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.util.*;

public class D {
	static final long MOD = (long) (1e9 + 7);
	public static void main(String[] args) {
		MyScanner in = new MyScanner();
		int n = in.nextInt();
		int[] supersets = new int[1 << 20];
		for (int i = 0; i < n; i++)
			supersets[in.nextInt()]++;
		for (int i = 0; i < 20; i++) {
			for (int mask = 0; mask < supersets.length; mask++) {
				if (((1 << i) & mask) != 0) {
					supersets[mask ^ (1 << i)] += supersets[mask];
				}
			}
		}
		long[] pow2 = new long[n + 1];
		pow2[0] = 1;
		for (int i = 1; i < n + 1; i++)
			pow2[i] = (pow2[i - 1] * 2) % MOD;
		long ans = 0;
		for (int i = 0; i < supersets.length; i++) {
			ans += pow2[supersets[i]] * (Integer.bitCount(i) % 2 == 0 ? 1 : -1);
			ans = (ans + MOD) % MOD;
		}
		System.out.println(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(next());
		}
	}
}