Number of Subset Xors

Given an array of n integers, your task is to find the number of different subset xors.

Input

The first line has an integer n: the size of the array. The next line has n integers x_1,x_2,\dots,x_n: the contents of the array.

Output

Print one integer: the number of different subset xors.

Constraints

$1 \le n \le 2$ \cdot 10^5$

$0 \le x_i \le 10^9$

Example

Input

3
3 6 5

Output

4

Explanation: The following values can be the xor of a subset:

0 = \text{xor of the empty set}

3 = 3

5 = 3 \oplus 6

6 = 3 \oplus 5

In this case, no other values can be the xor of a subset.