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 Rust (1.15.1) (judge verdict: Accepted)

/*------------------------------------------------------------------*/
/*------------------------- begin template -------------------------*/
/*------------------------------------------------------------------*/

// ref: tanakh <https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8>
// diff: using Parser
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut parser = Parser::from_str($s);
        input_inner!{parser, $($r)*}
    };
    (parser = $parser:ident, $($r:tt)*) => {
        input_inner!{$parser, $($r)*}
    };
    (new_stdin_parser = $parser:ident, $($r:tt)*) => {
        let stdin = std::io::stdin();
        let reader = std::io::BufReader::new(stdin.lock());
        let mut $parser = Parser::new(reader);
        input_inner!{$parser, $($r)*}
    };
    ($($r:tt)*) => {
        input!{new_stdin_parser = parser, $($r)*}
    };
}

macro_rules! input_inner {
    ($parser:ident) => {};
    ($parser:ident, ) => {};
    ($parser:ident, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($parser, $t);
        input_inner!{$parser $($r)*}
    };
}

macro_rules! read_value {
    ($parser:ident, ( $($t:tt),* )) => {
        ( $(read_value!($parser, $t)),* )
    };
    ($parser:ident, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($parser, $t)).collect::<Vec<_>>()
    };
    ($parser:ident, chars) => {
        read_value!($parser, String).chars().collect::<Vec<char>>()
    };
    ($parser:ident, char_) => {
        read_value!($parser, String).chars().collect::<Vec<char>>()[0]
    };
    ($parser:ident, usize1) => {
        read_value!($parser, usize) - 1
    };
    ($parser:ident, i64_) => {
        $parser.fast_i64()
    };
    ($parser:ident, usize_) => {
        $parser.fast_i64() as usize
    };
    ($parser:ident, usize1_) => {
        ($parser.fast_i64() - 1) as usize
    };
    ($parser:ident, $t:ty) => {
        $parser.next::<$t>().expect("Parse error")
    };
}

use std::io;
use std::io::BufRead;
use std::str;

// ref: tatsuya6502 <https://qiita.com/tatsuya6502/items/cd448486f7ef7b5b8c7e>
// ref: wariuni <https://qiita.com/tatsuya6502/items/cd448486f7ef7b5b8c7e#comment-7040a5ae96305e884eb9>
// diff: using std::io::BufRead::fill_buf()
pub struct Parser<R> {
    pub reader: R,
    buf: Vec<u8>,
    pos: usize,
}

impl Parser<io::Empty> {
    pub fn from_str(s: &str) -> Parser<io::Empty> {
        Parser {
            reader: io::empty(),
            buf: s.as_bytes().to_vec(),
            pos: 0,
        }
    }
}

impl<R: BufRead> Parser<R> {
    pub fn new(reader: R) -> Parser<R> {
        Parser {
            reader: reader,
            buf: vec![],
            pos: 0,
        }
    }
    pub fn update_buf(&mut self) {
        self.buf.clear();
        self.pos = 0;
        loop {
            let (len, complete) = {
                let buf2 = self.reader.fill_buf().unwrap();
                self.buf.extend_from_slice(buf2);
                let len = buf2.len();
                (len, buf2[len - 1] <= 0x20)
            };
            self.reader.consume(len);
            if complete {
                break;
            }
        }
    }
    pub fn next<T: str::FromStr>(&mut self) -> Result<T, T::Err> {
        loop {
            let mut begin = self.pos;
            while begin < self.buf.len() && (self.buf[begin] <= 0x20) {
                begin += 1;
            }
            let mut end = begin;
            while end < self.buf.len() && (self.buf[end] > 0x20) {
                end += 1;
            }
            if begin != self.buf.len() {
                self.pos = end;
                return unsafe { str::from_utf8_unchecked(&self.buf[begin..end]) }.parse::<T>();
            } else {
                self.update_buf();
            }
        }
    }
    pub fn fast_i64(&mut self) -> i64 {
        loop {
            let mut begin = self.pos;
            while begin < self.buf.len() && (self.buf[begin] <= 0x20) {
                begin += 1;
            }
            if begin == self.buf.len() {
                self.update_buf();
                continue;
            }
            let mut res = 0;
            let (is_positive, mut end) = match self.buf[begin] {
                b'+' => (true, begin + 1),
                b'-' => (false, begin + 1),
                _ => (true, begin),
            };
            while end < self.buf.len() && (self.buf[end] > 0x20) {
                res = res * 10 + (self.buf[end] as i64 - '0' as i64);
                end += 1;
            }
            if begin != self.buf.len() {
                self.pos = end;
                return if is_positive { res } else { -res };
            } else {
                self.update_buf();
            }
        }
    }
}

#[allow(unused_imports)]
use std::cmp::*;
use std::ops::*;

pub fn gen_cum<T: Add<Output = T> + Copy>(zero: T, xs: &Vec<T>) -> Vec<T> {
    let mut res = vec![zero; xs.len() + 1];
    for (i, &x) in xs.iter().enumerate() {
        res[i + 1] = res[i] + x;
    }
    res
}

use std::marker::PhantomData;

pub trait ModP {
    fn as_u64() -> u64;
}

#[allow(non_camel_case_types)]
#[derive(Clone, Copy, Debug)]
pub struct Mod_1_000_000_007();
impl ModP for Mod_1_000_000_007 {
    fn as_u64() -> u64 {
        1_000_000_007
    }
}

#[allow(non_camel_case_types)]
#[derive(Clone, Copy, Debug)]
pub struct Mod_998_244_353();
impl ModP for Mod_998_244_353 {
    fn as_u64() -> u64 {
        998_244_353
    }
}

#[derive(Clone, Copy, PartialEq, Debug)]
pub struct Modular<P: ModP + Copy>(u32, PhantomData<P>);

impl<P: ModP + Copy> Modular<P> {
    pub fn new(x: u32) -> Modular<P> {
        Modular((x as u64 % P::as_u64()) as u32, PhantomData)
    }
    pub fn pow(self, n: u64) -> Modular<P> {
        if n == 0 {
            return Modular(1, PhantomData);
        }
        let t = self.pow(n / 2);
        if n % 2 == 0 {
            t * t
        } else {
            t * t * self
        }
    }
    pub fn as_u32(self) -> u32 {
        self.0
    }
}

impl<P: ModP + Copy> Add for Modular<P> {
    type Output = Self;
    fn add(self, rhs: Self) -> Self::Output {
        let t = (self.0 + rhs.0) as u64;
        let u = if t < P::as_u64() { t } else { t - P::as_u64() };
        Modular(u as u32, PhantomData)
    }
}

impl<P: ModP + Copy> AddAssign for Modular<P> {
    fn add_assign(&mut self, rhs: Self) {
        *self = *self + rhs;
    }
}

impl<P: ModP + Copy> Sub for Modular<P> {
    type Output = Self;
    fn sub(self, rhs: Self) -> Self::Output {
        let t = if self.0 >= rhs.0 {
            self.0 as u64 - rhs.0 as u64
        } else {
            self.0 as u64 + P::as_u64() - rhs.0 as u64
        };
        assert!(t < P::as_u64());
        Modular(t as u32, PhantomData)
    }
}

impl<P: ModP + Copy> SubAssign for Modular<P> {
    fn sub_assign(&mut self, rhs: Self) {
        *self = *self - rhs;
    }
}

impl<P: ModP + Copy> Neg for Modular<P> {
    type Output = Modular<P>;
    fn neg(self) -> Modular<P> {
        Modular((P::as_u64() - self.0 as u64) as u32, PhantomData)
    }
}

impl<P: ModP + Copy> Mul for Modular<P> {
    type Output = Self;
    fn mul(self, rhs: Self) -> Self::Output {
        Modular(
            ((self.0 as u64 % P::as_u64()) * (rhs.0 as u64 % P::as_u64()) % P::as_u64()) as u32,
            PhantomData,
        )
    }
}

impl<P: ModP + Copy> MulAssign for Modular<P> {
    fn mul_assign(&mut self, rhs: Self) {
        *self = *self * rhs;
    }
}

impl<P: ModP + Copy> Div for Modular<P> {
    type Output = Self;
    fn div(self, rhs: Self) -> Self::Output {
        if rhs.0 == 0 {
            loop {}
        }
        assert!(rhs.0 != 0);
        self * rhs.pow(P::as_u64() - 2)
    }
}

pub fn gen_fact_table<P: ModP + Copy>(n: usize) -> Vec<Modular<P>> {
    let mut res = vec![Modular::<P>::new(1); n + 1];
    for i in 0..n {
        res[i + 1] = res[i] * Modular::<P>::new((i + 1) as u32);
    }
    res
}

pub fn gen_inv_table<P: ModP + Copy>(n: usize) -> Vec<Modular<P>> {
    let mut res = vec![Modular::<P>::new(0); n + 1];
    res[1] = Modular::<P>::new(1);
    for i in 2..n + 1 {
        res[i] =
            -res[P::as_u64() as usize % i] * Modular::<P>::new((P::as_u64() / i as u64) as u32);
    }
    res
}

fn main() {
    input! {
        new_stdin_parser = parser,
    }
    let res = solve(&mut parser);
    print!("{}", res);
}

/*------------------------------------------------------------------*/
/*-------------------------- end template --------------------------*/
/*------------------------------------------------------------------*/

type Mod = Modular<Mod_1_000_000_007>;

use std::fmt::Write;
fn solve<R: BufRead>(parser: &mut Parser<R>) -> String {
    let mut buf = String::new();
    input! {
        parser = parser,
        n: usize,
        xs: [i64; n],
    }
    let mut ys = vec![0];
    for i in 0..n {
        let t = ys[i] ^ xs[i];
        ys.push(t);
    }
    let ys_zero_cum = {
        let ts: Vec<i64> = ys.iter().map(|&x| if x == 0 { 1 } else { 0 }).collect();
        gen_cum(0, &ts)
    };
    // eprintln!("ys = {:?}", ys);
    let mut a_to_i = vec![vec![]; 1 << 20];
    for (i, &y) in ys.iter().enumerate() {
        a_to_i[y as usize].push(i);
    }
    if ys.last().unwrap() == &0 {
        let mut res = Mod::new(0);
        // 0
        res += Mod::new(2).pow(a_to_i[0].len() as u64 - 2);
        // 1..2^20
        for a in 1..1 << 20 {
            let mut total_zero = Mod::new(1);
            let mut total_non_zero = Mod::new(0);
            for ii in (0..a_to_i[a].len()).rev() {
                let i = a_to_i[a][ii];
                total_non_zero += total_zero;
                if ii != 0 {
                    total_zero += Mod::new(
                        (ys_zero_cum[a_to_i[a][ii]] - ys_zero_cum[a_to_i[a][ii - 1]]) as u32,
                    ) * total_non_zero;
                }
            }
            if a <= 16 {
                // eprintln!("a = {}, res = {}", a, total_non_zero.as_u32());
            }
            res += total_non_zero;
        }
        writeln!(buf, "{}", res.as_u32());
    } else {
        let last = *ys.last().unwrap();
        let mut total_non_zero = Mod::new(1);
        let mut total_zero = Mod::new(0);
        let mut last_count = 0;
        for (i, &y) in ys.iter().enumerate().rev() {
            if i == ys.len() - 1 {
                continue;
            }
            if y == 0 {
                let t = total_non_zero;
                total_zero += t;
            // eprintln!("i={},y={},total_zero = {:?}", i, y, total_zero);
            } else if y == last {
                let t = total_zero;
                total_non_zero += t;
                // eprintln!("i={},y={},total_non_zero = {:?}", i, y, total_non_zero);
            }
        }
        writeln!(buf, "{}", total_non_zero.as_u32());
    }
    buf
}