Solve the programming task below in a Python markdown code block.
The beauty of a sequence a of length n is defined as a_1 \oplus \cdots \oplus a_n, where \oplus denotes the bitwise exclusive or (XOR).

You are given a sequence A of length N. Snuke will insert zero or more partitions in A to divide it into some number of non-empty contiguous subsequences.

There are 2^{N-1} possible ways to insert partitions. How many of them divide A into sequences whose beauties are all equal? Find this count modulo 10^{9}+7.

Constraints

* All values in input are integers.
* 1 \leq N \leq 5 \times 10^5
* 0 \leq A_i < 2^{20}

Input

Input is given from Standard Input in the following format:


N
A_1 A_2 \ldots A_{N}


Output

Print the answer.

Examples

Input

3
1 2 3


Output

3


Input

3
1 2 2


Output

1


Input

32
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0


Output

147483634


Input

24
1 2 5 3 3 6 1 1 8 8 0 3 3 4 6 6 4 0 7 2 5 4 6 2


Output

292