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# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using static System.Console;
using static System.Math;

namespace AtTest.diverta2019
{
    class E
    {
        static void Main(string[] args)
        {
            Method(args);
        }

        static void Method(string[] args)
        {
            int n = ReadInt();
            int[] array = ReadInts();

            int[] xors = new int[n];
            xors[0] = array[0];
            for(int i = 1; i < n; i++)
            {
                xors[i] = array[i] ^ xors[i - 1];
            }

            long mask = 1000000000 + 7;
            var dp = new Dictionary<int, long>[n];
            dp[0] = new Dictionary<int, long>();
            dp[0].Add(xors[0], 1);

            for(int i = 1; i < n; i++)
            {
                dp[i] = new Dictionary<int, long>();
                for(int j = 0; j < i; j++)
                {
                    foreach(int key in dp[j].Keys)
                    {
                        if (key != (xors[i] ^ xors[j])) continue;

                        if (!dp[i].ContainsKey(key))
                        {
                            dp[i].Add(key, 0);
                        }
                        dp[i][key] += dp[j][key];
                        dp[i][key] %= mask;
                    }
                }

                if (!dp[i].ContainsKey(xors[i]))
                {
                    dp[i].Add(xors[i], 0);
                }
                dp[i][xors[i]]++;
            }

            long res = 0;
            foreach(int key in dp[n - 1].Keys)
            {
                res += dp[n - 1][key];
                res %= mask;
            }
            WriteLine(res);
        }

        class SegTree<T>
        {
            int totalLength;
            T[] tree;
            Func<T, T, T> integrate;
            T exValue;

            public SegTree(int length, Func<T, T, T> integrate, T exValue)
            {
                this.integrate = integrate;
                this.exValue = exValue;
                totalLength = 1;
                while (totalLength < length) totalLength *= 2;

                tree = new T[2 * totalLength - 1];
                for (int i = 0; i < tree.Length; i++) tree[i] = exValue;
            }

            public SegTree(int length, T initialValue,
                Func<T, T, T> integrate, T exValue)
                : this(length, integrate, exValue)
            {
                for (int i = 0; i < length; i++)
                {
                    tree[i + totalLength - 1] = initialValue;
                }
                UpdateAll();
            }

            public void AssignWithoutUpdate(int i, T value)
            {
                tree[i + totalLength - 1] = value;
            }

            public void Update(int i, T value)
            {
                int now = i + totalLength - 1;
                tree[now] = value;
                while (now > 0)
                {
                    now = (now - 1) / 2;
                    tree[now] = integrate(
                        tree[now * 2 + 1], tree[now * 2 + 2]);
                }
            }

            public void UpdateAll()
            {
                for (int i = totalLength - 2; i >= 0; i--)
                {
                    tree[i] = integrate(tree[i * 2 + 1], tree[i * 2 + 2]);
                }
            }

            public T Look(int i) { return tree[i + totalLength - 1]; }

            //[top,last)
            public T Scan(int top, int last)
            {
                return Query(top, last, 0, 0, totalLength);
            }

            T Query(int top, int last, int i, int left, int right)
            {
                if (right <= top || last <= left) return exValue;
                if (top <= left && right <= last) return tree[i];

                T leftValue = Query(top, last, i * 2 + 1,
                    left, (left + right) / 2);
                T rightValue = Query(top, last, (i + 1) * 2,
                    (left + right) / 2, right);

                return integrate(leftValue, rightValue);
            }
        }

        private static string Read() { return ReadLine(); }
        private static char[] ReadChars() { return Array.ConvertAll(Read().Split(), a => a[0]); }
        private static int ReadInt() { return int.Parse(Read()); }
        private static long ReadLong() { return long.Parse(Read()); }
        private static double ReadDouble() { return double.Parse(Read()); }
        private static int[] ReadInts() { return Array.ConvertAll(Read().Split(), int.Parse); }
        private static long[] ReadLongs() { return Array.ConvertAll(Read().Split(), long.Parse); }
        private static double[] ReadDoubles() { return Array.ConvertAll(Read().Split(), double.Parse); }
    }
}