Problem:
Score : 800 points

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.

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.

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

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<bits/stdc++.h>
#define ll long long
using namespace std;
const int maxn = 5e5+5;
const int mod =  1e9+7;
const int N = (1<<20)+5;
ll dp[N];
int sum[maxn],n;
int zero[maxn];
int last[N];
int main() {
	cin>>n;
	for(int i=1; i<=n; i++) {
		scanf("%d",&sum[i]);
		sum[i]^=sum[i-1];
		zero[i]=zero[i-1]+(sum[i]==0);
	}
	for(int i=1; i<n;i++) {
		if(sum[i]) {
			if(!last[sum[i]])dp[sum[i]]=1;
			else {
				dp[sum[i]]=((ll)dp[sum[i]]*(zero[i]-zero[last[sum[i]]]+1)%mod+1)%mod;
				dp[sum[i]]%=mod;
			}
			last[sum[i]]=i;
		}
	}
	if(sum[n]) {
		cout<<(dp[sum[n]]*(zero[n]-zero[last[sum[n]]])%mod+1)%mod<<endl;
	} else {
		ll ans=0;
		for(int i=1; i<(1<<20); i++) {
			if(dp[i]) {
				ans += dp[i];
				ans%=mod;
			}
		}
		ll ret =1;
		for(int i=1; i<zero[n]; i++)ret = ret*2%mod;
		ans += ret;
		ans %= mod;
		cout<<ans<<endl;
	}
	return 0;
}