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>
using namespace std;
const int maxn = 1e5 + 5;
long long ans[maxn], a[maxn], vis[maxn];
int main() {
  long long x, n, all, m;
  scanf("%I64d", &n);
  for (int i = 1; i <= n; i++) {
    scanf("%I64d", &x);
    all = 0;
    while (x > 0) {
      m = x & 1;
      all += m;
      x = x >> 1;
    }
    a[i] = all;
    ans[all]++;
  }
  long long sum = 0;
  for (int i = 1; i <= n; i++) {
    if (vis[a[i]] == 0) {
      sum += (ans[a[i]] - 1) * ans[a[i]] / 2;
      vis[a[i]] = 1;
    }
  }
  printf("%I64d", sum);
}
