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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)


import java.util.Arrays;

public class Main {


  private static void solve() {
    int n = ni();
    int[] a = na(n);
    for (int i = 0; i < n - 1; i ++) {
      a[i + 1] ^= a[i];
    }
    int mod = 1000000000 + 7;
    
    long[] dp1 = new long[1 << n];
    long[] dp0 = new long[1 << n];
    long[] cnt = new long[1 << n];
    Arrays.fill(dp0, 1);
    int x = 0;
    for (int i = 0; i < n; i ++) {
      if (a[i] == 0) {
        x ++;
      } else {
        dp0[a[i]] += dp1[a[i]] * (x - cnt[a[i]]);
        dp1[a[i]] += dp0[a[i]];
        dp0[a[i]] %= mod;
        dp1[a[i]] %= mod;
        
        cnt[a[i]] = x;
      }
    }
    
    if (a[n - 1] > 0) {
      System.out.println(dp0[a[n-1]]);
    } else {
      long ret = 1;
      for (int i = 0; i < x - 1; i ++) {
        ret = ret * 2 % mod;
      }
      for (int i = 0; i < (1 << n); i ++) {
        ret += dp1[i];
        ret %= mod;
      }
      System.out.println(ret);
    }
  }
  
  
  public static long CX(long n, long r, int p, int[][] fif)
  {
      if(n < 0 || r < 0 || r > n)return 0;
      int np = (int)(n%p), rp = (int)(r%p);
      if(np < rp)return 0;
      if(n == 0 && r == 0)return 1;
      int nrp = np-rp;
      if(nrp < 0)nrp += p;
      return (long)fif[0][np]*fif[1][rp]%p*fif[1][nrp]%p*CX(n/p, r/p, p, fif)%p;
  }
  
  public static int[][] enumFIF(int n, int mod)
  {
      int[] f = new int[n+1];
      int[] invf = new int[n+1];
      f[0] = 1;
      for(int i = 1;i <= n;i++){
          f[i] = (int)((long)f[i-1] * i % mod);
      }
      long a = f[n];
      long b = mod;
      long p = 1, q = 0;
      while(b > 0){
          long c = a / b;
          long d;
          d = a; a = b; b = d % b;
          d = p; p = q; q = d - c * q;
      }
      invf[n] = (int)(p < 0 ? p + mod : p);
      for(int i = n-1;i >= 0;i--){
          invf[i] = (int)((long)invf[i+1] * (i+1) % mod);
      }
      return new int[][]{f, invf};
  }

  public static void main(String[] args) {
    new Thread(null, new Runnable() {
      @Override
      public void run() {
        long start = System.currentTimeMillis();
        String debug = args.length > 0 ? args[0] : null;
        if (debug != null) {
          try {
            is = java.nio.file.Files.newInputStream(java.nio.file.Paths.get(debug));
          } catch (Exception e) {
            throw new RuntimeException(e);
          }
        }
        reader = new java.io.BufferedReader(new java.io.InputStreamReader(is), 32768);
        solve();
        out.flush();
        tr((System.currentTimeMillis() - start) + "ms");
      }
    }, "", 64000000).start();
  }

  private static java.io.InputStream is = System.in;
  private static java.io.PrintWriter out = new java.io.PrintWriter(System.out);
  private static java.util.StringTokenizer tokenizer = null;
  private static java.io.BufferedReader reader;

  public static String next() {
    while (tokenizer == null || !tokenizer.hasMoreTokens()) {
      try {
        tokenizer = new java.util.StringTokenizer(reader.readLine());
      } catch (Exception e) {
        throw new RuntimeException(e);
      }
    }
    return tokenizer.nextToken();
  }

  private static double nd() {
    return Double.parseDouble(next());
  }

  private static long nl() {
    return Long.parseLong(next());
  }

  private static int[] na(int n) {
    int[] a = new int[n];
    for (int i = 0; i < n; i++)
      a[i] = ni();
    return a;
  }

  private static char[] ns() {
    return next().toCharArray();
  }

  private static long[] nal(int n) {
    long[] a = new long[n];
    for (int i = 0; i < n; i++)
      a[i] = nl();
    return a;
  }

  private static int[][] ntable(int n, int m) {
    int[][] table = new int[n][m];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        table[i][j] = ni();
      }
    }
    return table;
  }

  private static int[][] nlist(int n, int m) {
    int[][] table = new int[m][n];
    for (int i = 0; i < n; i++) {
      for (int j = 0; j < m; j++) {
        table[j][i] = ni();
      }
    }
    return table;
  }

  private static int ni() {
    return Integer.parseInt(next());
  }

  private static void tr(Object... o) {
    if (is != System.in)
      System.out.println(java.util.Arrays.deepToString(o));
  }
}