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 <bits/stdc++.h>
#pragma comment(linker, "/STACK:67108864")
using namespace std;
long long i, N, A[100005], F[100] = {0};
long long f(long long X) {
  if (X == 0) return 0;
  return X & 1 ? f(X >> 1) + 1 : f(X >> 1);
}
int main() {
  freopen("input.txt", "r", stdin);
  freopen("output.txt", "w", stdout);
  scanf("%I64d", &N);
  for (i = 0; i < N; ++i) {
    scanf("%I64d", &A[i]);
    ++F[f(A[i])];
  }
  long long res = 0;
  for (i = 0; i < N; ++i) {
    res += F[f(A[i])] - 1;
    F[f(A[i])]--;
  }
  printf("%d\n", res);
  return 0;
}
