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.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class Round257Div1D {

	public static long mod = (long)1e9+7;
	
	public static void solve() {
		int n = s.nextInt(); 
		int m = 20;
		int size = 1<<m;
		int[] dp = new int[size];
		for(int i = 0 ;i<n;i++) {
			int x = s.nextInt();
			dp[x]++;
		}
		for(int i=0;i<m;i++) {
			for(int mask = 0;mask<size;mask++) {
				if((mask & (1<<i))==0) {
					dp[mask]+=dp[mask|(1<<i)];
				}
			}
		}
		long ans = 0;
		for(int i=0;i<size;i++) {
			int bits = Integer.bitCount(i);
			if((bits&1)==0) {
				ans = ans + fast(2,dp[i]);
				ans%=mod;
			}else {
				ans = ans - fast(2,dp[i]);
				ans%=mod;
				if(ans<0) {
					ans+=mod;
				}
			}
		}
		out.println(ans);
	}

	public static long fast(long a,long n) {
		if(n == 1) {
			return a%mod;
		}else if(n==0) {
			return 1;
		}
		long ans= fast(a,n/2);
		ans = ans * ans;
		ans%=mod;
		if((n&1)==1) {
			ans = ans * a;
			ans%=mod;
		}
		return ans;
	}
	
	public static void main(String[] args) {
		out = new PrintWriter(new BufferedOutputStream(System.out));
		s = new FastReader();
		solve();
		out.close();
	}

	public static FastReader s;
	public static PrintWriter out;

	public static class FastReader {
		BufferedReader br;
		StringTokenizer st;

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

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

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

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

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

		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			} catch (Exception e) {
				e.printStackTrace();
			}
			return str;
		}
	}

	
}