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.
var i,f={},m=1000000000/2, n = parseInt(readline());


f[0]=0;
// pre-calc
/*
for( i=0;i<=m/2;i++) {
   f[2*i+1] = f[i]+1;
   f[2*i] = f[i];
}
//end of pre-calc */ 

var find= function(x){ 
          if(x<=0) return 0;
          return ( find(parseInt(x/2)) + (x%2) );
};

var ar = readline().split(' ');
for(i=0;i<ar.length;i++){
 ar[i]=parseInt(ar[i]);

   ar[i]=find(ar[i]);
}


ar.sort();


var best =0,cnt=0,res=0;
for(i=1;i<ar.length;i++){
   
   if(ar[i-1]===ar[i]) cnt++;
   else cnt = 0;

   res=Math.max(res,cnt*(cnt+1)/2);
}

print(res);