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.InputStreamReader;
import java.util.Arrays;
import java.util.Scanner;
import java.util.StringTokenizer;

public class D257 {
	static final long MOD = (long)(1e9+7);
	static long[] fs;
	static long[][] memo;
	public static void main(String[] args) {
		MyScanner in = new MyScanner();
		int n = in.nextInt();
		fs = new long[1 << 20];
		for(int i=0;i<n;i++) {
			fs[in.nextInt()]++;
		}
		memo = new long[20][1 << 20];
		for(long[] arr : memo)
			Arrays.fill(arr, -1);
		long ans = 0;
		for(int i=0;i<fs.length;i++) {
			int bitcount = Integer.bitCount(i);
			ans += fmpow(2,countSupersets(i, 0)) * (bitcount % 2 == 0 ? 1 : -1);
			ans %= MOD;
		}
		if(ans < 0)
			ans += MOD;
		System.out.println(ans);
		
	}
	static long fmpow(long a, long b) {
		if(b == 0)
			return 1;
		if(b == 1)
			return a;
		long bonus = 1;
		while(b > 1) {
			if(b % 2 != 0)
				bonus = (bonus * a) % MOD;
			b /= 2;
			a = (a*a)%MOD;
		}
		return (a*bonus)%MOD;
	}
	public static long countSupersets(int mask, int idx) {
		 if(idx == 20)
			 return fs[mask];
		 if(memo[idx][mask] != -1)
			 return memo[idx][mask];
		 long ans = countSupersets(mask, idx+1);
		 int bit = 1 << idx;
		 if((mask & bit) == 0)
			 ans += countSupersets(mask|bit,idx+1);
		 return memo[idx][mask] = ans;
	}

	private static class MyScanner {
		BufferedReader br;
		StringTokenizer st;

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

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

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

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