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;
typedef long long ll;

vector<ll> g[1000];

int a[10000]={0},y[10000]={0};


ll visited[1000]={0};

ll dfs(ll i,ll count,int n){
	ll c=1;
	visited[i]=1;
	
	for(ll k=0;k<n;k++){
		if(a[k]==a[i]||y[k]==y[i]){
			if(visited[k]==0)
		dfs(k,0,n);
		}
	}
	return c;
}

int nones(ll n){
	int c=0;
	while(n&(n-1)){
		c++;
		n&=n-1;
	}
	return c;
}

ll LCM(ll a,ll b){
	return a*b/__gcd(a,b);
}
int main(){
	int n;
	cin>>n;
	int odds=0,evens=0;
	ll ans=0;
	map<int,int> mp;
	ll a[n];
	for(int i=0;i<n;i++){
		cin>>a[i];
		int ones=nones(a[i]);
		mp[ones]++;
	}
	for(auto i:mp){
		ans+=i.second*(i.second-1)/2;
		
	}
	
	cout<<ans;
	}