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>
using namespace std;

int main(){
    typedef pair<long long, long long> P;
    int mod = 1'000'000'007;
    int n;
    cin >> n;
    vector<long long> a(n);
    for (int i = 0; i<n; i++) cin >> a[i];
    vector<long long> acc(n+1);
    acc[0] = 0;
    for (int i = 0; i<n; i++){
        acc[i+1] = 0;
        acc[i+1] = (acc[i]^a[i]);
    }
    long long p = acc.back();
    vector<P> stc(n+1);
    stc[0] = {0, 0};
    for (int i = 0; i<n+1; i++){
        if (acc[i]==0) stc[i].first++;
        if (acc[i]==p) stc[i].second++;
        if (i!=n){
            stc[i+1] = stc[i];
        }
    }
    long long ans = 1;
    for (int i = 1; i<n+1; i++){
        ans += min(stc.back().first - stc[i+1].first, stc.back().second - stc[i+1].second);
        ans %= mod;
    }
    cout << ans << endl;
}