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.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.util.StringTokenizer;


public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Task solver = new Task();
        solver.solve(1, in, out);
        out.close();
    }


    static class Task {
        private static final long MOD = (long)1e9 + 7;
        long[] dp = new long[(1 << 20) + 10];
        public void solve(int testNumber, InputReader in, PrintWriter out) {
            /*
            try{

            }catch(RuntimeException e){
                return;
            }
            */
            long n = in.nextLong();
            for(int i = 0; i < n; i++){
                dp[in.nextInt()]++;
            }
            long ans = 0;
            fun(1);
            for(int i = 0; i < (1 << 20); i++)dp[i] = pow(dp[i]);
            fun(-1);
            out.println(dp[0]);
        }
        long mod(final long x){
            return ((x % MOD) + MOD) % MOD;
        }
        long pow(long exp){
            long ans = 1, a = 2;
            while(exp > 0){
                if(exp % 2 == 1)ans = mod(ans * a);
                a = mod(a * a);
                exp >>= 1;
            }
            return ans;
        }
        void fun(final int op){
            for(int i = 0; i < 20; i++){
                for(int j = (1 << 20) - 1; j >= 0; j--) {
                    if((~j & (1 << i)) != 0) dp[j] = mod(dp[j] + dp[j | (1 << i)] * op);
                }
            }
        }
    }


    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;
        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

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

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

        public BigInteger nextBigInteger() {
            return new BigInteger(next());
        }

        public BigDecimal nextBigDecimal() {
            return new BigDecimal(next());
        }

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