Problem: Jzzhu have n non-negative integers a1, a2, ..., an. We will call a sequence of indexes i1, i2, ..., ik (1 ≤ i1 < i2 < ... < ik ≤ n) a group of size k. 

Jzzhu wonders, how many groups exists such that ai1 & ai2 & ... & aik = 0 (1 ≤ k ≤ n)? Help him and print this number modulo 1000000007 (109 + 7). Operation x & y denotes bitwise AND operation of two numbers.

Input

The first line contains a single integer n (1 ≤ n ≤ 106). The second line contains n integers a1, a2, ..., an (0 ≤ ai ≤ 106).

Output

Output a single integer representing the number of required groups modulo 1000000007 (109 + 7).

Examples

Input

3
2 3 3


Output

0


Input

4
0 1 2 3


Output

10


Input

6
5 2 0 5 2 1


Output

53

Solution (in JAVA):

Solution:
import java.io.*;
import java.math.*;
import java.util.*;

public class Main{
    FastScanner in;
    PrintWriter out;

    int mod = (int)1e9+7;

    public void solve()
    {
        int n = in.nextInt();
        int[] f = new int[(1<<21)];
        for (int i = 0; i < n; i++) {
            f[in.nextInt()]++;
        }

        for (int i = 0; i <= 19; i++)
            for (int j = 1000000; j >= 0; j--)
                if ((j & (1 << i)) != 0)
                    f[j - (1 << i)] += f[j];

        int[] pow = new int[1000001];
        pow[0] = 1;
        for (int i = 1; i < 1000001; i++) {
            pow[i] = pow[i-1] + pow[i-1];
            if (pow[i] >= mod)
                pow[i] -= mod;
        }


        int ans = 0;
        int cnt;

        for (int i = 0; i < (1 << 20); i++) {
            cnt = 0;
            for (int j = 0; j < 21; j++) {
                if ((i >> j) % 2 == 1)
                    cnt++;
            }

            if (cnt % 2 == 0)
                ans += pow[f[i]];
            else
                ans += mod - pow[f[i]];

            if (ans >= mod)
                ans -= mod;
        }

        out.println(ans);
    }

    public void run()
    {
        in = new FastScanner();
        out = new PrintWriter(System.out);

        solve();

        out.close();
    }


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

    class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        FastScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }

        long nextLong() {
            return Long.parseLong(next());
        }

        double nextDouble() {
            return Double.parseDouble(next());
        }
    }
}