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.
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.*;

public class B implements Runnable {

    private void solve() throws IOException {
        int n = nextInt();
        Integer[] a = new Integer[n];
        
        for (int i = 0; i < n; i++)
            a[i] = nextInt();
        
        Arrays.sort(a);
        int[] b = new int[n];
        for (int i = 0; i < b.length; i++) {
            b[i] = (int) a[i];
        }
        int res = 0;
        
        for (int i = 0; i < n; i++) {
            if (b[i] == 1 || b[i] % 2 == 0) {
                if (i + 1 < n) {
                    if (Arrays.binarySearch(b, i + 1, n, 2 * b[i]) >= 0) ++res;
                    if (Arrays.binarySearch(b, i + 1, n, 2 * b[i] + 1) >= 0) ++res;
                    if (b[i] + 1 == b[i + 1]) ++res;
                }
            } else {
                if (i + 1  < n)
                    if (Arrays.binarySearch(b, i + 1, n, 2 * b[i] + 1) >= 0) ++res;             
            }
        }
        pl(res);
        
    }

    public static void main(String[] args) {
        new B().run();
    }

    BufferedReader reader;
    StringTokenizer tokenizer;
    PrintWriter writer;

    public void run() {
        try {
            reader = new BufferedReader(new BufferedReader(new InputStreamReader(System.in)));
            writer = new PrintWriter(System.out);
            tokenizer = null;
            solve();
            reader.close();
            writer.close();
        } catch (Exception e) {
            e.printStackTrace();
            System.exit(1);
        }
    }

    int nextInt() throws IOException {
        return Integer.parseInt(nextToken());
    }

    long nextLong() throws IOException {
        return Long.parseLong(nextToken());
    }

    double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }

    BigInteger nextBigInteger() throws IOException {
        return new BigInteger(nextToken());
    }

    String nextToken() throws IOException {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            tokenizer = new StringTokenizer(reader.readLine());
        }
        return tokenizer.nextToken();
    }

    void p(Object... objects) {
        for (int i = 0; i < objects.length; i++) {
            if (i != 0)
                writer.print(' ');
            writer.print(objects[i]);
        }
    }

    void pl(Object... objects) {
        p(objects);
        writer.println();
    }

    int cc;

    void pf() {
        writer.printf("Case #%d: ", ++cc);
    }

}