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 <cstdio>
#include <fstream>
#include <iostream>

#define MAX_N 50

using namespace std;

int n;
int fr[MAX_N];

inline int function(int x) {
    int count = 0;
    while (x) {
        if (x & 1)
            ++count;

        x >>= 1;
    }

    return count;
}

int main() {
    scanf("%d", &n);

    for (int i = 1; i <= n; ++i) {
        int x;
        scanf("%d", &x);

        ++fr[function(x)];
    }

    

    long long total = 0;
    for (int i = 0; i < MAX_N; ++i)
        if (fr[i] > 1)
            total = (long long) total + (fr[i] * (fr[i] - 1) / 2);
    
    cout << total;
}

