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.
#include <vector>
#include <iostream>

using namespace std;

void main() {
    int N;
    cin >> N;

    int v;
    int k = 0;;
    __int64 result = 0;
    vector< int > r = vector< int >(64);
    for( int i = 0; i < N; i++ ) {
        cin >> v;
        k = 0;
        for( int j = 0; j < 64; j++ ) {
            if ( v % 2 != 0 )
                k++;
            v >>= 1;
        }
        r[k]++;
    }

    for( int i = 0; i < 64; i++ )
        result += r[i] * ( r[i] - 1 ) / 2;

    cout << result;
}