Problem Statement

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.

Input

Input is given from Standard Input in the following format:
N
$A_1 A_2 \ldots A_{N}$

Output

Print the answer.

Constraints

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

Sample Input 1

3
1 2 3

Sample Output 1

3

Four ways of dividing A shown below satisfy the condition. The condition is not satisfied only if A is divided into (1),(2),(3).

• (1,2,3)
• (1),(2,3)
• (1,2),(3)

Sample Input 2

3
1 2 2

Sample Output 2

1

Sample Input 3

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

Sample Output 3

147483634

Find the count modulo 10^{9}+7.

Sample Input 4

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

Sample Output 4

292

见题面 Input 部分

见题面 Output 部分