Problem:
Score : 600 points

Problem Statement

Given are two sequences a=\{a_0,\ldots,a_{N-1}\} and b=\{b_0,\ldots,b_{N-1}\} of N non-negative integers each.

Snuke will choose an integer k such that 0 \leq k < N and an integer x not less than 0, to make a new sequence of length N, a'=\{a_0',\ldots,a_{N-1}'\}, as follows:

a_i'= a_{i+k \mod N}\ XOR \ x

Find all pairs (k,x) such that a' will be equal to b.

What is \mbox{ XOR }?

The XOR of integers A and B, A \mbox{ XOR } B, is defined as follows:

When A \mbox{ XOR } B is written in base two, the digit in the 2^k's place (k \geq 0) is 1 if either A or B, but not both, has 1 in the 2^k's place, and 0 otherwise.

For example, 3 \mbox{ XOR } 5 = 6. (In base two: 011 \mbox{ XOR } 101 = 110.)

Constraints

1 \leq N \leq 2 \times 10^5

0 \leq a_i,b_i < 2^{30}

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
a_0 a_1 ... a_{N-1}
b_0 b_1 ... b_{N-1}

Output

Print all pairs (k, x) such that a' and b will be equal, using one line for each pair, in ascending order of k (ascending order of x for pairs with the same k).

If there are no such pairs, the output should be empty.

Sample Input 1

3
0 2 1
1 2 3

Sample Output 1

1 3

If (k,x)=(1,3),

a_0'=(a_1\ XOR \ 3)=1

a_1'=(a_2\ XOR \ 3)=2

a_2'=(a_0\ XOR \ 3)=3

and we have a' = b.

Sample Input 2

5
0 0 0 0 0
2 2 2 2 2

Sample Output 2

0 2
1 2
2 2
3 2
4 2

Sample Input 3

6
0 1 3 7 6 4
1 5 4 6 2 3

Sample Output 3

2 2
5 5

Sample Input 4

2
1 2
0 0

Sample Output 4

No pairs may satisfy the condition.

Solution in Rust (1.15.1) (judge verdict: Accepted)

fn read_stdin() -> String {
    use std::io::Read;
    let mut input = String::new();
    std::io::stdin().read_to_string(&mut input).unwrap();
    input
}

fn scan<'a, I: Iterator<Item = &'a str>, T: std::str::FromStr>(tokens: &mut I) -> T {
    tokens.next().unwrap().parse().ok().unwrap()
}

fn rep<T, F: FnMut() -> T>(n: usize, mut f: F) -> Vec<T> {
    (0..n).map(|_| f()).collect()
}

fn main() {
    let input = read_stdin();
    let tokens = &mut input.split_whitespace();
    let n: usize = scan(tokens);
    let a: Vec<usize> = rep(n, || scan(tokens));
    let b: Vec<usize> = rep(n, || scan(tokens));
    let mut c = Vec::with_capacity(2 * n - 1);
    let mut d = Vec::with_capacity(n);
    for i in 0..n - 1 {
        c.push(a[i] ^ a[i + 1]);
        d.push(b[i] ^ b[i + 1]);
    }
    c.push(a[n - 1] ^ a[0]);
    d.push(b[n - 1] ^ b[0]);
    for i in 0..n - 1 {
        let tmp = c[i];
        c.push(tmp);
    }
    let r = {
        let mut r = vec![0; n + 1];
        let mut i = 0;
        let mut j = 1;
        while j < n {
            if d[i] == d[j] {
                i += 1;
                j += 1;
                r[j] = i;
            } else if i > 0 {
                i = d[i];
            } else {
                j += 1;
            }
        }
        r
    };
    let mut i = 0;
    let mut j = 0;
    while j < 2 * n - 1 {
        if d[i] == c[j] {
            i += 1;
            j += 1;
            if i == n {
                println!("{} {}", j - n, a[j - n] ^ b[0]);
                i = r[i];
            }
        } else if i > 0 {
            i = d[i];
        } else {
            j += 1;
        }
    }
}