Problem:
Score : 500 points

Problem Statement

There are N Snuke Cats numbered 1, 2, \ldots, N, where N is even.

Each Snuke Cat wears a red scarf, on which his favorite non-negative integer is written.

Recently, they learned the operation called xor (exclusive OR).

What is xor?

For n non-negative integers x_1, x_2, \ldots, x_n, their xor, x_1~\textrm{xor}~x_2~\textrm{xor}~\ldots~\textrm{xor}~x_n is defined as follows:

When x_1~\textrm{xor}~x_2~\textrm{xor}~\ldots~\textrm{xor}~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~\textrm{xor}~5 = 6.

They wanted to use this operation quickly, so each of them calculated the xor of the integers written on their scarfs except his scarf.

We know that the xor calculated by Snuke Cat i, that is, the xor of the integers written on the scarfs except the scarf of Snuke Cat i is a_i.
Using this information, restore the integer written on the scarf of each Snuke Cat.

Constraints

All values in input are integers.

2 \leq N \leq 200000

N is even.

0 \leq a_i \leq 10^9

There exists a combination of integers on the scarfs that is consistent with the given information.

Input

Input is given from Standard Input in the following format:

N
a_1 a_2 \ldots a_N

Output

Print a line containing N integers separated with space.

The i-th of the integers from the left should represent the integer written on the scarf of Snuke Cat i.

If there are multiple possible solutions, you may print any of them.

Sample Input 1

4
20 11 9 24

Sample Output 1

26 5 7 22

5~\textrm{xor}~7~\textrm{xor}~22 = 20

26~\textrm{xor}~7~\textrm{xor}~22 = 11

26~\textrm{xor}~5~\textrm{xor}~22 = 9

26~\textrm{xor}~5~\textrm{xor}~7 = 24

Thus, this output is consistent with the given information.

Solution in Rust (1.42.0) (judge verdict: Accepted)

#![allow(unused_imports, non_snake_case)]
#![allow(dead_code)]
use crate::ext::iter::IterExtra;
use crate::scanner::Scanner;
fn main() {
    let mut scan = Scanner::new();
    let n = scan.read::<i32>();
    let a = scan.readn::<i64>(n);
    let s = a.fold(0, |acc, x| acc ^ x);
    println!("{}", (0..n).map(|i| a[i] ^ s).to_list());
}
pub mod ext {
    pub mod range {
        use crate::independent::integer::Int;
        use std::cmp::{max, min};
        use std::ops::{Bound, Range, RangeBounds, RangeInclusive};
        pub trait RangeEx<T> {
            fn width(&self) -> T;
            fn empty(&self) -> bool;
            fn contain_range(&self, inner: &Self) -> bool;
            fn separate_range(&self, other: &Self) -> bool;
            type ReturnRange;
            fn overlap(&self, other: &Self) -> Self::ReturnRange;
        }
        impl<T: Int> RangeEx<T> for Range<T> {
            fn width(&self) -> T {
                if self.empty() {
                    T::zero()
                } else {
                    self.end - self.start
                }
            }
            fn empty(&self) -> bool {
                !(self.start < self.end)
            }
            fn contain_range(&self, inner: &Self) -> bool {
                self.start <= inner.start && inner.end <= self.end
            }
            fn separate_range(&self, other: &Self) -> bool {
                self.end <= other.start || other.end <= self.start
            }
            type ReturnRange = Range<T>;
            fn overlap(&self, other: &Self) -> Self::ReturnRange {
                let left = max(self.start, other.start);
                let right = min(self.end, other.end);
                left..right
            }
        }
        impl<T: Int> RangeEx<T> for RangeInclusive<T> {
            fn width(&self) -> T {
                if self.empty() {
                    T::zero()
                } else {
                    *self.end() - *self.start() + T::one()
                }
            }
            fn empty(&self) -> bool {
                !(self.start() <= self.end())
            }
            fn contain_range(&self, inner: &Self) -> bool {
                self.start() <= inner.start() && inner.end() <= self.end()
            }
            fn separate_range(&self, other: &Self) -> bool {
                self.end() <= other.start() || other.end() <= self.start()
            }
            type ReturnRange = RangeInclusive<T>;
            fn overlap(&self, other: &Self) -> Self::ReturnRange {
                let left = *max(self.start(), other.start());
                let right = *min(self.end(), other.end());
                left..=right
            }
        }
        pub trait IntRangeBounds<U: Int>: RangeBounds<U> {
            #[doc = " inclusive"]
            fn lower_bound(&self, lower_bound: U) -> U {
                match self.start_bound() {
                    Bound::Included(x) => max(lower_bound, *x),
                    Bound::Excluded(x) => max(lower_bound, *x + U::one()),
                    Bound::Unbounded => lower_bound,
                }
            }
            #[doc = " exclusive"]
            fn upper_bound(&self, upper_bound: U) -> U {
                match self.end_bound() {
                    Bound::Included(x) => min(upper_bound, *x + U::one()),
                    Bound::Excluded(x) => min(upper_bound, *x),
                    Bound::Unbounded => upper_bound,
                }
            }
            fn to_harfopen(&self, lb: U, ub: U) -> Range<U> {
                self.lower_bound(lb)..self.upper_bound(ub)
            }
        }
        impl<T: ?Sized, U: Int> IntRangeBounds<U> for T where T: RangeBounds<U> {}
    }
    pub mod iter {
        use crate::arraylist::List;
        pub trait IterExtra: Iterator {
            fn to_list(self) -> List<Self::Item>
            where
                Self: Sized,
            {
                self.collect()
            }
            fn icount(self) -> i32
            where
                Self: Sized,
            {
                self.count() as i32
            }
            fn ienumerate(
                self,
            ) -> std::iter::Map<
                std::iter::Enumerate<Self>,
                fn((usize, Self::Item)) -> (i32, Self::Item),
            >
            where
                Self: Sized,
            {
                self.enumerate().map(|t| (t.0 as i32, t.1))
            }
        }
        impl<T: ?Sized> IterExtra for T where T: Iterator {}
    }
}
pub mod scanner {
    use crate::arraylist::List;
    use std::io::{stdin, BufReader, Bytes, Read, Stdin};
    use std::str::FromStr;
    pub struct Scanner {
        buf: Bytes<BufReader<Stdin>>,
    }
    impl Scanner {
        pub fn new() -> Scanner {
            Scanner {
                buf: BufReader::new(stdin()).bytes(),
            }
        }
        pub fn read_next<T: FromStr>(&mut self) -> Option<T> {
            let token = self
                .buf
                .by_ref()
                .map(|c| c.unwrap() as char)
                .skip_while(|c| c.is_whitespace())
                .take_while(|c| !c.is_whitespace())
                .collect::<String>();
            token.parse::<T>().ok()
        }
        pub fn read<T: FromStr>(&mut self) -> T {
            self.read_next().unwrap()
        }
        pub fn readn<T: FromStr>(&mut self, n: i32) -> List<T> {
            (0..n).map(|_| self.read::<T>()).collect()
        }
        pub fn chars(&mut self) -> List<char> {
            self.read::<String>().chars().collect()
        }
        pub fn bytes(&mut self) -> List<u8> {
            self.read::<String>().bytes().collect()
        }
    }
}
pub mod arraylist {
    use crate::{ext::range::IntRangeBounds, independent::integer::Int};
    use std::fmt::Formatter;
    use std::iter::FromIterator;
    use std::ops::{Index, IndexMut, RangeBounds};
    use std::slice::Iter;
    #[derive(Clone, PartialEq, Eq)]
    pub struct List<T> {
        pub vec: Vec<T>,
    }
    impl<T> List<T> {
        #[inline]
        pub fn new() -> List<T> {
            List { vec: vec![] }
        }
        #[inline]
        pub fn init(init: T, n: i32) -> List<T>
        where
            T: Clone,
        {
            List {
                vec: vec![init; n as usize],
            }
        }
        #[inline]
        pub fn from_vec(vec: Vec<T>) -> List<T> {
            List { vec }
        }
        #[inline]
        pub fn ilen(&self) -> i32 {
            self.vec.len() as i32
        }
        #[inline]
        pub fn iter(&self) -> Iter<'_, T> {
            self.vec.iter()
        }
        #[inline]
        pub fn push(&mut self, item: T) {
            self.vec.push(item);
        }
        #[inline]
        pub fn sort(&mut self)
        where
            T: Ord,
        {
            self.vec.sort();
        }
        #[inline]
        pub fn reverse(&mut self) {
            self.vec.reverse();
        }
        #[inline]
        pub fn sort_by<F>(&mut self, compare: F)
        where
            F: FnMut(&T, &T) -> std::cmp::Ordering,
        {
            self.vec.sort_by(compare)
        }
        #[inline]
        pub fn sort_by_key<K, F>(&mut self, compare: F)
        where
            F: FnMut(&T) -> K,
            K: Ord,
        {
            self.vec.sort_by_key(compare)
        }
        #[inline]
        pub fn first(&self) -> Option<&T> {
            self.vec.first()
        }
        #[inline]
        pub fn last(&self) -> Option<&T> {
            self.vec.last()
        }
        #[inline]
        pub fn pop(&mut self) -> Option<T> {
            self.vec.pop()
        }
        #[inline]
        pub fn swap(&mut self, i: i32, j: i32) {
            self.vec.swap(i as usize, j as usize);
        }
        #[inline]
        pub fn append(&mut self, mut other: Self) {
            self.vec.append(&mut other.vec);
        }
        #[inline]
        pub fn extend(&mut self, other: impl Iterator<Item = T>) {
            self.vec.extend(other);
        }
        #[inline]
        pub fn mirror(&self) -> std::iter::Cloned<Iter<T>>
        where
            T: Clone,
        {
            self.iter().cloned()
        }
        #[inline]
        pub fn join(&self, sep: &str) -> String
        where
            T: std::fmt::Display,
        {
            self.iter()
                .map(|x| format!("{}", x))
                .collect::<Vec<_>>()
                .join(sep)
        }
        #[inline]
        pub fn map<B, F>(&self, f: F) -> List<B>
        where
            T: Clone,
            F: FnMut(T) -> B,
        {
            self.mirror().map(f).collect()
        }
        #[inline]
        pub fn filter<P>(&self, predicate: P) -> List<T>
        where
            T: Clone,
            P: FnMut(&T) -> bool,
        {
            self.mirror().filter(predicate).collect()
        }
        #[inline]
        pub fn filter_map<B, F>(&self, f: F) -> List<B>
        where
            T: Clone,
            F: FnMut(T) -> Option<B>,
        {
            self.mirror().filter_map(f).collect()
        }
        #[doc = " |acc, x| -> acc"]
        #[inline]
        pub fn fold<B, F>(&self, init: B, f: F) -> B
        where
            T: Clone,
            F: FnMut(B, T) -> B,
        {
            self.mirror().fold(init, f)
        }
        #[inline]
        pub fn any<P>(&self, predicate: P) -> bool
        where
            P: FnMut(&T) -> bool,
        {
            self.iter().any(predicate)
        }
        #[inline]
        pub fn all<P>(&self, predicate: P) -> bool
        where
            P: FnMut(&T) -> bool,
        {
            self.iter().all(predicate)
        }
        #[inline]
        pub fn sum(&self) -> T
        where
            T: Int,
        {
            self.iter().cloned().fold(T::zero(), |acc, x| acc + x)
        }
        #[inline]
        pub fn enumerate(&self) -> List<(i32, T)>
        where
            T: Clone,
        {
            self.mirror()
                .enumerate()
                .map(|p| (p.0 as i32, p.1))
                .collect()
        }
        #[inline]
        pub fn find<P>(&self, mut predicate: P) -> Option<&T>
        where
            P: FnMut(&T) -> bool,
        {
            self.iter().find(|x| predicate(*x))
        }
        #[inline]
        pub fn index_of<P>(&self, mut predicate: P) -> Option<i32>
        where
            P: FnMut(&T) -> bool,
        {
            self.iter()
                .enumerate()
                .find(|&(_i, x)| predicate(x))
                .map(|p| p.0 as i32)
        }
        #[inline]
        pub fn to<B: FromIterator<T>>(&self) -> B
        where
            T: Clone,
        {
            self.mirror().collect()
        }
        #[inline]
        pub fn min(&self) -> Option<&T>
        where
            T: Ord,
        {
            self.iter().min()
        }
        #[inline]
        pub fn max(&self) -> Option<&T>
        where
            T: Ord,
        {
            self.iter().max()
        }
        #[inline]
        pub fn argmin(&self) -> Option<i32>
        where
            T: Ord,
        {
            let item = self.iter().min()?;
            self.iter()
                .enumerate()
                .find(|p| p.1 == item)
                .map(|p| p.0 as i32)
        }
        #[inline]
        pub fn argmax(&self) -> Option<i32>
        where
            T: Ord,
        {
            let item = self.iter().max()?;
            self.iter()
                .enumerate()
                .find(|p| p.1 == item)
                .map(|p| p.0 as i32)
        }
        #[inline]
        pub fn part<U>(&self, range: U) -> List<T>
        where
            T: Clone,
            U: RangeBounds<i32>,
        {
            List::from_vec(
                self.vec[range.lower_bound(0) as usize..range.upper_bound(self.ilen()) as usize]
                    .to_vec(),
            )
        }
        #[inline]
        pub fn first_exn(&self) -> &T {
            self.first().unwrap()
        }
        #[inline]
        pub fn last_exn(&self) -> &T {
            self.last().unwrap()
        }
        #[inline]
        pub fn pop_exn(&mut self) -> T {
            self.pop().unwrap()
        }
        #[inline]
        pub fn min_exn(&self) -> &T
        where
            T: Ord,
        {
            self.min().unwrap()
        }
        #[inline]
        pub fn max_exn(&self) -> &T
        where
            T: Ord,
        {
            self.max().unwrap()
        }
        #[inline]
        pub fn argmin_exn(&self) -> i32
        where
            T: Ord,
        {
            self.argmin().unwrap()
        }
        #[inline]
        pub fn argmax_exn(&self) -> i32
        where
            T: Ord,
        {
            self.argmax().unwrap()
        }
        #[inline]
        pub fn find_exn<P>(&self, predicate: P) -> &T
        where
            P: FnMut(&T) -> bool,
        {
            self.find(predicate).unwrap()
        }
        #[inline]
        pub fn index_of_exn<P>(&self, predicate: P) -> i32
        where
            P: FnMut(&T) -> bool,
        {
            self.index_of(predicate).unwrap()
        }
    }
    impl<T> Index<i32> for List<T> {
        type Output = T;
        #[inline]
        fn index(&self, index: i32) -> &Self::Output {
            if cfg!(debug_assertions) {
                self.vec.index(index as usize)
            } else {
                unsafe { self.vec.get_unchecked(index as usize) }
            }
        }
    }
    impl<T> IndexMut<i32> for List<T> {
        #[inline]
        fn index_mut(&mut self, index: i32) -> &mut Self::Output {
            if cfg!(debug_assertions) {
                self.vec.index_mut(index as usize)
            } else {
                unsafe { self.vec.get_unchecked_mut(index as usize) }
            }
        }
    }
    impl<T> FromIterator<T> for List<T> {
        fn from_iter<U: IntoIterator<Item = T>>(iter: U) -> Self {
            let mut vec = vec![];
            for i in iter {
                vec.push(i);
            }
            List { vec }
        }
    }
    impl<T> IntoIterator for List<T> {
        type Item = T;
        type IntoIter = std::vec::IntoIter<T>;
        fn into_iter(self) -> std::vec::IntoIter<T> {
            self.vec.into_iter()
        }
    }
    impl<'a, T> IntoIterator for &'a List<T> {
        type Item = &'a T;
        type IntoIter = Iter<'a, T>;
        fn into_iter(self) -> Iter<'a, T> {
            self.vec.iter()
        }
    }
    impl<T: std::fmt::Display> std::fmt::Display for List<T> {
        fn fmt(&self, f: &mut std::fmt::Formatter) -> std::fmt::Result {
            write!(
                f,
                "{}",
                self.iter()
                    .map(|x| format!("{}", x))
                    .collect::<Vec<_>>()
                    .join(" ")
            )
        }
    }
    impl<T: std::fmt::Debug> std::fmt::Debug for List<T> {
        fn fmt(&self, f: &mut Formatter<'_>) -> std::fmt::Result {
            write!(
                f,
                "[{}]",
                self.iter()
                    .map(|x| format!("{:?}", x))
                    .collect::<Vec<_>>()
                    .join(", ")
            )
        }
    }
    impl<T> From<Vec<T>> for List<T> {
        fn from(vec: Vec<T>) -> Self {
            Self::from_vec(vec)
        }
    }
    impl<T: Clone> From<&[T]> for List<T> {
        fn from(slice: &[T]) -> Self {
            slice.iter().cloned().collect()
        }
    }
    #[macro_export]
    macro_rules ! list { ( ) => { $ crate :: arraylist :: List :: new ( ) } ; ( $ v : expr ; $ a : expr ) => { $ crate :: arraylist :: List :: init ( $ v , $ a ) } ; ( $ v : expr ; $ a : expr ; $ ( $ rest : expr ) ;+ ) => { $ crate :: arraylist :: List :: init ( list ! ( $ v ; $ ( $ rest ) ;+ ) , $ a ) } ; }
}
pub mod independent {
    pub mod integer {
        pub trait Int:
            std::ops::Add<Output = Self>
            + std::ops::Sub<Output = Self>
            + std::ops::Mul<Output = Self>
            + std::ops::Div<Output = Self>
            + std::ops::Rem<Output = Self>
            + std::ops::AddAssign
            + std::ops::SubAssign
            + std::ops::MulAssign
            + std::ops::DivAssign
            + std::hash::Hash
            + PartialEq
            + Eq
            + PartialOrd
            + Ord
            + Copy
        {
            fn to_u8(&self) -> u8;
            fn to_u16(&self) -> u16;
            fn to_u32(&self) -> u32;
            fn to_u64(&self) -> u64;
            fn to_u128(&self) -> u128;
            fn to_i8(&self) -> i8;
            fn to_i16(&self) -> i16;
            fn to_i32(&self) -> i32;
            fn to_i64(&self) -> i64;
            fn to_i128(&self) -> i128;
            fn to_usize(&self) -> usize;
            fn to_isize(&self) -> isize;
            fn from_u8(x: u8) -> Self;
            fn from_u16(x: u16) -> Self;
            fn from_u32(x: u32) -> Self;
            fn from_u64(x: u64) -> Self;
            fn from_u128(x: u128) -> Self;
            fn from_i8(x: i8) -> Self;
            fn from_i16(x: i16) -> Self;
            fn from_i32(x: i32) -> Self;
            fn from_i64(x: i64) -> Self;
            fn from_i128(x: i128) -> Self;
            fn from_usize(x: usize) -> Self;
            fn from_isize(x: isize) -> Self;
            fn zero() -> Self;
            fn one() -> Self;
            fn next(&self) -> Self {
                *self + Self::one()
            }
        }
        macro_rules ! impl_integer_functions { ( $ selftpe : ident , $ ( $ tofn : ident , $ fromfn : ident , $ tpe : ident ) ,* ) => { $ ( fn $ tofn ( & self ) -> $ tpe { * self as $ tpe } fn $ fromfn ( x : $ tpe ) -> Self { x as $ selftpe } ) * } ; }
        macro_rules ! impl_integer { ( $ ( $ tpe : ident ) ,* ) => { $ ( impl Int for $ tpe { impl_integer_functions ! ( $ tpe , to_u8 , from_u8 , u8 , to_u16 , from_u16 , u16 , to_u32 , from_u32 , u32 , to_u64 , from_u64 , u64 , to_u128 , from_u128 , u128 , to_i8 , from_i8 , i8 , to_i16 , from_i16 , i16 , to_i32 , from_i32 , i32 , to_i64 , from_i64 , i64 , to_i128 , from_i128 , i128 , to_usize , from_usize , usize , to_isize , from_isize , isize ) ; fn zero ( ) -> Self { 0 } fn one ( ) -> Self { 1 } } ) * } ; }
        impl_integer!(u8, u16, u32, u64, u128, i8, i16, i32, i64, i128, usize, isize);
    }
}