int num){
		if(num==0){
			return 0;
		}
		if(num > 10000000){
			if (num % 2 == 0){
				return build(num/2);
			}
			else{
				return build((num)/2)+1;
			}
		}
		else{
		if(dp[num]!=0){
			return dp[num];
		}
		if (num % 2 == 0){
			dp[num]= build(num/2);
		}
		else{
			dp[num]= build((num)/2)+1;
		}
		return dp[num];
		}
	}
	public static BigInteger Combine(int m){
		return BigInteger.valueOf(m).multiply(BigInteger.valueOf(m-1)).divide(BigInteger.valueOf(2));
	}
}
class FastScanner{
	BufferedReader br;
	StringTokenizer st;
	public FastScanner(File f){
		try{
			br = new BufferedReader(new FileReader(f));
			}
		catch(FileNotFoundException e) {
			e.printStackTrace();
			}
		}
		public FastScanner(InputStream f){
			br = new BufferedReader(new InputStreamReader(f));
		}
		int nextInt(){
			return Integer.parseInt(next());
		}
		long nextLong(){
			return Long.parseLong(next());
		}
		String next(){
		while(st==null || !st.hasMoreTokens()){
		String s = null ;
		try{
			s = br.readLine();
			}
			catch(IOException e){
			e.printStackTrace();
			}
			if(s==null)
				return null ;
			st = new StringTokenizer(s);
			}
			return st.nextToken();
			}
		boolean hasMoreTokens(){
		while(st==null || !st.hasMoreTokens()){
			String s = null;
			try{
			s = br.readLine();
			}
			catch(IOException e) {
				e.printStackTrace();
				}
				if(s==null)
					return false ;
				st=new StringTokenizer(s);
				}
			return true ;
		}
}