CODEFORCES 272B Dima and Sequence

传送门：http://codeforces.com/problemset/problem/272/B

B. Dima and Sequence

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

Dima got into number sequences. Now he's got sequence a1, a2, ..., an, consisting of n positive integers. Also, Dima has got a functionf(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 %I64dspecifier.

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
#include 
#include 

using namespace std;

int r[35];
int main()
{
    int N,a,p;
    long long s=0;
    scanf("%d",&N);
    for(int i=0; i>=1;
        s+=r[p];
        r[p]++;
    }
    printf("%I64d\n",s);
    return 0;
}