XOR Partitioning

AtCoder

IDdiverta2019_e

Time2000ms

Memory256MB

Difficulty—

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: $N$ $A_1$ $A_2$ $\ldots$ $A_{N}$ [samples]

Samples

Input #1

3
1 2 3

Output #1

3

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

*   $(1,2,3)$
*   $(1),(2,3)$
*   $(1,2),(3)$

Input #2

3
1 2 2

Output #2

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

Output #3

147483634

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

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

Output #4

API Response (JSON)

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  "problem": {
    "name": "XOR Partitioning",
    "description": {
      "content": "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",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "diverta2019_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "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).\nYou are given a sequence $A$ of length $N$. Snuke will...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments