Problem:
Score: 600 points

Problem Statement

We have N non-negative integers: A_1, A_2, ..., A_N.

Consider painting at least one and at most N-1 integers among them in red, and painting the rest in blue.

Let the beauty of the painting be the \mbox{XOR} of the integers painted in red, plus the \mbox{XOR} of the integers painted in blue.

Find the maximum possible beauty of the painting.

What is \mbox{XOR}?

The bitwise \mbox{XOR} x_1 \oplus x_2 \oplus \ldots \oplus x_n of n non-negative integers x_1, x_2, \ldots, x_n is defined as follows:

When x_1 \oplus x_2 \oplus \ldots \oplus x_n is written in base two, the digit in the 2^k's place (k \geq 0) is 1 if the number of integers among x_1, x_2, \ldots, x_n whose binary representations have 1 in the 2^k's place is odd, and 0 if that count is even.

For example, 3 \oplus 5 = 6.

Constraints

All values in input are integers.

2 \leq N \leq 10^5

0 \leq A_i < 2^{60}\ (1 \leq i \leq N)

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

Print the maximum possible beauty of the painting.

Sample Input 1

3
3 6 5

Sample Output 1

12

If we paint 3, 6, 5 in blue, red, blue, respectively, the beauty will be (6) + (3 \oplus 5) = 12.

There is no way to paint the integers resulting in greater beauty than 12, so the answer is 12.

Sample Input 2

4
23 36 66 65

Sample Output 2

188

Sample Input 3

20
1008288677408720767 539403903321871999 1044301017184589821 215886900497862655 504277496111605629 972104334925272829 792625803473366909 972333547668684797 467386965442856573 755861732751878143 1151846447448561405 467257771752201853 683930041385277311 432010719984459389 319104378117934975 611451291444233983 647509226592964607 251832107792119421 827811265410084479 864032478037725181

Sample Output 3

2012721721873704572

A_i and the answer may not fit into a 32-bit integer type.

Solution in Rust (1.15.1) (judge verdict: Wrong Answer)

pub trait Readable {
    type Output;
    fn words_count() -> usize;
    fn read_words(words: &[&str]) -> Result<Self::Output, String>;
}
#[macro_export]
macro_rules! readable {
    ( $ t : ty , $ words_count : expr , |$ words : ident | $ read_words : expr ) => {
        impl Readable for $t {
            type Output = $t;
            fn words_count() -> usize {
                $words_count
            }
            fn read_words($words: &[&str]) -> Result<$t, String> {
                Ok($read_words)
            }
        }
    };
}
readable!((), 1, |_ss| ());
readable!(String, 1, |ss| ss[0].to_string());
impl Readable for char {
    type Output = char;
    fn words_count() -> usize {
        1
    }
    fn read_words(words: &[&str]) -> Result<char, String> {
        let chars: Vec<char> = words[0].chars().collect();
        if chars.len() == 1 {
            Ok(chars[0])
        } else {
            Err(format!("cannot parse `{}` as a char", words[0]))
        }
    }
}
pub struct Chars();
impl Readable for Chars {
    type Output = Vec<char>;
    fn words_count() -> usize {
        1
    }
    fn read_words(words: &[&str]) -> Result<Vec<char>, String> {
        Ok(words[0].chars().collect())
    }
}
macro_rules ! impl_readable_for_ints { ( $ ( $ t : ty ) * ) => { $ ( impl Readable for $ t { type Output = Self ; fn words_count ( ) -> usize { 1 } fn read_words ( words : & [ & str ] ) -> Result <$ t , String > { use std :: str :: FromStr ; <$ t >:: from_str ( words [ 0 ] ) . map_err ( | _ | { format ! ( "cannot parse `{}` as {}" , words [ 0 ] , stringify ! ( $ t ) ) } ) } } ) * } ; }
impl_readable_for_ints ! ( i8 u8 i16 u16 i32 u32 i64 u64 isize usize f32 f64 ) ;
macro_rules ! define_one_origin_int_types { ( $ new_t : ident $ int_t : ty ) => { # [ doc = " Converts 1-origin integer into 0-origin when read from stdin." ] # [ doc = "" ] # [ doc = " # Example" ] # [ doc = "" ] # [ doc = " ```no_run" ] # [ doc = " # #[macro_use] extern crate atcoder_snippets;" ] # [ doc = " # use atcoder_snippets::read::*;" ] # [ doc = " // Stdin: \"1\"" ] # [ doc = " read!(a = usize_);" ] # [ doc = " assert_eq!(a, 0);" ] # [ doc = " ```" ] # [ allow ( non_camel_case_types ) ] pub struct $ new_t ; impl Readable for $ new_t { type Output = $ int_t ; fn words_count ( ) -> usize { 1 } fn read_words ( words : & [ & str ] ) -> Result < Self :: Output , String > { <$ int_t >:: read_words ( words ) . map ( | n | n - 1 ) } } } ; ( $ new_t : ident $ int_t : ty ; $ ( $ inner_new_t : ident $ inner_int_t : ty ) ;* ) => { define_one_origin_int_types ! ( $ new_t $ int_t ) ; define_one_origin_int_types ! ( $ ( $ inner_new_t $ inner_int_t ) ;* ) ; } ; }
define_one_origin_int_types ! ( u8_ u8 ; u16_ u16 ; u32_ u32 ; u64_ u64 ; usize_ usize ) ;
macro_rules ! impl_readable_for_tuples { ( $ t : ident $ var : ident ) => ( ) ; ( $ t : ident $ var : ident ; $ ( $ inner_t : ident $ inner_var : ident ) ;* ) => { impl_readable_for_tuples ! ( $ ( $ inner_t $ inner_var ) ;* ) ; impl <$ t : Readable , $ ( $ inner_t : Readable ) ,*> Readable for ( $ t , $ ( $ inner_t ) ,* ) { type Output = ( <$ t >:: Output , $ ( <$ inner_t >:: Output ) ,* ) ; fn words_count ( ) -> usize { let mut n = <$ t >:: words_count ( ) ; $ ( n += <$ inner_t >:: words_count ( ) ; ) * n } # [ allow ( unused_assignments ) ] fn read_words ( words : & [ & str ] ) -> Result < Self :: Output , String > { let mut start = 0 ; let $ var = <$ t >:: read_words ( & words [ start .. start +<$ t >:: words_count ( ) ] ) ?; start += <$ t >:: words_count ( ) ; $ ( let $ inner_var = <$ inner_t >:: read_words ( & words [ start .. start +<$ inner_t >:: words_count ( ) ] ) ?; start += <$ inner_t >:: words_count ( ) ; ) * Ok ( ( $ var , $ ( $ inner_var ) ,* ) ) } } } ; }
impl_readable_for_tuples ! ( T8 x8 ; T7 x7 ; T6 x6 ; T5 x5 ; T4 x4 ; T3 x3 ; T2 x2 ; T1 x1 ) ;
pub trait ReadableFromLine {
    type Output;
    fn read_line(line: &str) -> Result<Self::Output, String>;
}
fn split_into_words(line: &str) -> Vec<&str> {
    #[allow(deprecated)]
    line.trim_right_matches('\n').split_whitespace().collect()
}
impl<T: Readable> ReadableFromLine for T {
    type Output = T::Output;
    fn read_line(line: &str) -> Result<T::Output, String> {
        let words = split_into_words(line);
        if words.len() != T::words_count() {
            return Err(format!(
                "line `{}` has {} words, expected {}",
                line,
                words.len(),
                T::words_count()
            ));
        }
        T::read_words(&words)
    }
}
macro_rules ! impl_readable_from_line_for_tuples_with_from_iterator { ( $ u : ident : $ ( + $ bound : path ) * => $ seq_in : ty , $ seq_out : ty ; $ t : ident $ var : ident ) => { impl <$ u : Readable > ReadableFromLine for $ seq_in where <$ u as Readable >:: Output : Sized $ ( + $ bound ) * { type Output = $ seq_out ; fn read_line ( line : & str ) -> Result <$ seq_out , String > { let n = $ u :: words_count ( ) ; let words = split_into_words ( line ) ; if words . len ( ) % n != 0 { return Err ( format ! ( "line `{}` has {} words, expected multiple of {}" , line , words . len ( ) , n ) ) ; } let mut result = Vec :: new ( ) ; for chunk in words . chunks ( n ) { match $ u :: read_words ( chunk ) { Ok ( v ) => result . push ( v ) , Err ( msg ) => { let flagment_msg = if n == 1 { format ! ( "word {}" , result . len ( ) ) } else { let l = result . len ( ) ; format ! ( "words {}-{}" , n * l + 1 , ( n + 1 ) * l ) } ; return Err ( format ! ( "{} of line `{}`: {}" , flagment_msg , line , msg ) ) ; } } } Ok ( result . into_iter ( ) . collect ( ) ) } } impl < T : Readable , $ u : Readable > ReadableFromLine for ( T , $ seq_in ) where <$ u as Readable >:: Output : Sized $ ( + $ bound ) * { type Output = ( T :: Output , $ seq_out ) ; fn read_line ( line : & str ) -> Result < Self :: Output , String > { let n = T :: words_count ( ) ; # [ allow ( deprecated ) ] let trimmed = line . trim_right_matches ( '\n' ) ; let words_and_rest : Vec <& str > = trimmed . splitn ( n + 1 , ' ' ) . collect ( ) ; if words_and_rest . len ( ) < n { return Err ( format ! ( "line `{}` has {} words, expected at least {}" , line , words_and_rest . len ( ) , n ) ) ; } let words = & words_and_rest [ .. n ] ; let empty_str = "" ; let rest = words_and_rest . get ( n ) . unwrap_or ( & empty_str ) ; Ok ( ( T :: read_words ( words ) ?, <$ seq_in >:: read_line ( rest ) ? ) ) } } } ; ( $ u : ident : $ ( + $ bound : path ) * => $ seq_in : ty , $ seq_out : ty ; $ t : ident $ var : ident , $ ( $ inner_t : ident $ inner_var : ident ) ,+ ) => { impl_readable_from_line_for_tuples_with_from_iterator ! ( $ u : $ ( + $ bound ) * => $ seq_in , $ seq_out ; $ ( $ inner_t $ inner_var ) ,+ ) ; impl <$ t : Readable , $ ( $ inner_t : Readable ) ,+ , $ u : Readable > ReadableFromLine for ( $ t , $ ( $ inner_t ) ,+ , $ seq_in ) where <$ u as Readable >:: Output : Sized $ ( + $ bound ) * { type Output = ( $ t :: Output , $ ( $ inner_t :: Output ) ,+ , $ seq_out ) ; fn read_line ( line : & str ) -> Result < Self :: Output , String > { let mut n = $ t :: words_count ( ) ; $ ( n += $ inner_t :: words_count ( ) ; ) + # [ allow ( deprecated ) ] let trimmed = line . trim_right_matches ( '\n' ) ; let words_and_rest : Vec <& str > = trimmed . splitn ( n + 1 , ' ' ) . collect ( ) ; if words_and_rest . len ( ) < n { return Err ( format ! ( "line `{}` has {} words, expected at least {}" , line , words_and_rest . len ( ) , n ) ) ; } let words = & words_and_rest [ .. n ] ; let empty_str = "" ; let rest = words_and_rest . get ( n ) . unwrap_or ( & empty_str ) ; let ( $ var , $ ( $ inner_var ) ,* ) = < ( $ t , $ ( $ inner_t ) ,+ ) >:: read_words ( words ) ?; Ok ( ( $ var , $ ( $ inner_var ) ,* , <$ seq_in >:: read_line ( rest ) ? ) ) } } } ; }
#[macro_export]
macro_rules ! readable_collection { ( $ u : ident => $ collection_in : ty , $ collection_out : ty ) => { impl_readable_from_line_for_tuples_with_from_iterator ! ( $ u : => $ collection_in , $ collection_out ; T8 x8 , T7 x7 , T6 x6 , T5 x5 , T4 t4 , T3 t3 , T2 t2 , T1 t1 ) ; } ; ( $ u : ident : $ ( $ bound : path ) ,* => $ collection_in : ty , $ collection_out : ty ) => { impl_readable_from_line_for_tuples_with_from_iterator ! ( $ u : $ ( + $ bound ) * => $ collection_in , $ collection_out ; T8 x8 , T7 x7 , T6 x6 , T5 x5 , T4 t4 , T3 t3 , T2 t2 , T1 t1 ) ; } }
readable_collection ! ( U => Vec < U >, Vec < U :: Output > ) ;
readable_collection ! ( U : Eq , std :: hash :: Hash => std :: collections :: HashSet < U >, std :: collections :: HashSet < U :: Output > ) ;
pub fn read<T: ReadableFromLine>() -> T::Output {
    let mut line = String::new();
    std::io::stdin().read_line(&mut line).unwrap();
    T::read_line(&line).unwrap()
}
#[macro_export]
macro_rules ! read { ( ) => { let mut line = String :: new ( ) ; std :: io :: stdin ( ) . read_line ( & mut line ) . unwrap ( ) ; } ; ( $ pat : pat = $ t : ty ) => { let $ pat = read ::<$ t > ( ) ; } ; ( $ ( $ pat : pat = $ t : ty ) ,+ ) => { read ! ( ( $ ( $ pat ) ,* ) = ( $ ( $ t ) ,* ) ) ; } ; }
#[macro_export]
macro_rules ! readls { ( $ ( $ pat : pat = $ t : ty ) ,+ ) => { $ ( read ! ( $ pat = $ t ) ; ) * } ; }
pub fn readx<T: ReadableFromLine>() -> Vec<T::Output> {
    use std::io::{self, BufRead};
    let stdin = io::stdin();
    let result = stdin
        .lock()
        .lines()
        .map(|line_result| {
            let line = line_result.expect("read from stdin failed");
            T::read_line(&line).unwrap()
        })
        .collect();
    result
}
#[macro_export]
macro_rules ! readx_loop { ( |$ pat : pat = $ t : ty | $ body : expr ) => { { use std :: io :: BufRead ; let stdin = std :: io :: stdin ( ) ; for line in stdin . lock ( ) . lines ( ) { let line = line . expect ( "read from stdin failed" ) ; let $ pat = <$ t >:: read_line ( & line ) . unwrap ( ) ; $ body } } } ; ( |$ ( $ pat : pat = $ t : ty ) ,*| $ body : expr ) => { readx_loop ! ( | ( $ ( $ pat ) ,* ) = ( $ ( $ t ) ,* ) | $ body ) ; } ; }
pub fn readn<T: ReadableFromLine>(n: usize) -> Vec<T::Output> {
    use std::io::{self, BufRead};
    let stdin = io::stdin();
    let result: Vec<T::Output> = stdin
        .lock()
        .lines()
        .take(n)
        .map(|line_result| {
            let line = line_result.expect("read from stdin failed");
            T::read_line(&line).unwrap()
        })
        .collect();
    if result.len() < n {
        panic!(
            "expected reading {} lines, but only {} lines are read",
            n,
            result.len()
        );
    }
    result
}
#[macro_export]
macro_rules ! readn_loop { ( $ n : expr , |$ pat : pat = $ t : ty | $ body : expr ) => { { use std :: io :: BufRead ; let stdin = std :: io :: stdin ( ) ; let mut lock = stdin . lock ( ) ; for _ in 0 ..$ n { let mut line = String :: new ( ) ; lock . read_line ( & mut line ) . expect ( "read from stdin failed" ) ; let $ pat = <$ t >:: read_line ( & line ) . unwrap ( ) ; $ body } } } ; ( $ n : expr , |$ ( $ pat : pat = $ t : ty ) ,*| $ body : expr ) => { readn_loop ! ( $ n , | ( $ ( $ pat ) ,* ) = ( $ ( $ t ) ,* ) | $ body ) ; } ; }
pub trait Words {
    fn read<T: Readable>(&self) -> T::Output;
}
impl<'a> Words for [&'a str] {
    fn read<T: Readable>(&self) -> T::Output {
        T::read_words(self).unwrap()
    }
}
impl<'a> Words for &'a str {
    fn read<T: Readable>(&self) -> T::Output {
        T::read_words(&[self]).unwrap()
    }
}

#[macro_export]
#[cfg(local)]
macro_rules! dbg {
    ( ) => {{
        use std::io::{self, Write};
        writeln!(io::stderr(), "{}: dbg", line!()).unwrap();
    }};
    ( $ e : expr ) => {{
        use std::io::{self, Write};
        let result = $e;
        writeln!(
            io::stderr(),
            "{}: {} = {:?}",
            line!(),
            stringify!($e),
            result
        )
            .unwrap();
        result
    }};
}
#[macro_export]
#[cfg(not(local))]
macro_rules! dbg {
    ( ) => {};
    ( $ e : expr ) => {
        $e
    };
}

use std::collections::hash_map::DefaultHasher;
use std::collections::HashSet;
use std::hash::Hasher;

fn hash(xs: &[usize]) -> u64 {
    let mut hasher = DefaultHasher::new();
    for &x in xs {
        hasher.write_usize(x);
    }
    hasher.finish()
}

fn main() {
    read!(n = usize);
    read!(aa = Vec<u64>);
    let mut ans = 0;
    let mut hashes = HashSet::new();
    for i in (0..60).rev() {
        let mask = 1u64<<i;
        let ones: Vec<usize> = aa.iter().enumerate()
            .filter(|&(_, &a)| a & mask != 0)
            .map(|(i, _)| i)
            .collect();
        if ones.len() % 2 == 1 {
            ans += mask;
        } else if ones.len() > 0 {
            let h = hash(&ones);
            if hashes.contains(&h) {
                ans += 2*mask;
            } else {
                hashes.insert(h);
                if hashes.len() < n {
                    ans += 2*mask;
                }
            }
        }
    }
    println!("{}", ans);
}