Problem:
Score : 400 points

Problem Statement

There are two persons, numbered 0 and 1, and a variable x whose initial value is 0.
The two persons now play a game.
The game is played in N rounds. The following should be done in the i-th round (1 \leq i \leq N):

Person S_i does one of the following:

Replace x with x \oplus A_i, where \oplus represents bitwise XOR.

Do nothing.

Person 0 aims to have x=0 at the end of the game, while Person 1 aims to have x \neq 0 at the end of the game.

Determine whether x becomes 0 at the end of the game when the two persons play optimally.

Solve T test cases for each input file.

Constraints

1 \leq T \leq 100

1 \leq N \leq 200

1 \leq A_i \leq 10^{18}

S is a string of length N consisting of 0 and 1.

All numbers in input are integers.

Input

Input is given from Standard Input in the following format.
The first line is as follows:

T

Then, T test cases follow.
Each test case is given in the following format:

N
A_1 A_2 \cdots A_N
S

Output

For each test case, print a line containing 0 if x becomes 0 at the end of the game, and 1 otherwise.

Sample Input 1

3
2
1 2
10
2
1 1
10
6
2 3 4 5 6 7
111000

Sample Output 1

1
0
0

In the first test case, if Person 1 replaces x with 0 \oplus 1=1, we surely have x \neq 0 at the end of the game, regardless of the choice of Person 0.

In the second test case, regardless of the choice of Person 1, Person 0 can make x=0 with a suitable choice.

Solution in Rust (1.42.0) (judge verdict: Time Limit Exceeded)

#![allow(unused_imports)]
#![allow(non_snake_case)]
use std::cmp::*;
use std::collections::*;
use std::io::Write;

#[allow(unused_macros)]
macro_rules! debug {
    ($($e:expr),*) => {
        #[cfg(debug_assertions)]
        $({
            let (e, mut err) = (stringify!($e), std::io::stderr());
            writeln!(err, "{} = {:?}", e, $e).unwrap()
        })*
    };
}

fn main() {
    let t = read::<usize>();
    for _ in 0..t {
        if solve() {
            println!("0");
        } else {
            println!("1");
        }
    }
}

fn solve() -> bool {
    let n = read::<usize>();
    let a = read_vec::<i64>();
    let s = read::<String>().chars().collect::<Vec<_>>();
    let zero_poses = (0..n).filter(|&x| s[x] == '0').collect::<Vec<_>>();
    let one_poses = (0..n).filter(|&x| s[x] == '1').collect::<Vec<_>>();

    let mut dp = vec![HashSet::new(); n];
    dp[zero_poses[zero_poses.len() - 1]].insert(0);
    dp[zero_poses[zero_poses.len() - 1]].insert(a[zero_poses[zero_poses.len() - 1]]);
    for i in (0..zero_poses.len() - 1).rev() {
        let mut next = dp[zero_poses[i + 1]].clone();
        for &elem in &dp[zero_poses[i + 1]] {
            next.insert(elem ^ a[zero_poses[i]]);
        }
        dp[zero_poses[i]] = next;
    }

    let mut cur = vec![0];
    for one_pos in one_poses {
        let next_zero_idx = zero_poses.lower_bound(&one_pos);
        if next_zero_idx == zero_poses.len() {
            return false;
        }
        let next_zero = zero_poses[next_zero_idx];

        let mut next = vec![];
        for &elem in &cur {
            next.push(elem ^ a[one_pos]);
            if !dp[next_zero].contains(&(elem ^ a[one_pos])) {
                // debug!(next_zero);
                // debug!(dp[next_zero]);
                return false;
            }
        }
        for &elem in &cur {
            next.push(elem);
        }
        next.sort();
        next.dedup();
        cur = next;
    }
    true // zero wins
}

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>()
        .split_whitespace()
        .map(|e| e.parse().ok().unwrap())
        .collect()
}

use std::cmp::Ordering;

pub trait BinarySearch<T> {
    fn lower_bound(&self, x: &T) -> usize;
    fn upper_bound(&self, x: &T) -> usize;
}

impl<T: Ord> BinarySearch<T> for [T] {
    fn lower_bound(&self, x: &T) -> usize {
        let mut low = 0;
        let mut high = self.len();

        while low != high {
            let mid = (low + high) / 2;
            match self[mid].cmp(x) {
                Ordering::Less => {
                    low = mid + 1;
                }
                Ordering::Equal | Ordering::Greater => {
                    high = mid;
                }
            }
        }
        low
    }

    fn upper_bound(&self, x: &T) -> usize {
        let mut low = 0;
        let mut high = self.len();

        while low != high {
            let mid = (low + high) / 2;
            match self[mid].cmp(x) {
                Ordering::Less | Ordering::Equal => {
                    low = mid + 1;
                }
                Ordering::Greater => {
                    high = mid;
                }
            }
        }
        low
    }
}