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: Accepted)

#[allow(unused_macros)]
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        let mut next = || { iter.next().unwrap() };
        input_inner!{next, $($r)*}
    };
    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        let mut next = move || -> String{
            bytes
                .by_ref()
                .map(|r|r.unwrap() as char)
                .skip_while(|c|c.is_whitespace())
                .take_while(|c|!c.is_whitespace())
                .collect()
        };
        input_inner!{next, $($r)*}
    };
}
 
#[allow(unused_macros)]
macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr, ) => {};
 
    ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
        let mut $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };
}
 
#[allow(unused_macros)]
macro_rules! read_value {
    ($next:expr, ( $($t:tt),* )) => {
        ( $(read_value!($next, $t)),* )
    };
 
    ($next:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };
 
    ($next:expr, chars) => {
        read_value!($next, String).chars().collect::<Vec<char>>()
    };
 
    ($next:expr, bytes) => {
        read_value!($next, String).into_bytes()
    };
 
    ($next:expr, usize1) => {
        read_value!($next, usize) - 1
    };
 
    ($next:expr, $t:ty) => {
        $next().parse::<$t>().expect("Parse error")
    };
}
 
use std::cmp::Ordering;
use std::cmp;
use std::cmp::min;
use std::collections::BTreeMap;
use std::process;
use std::cmp::Ord;
use std::collections::HashMap;
use std::collections::HashSet;
use std::collections::VecDeque;
use std::collections::BTreeSet;
use std::mem;
use std::collections::BinaryHeap;
use std::hash::{Hash, Hasher};
fn modpow(x:usize, n:usize, p:usize) -> usize{
        let mut ans = 1;
        let mut n = n;
        let mut x = x;
        while(n != 0){
            if (n&1 == 1){ans = ans*x%p;}
            x = x*x%p;
            n = n>>1;
        }
        ans
}
fn comb(a:usize, b:usize,  fac:&Vec<usize>, ifac:&Vec<usize>, p:usize)->usize{
        let mut a = a;
        let mut b = b;
        if a == 0 && b == 0{return 1;}
        if a<b || a<0{return 0;}
        let mut tmp = ifac[a-b]*ifac[b] % p;
        return tmp * fac[a] % p;
}

fn invs(p:usize)->(Vec<usize>, Vec<usize>){
    let mut ma = 3000001;
    let mut fac = vec![0;300001];
    let mut ifac = vec![0;300001];
    fac[0] = 1;
    ifac[0] = 1;
    for i in 0..ma{
        fac[i+1] = fac[i] * (i+1) % p;
        ifac[i+1] = ifac[i] * modpow(i+1, p - 2, p) % p;
    }
    (fac, ifac)
}


#[macro_use]
fn solve(){
    //let sssss = std::io::stdin();
    //let mut sc = Scanner { stdin: sssss.lock() };
    input!{
        N:usize,
        a:[usize;N],
    }
    let mut h = BinaryHeap::new();
    let mut num = vec![0;61];
    let mut x = 0;
    for i in 0..N{
        x = x^a[i];
        for j in 0..64{
            if (a[i]>>j)&1 == 1{
                num[j]+=1;
            }
        }
    }
    for i in 0..N{
        let mut p = a[i];
        for j in 0..61{
            if num[j]%2 == 1 && (p>>j)&1 == 1{
                p = p^(1<<j);
            }
        }
        h.push(p);
    }
    let mut v = vec![];
    for i in 0..61{
        if h.len()==0{
            break;
        }
        let mut t = h.pop().unwrap();
        if t == 0{
            break;
        }
        let mut msb = 0;
        for j in 0..61{
            if (t>>j)&1==1{
                msb = j;
            }
        }
        let mut nxt = BinaryHeap::new();
        for j in 0..h.len(){
            let mut tt = h.pop().unwrap();
            if (tt>>msb)&1==1{
                nxt.push(tt^t);
            }
            else{
                nxt.push(tt);
            }
        }
        v.push(t);
        mem::swap(&mut nxt, &mut h);
    }
    let mut res = 0usize;
    for i in 0..v.len(){
        res = cmp::max(res, res^v[i]);
    }
    res*=2;
    for i in 0..61{
        if num[i]%2==1{
            res+=1<<i;
        }
    }
    println!("{}", res);



}

fn main(){
    solve();
}
const PI:f64 = std::f64::consts::PI;

pub static MOD:i64 = 998244353;
pub static MODu:usize = 998244353;
pub static eps:f64 = 1e-6;
const INF: i64 = 1 << 60;