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: Accepted)

// おこりうる遷移を全部見る
fn dfs(s: &Vec<char>, a: &Vec<usize>, n: usize, x: usize, res: &mut Vec<(usize, String)>) {
    if s.len() == n {
        println!("{}: {:?}", n, res);
        return;
    }
    if s[n] == '0' {
        res[n] = (0, format!("{:b}", x));
        dfs(s, a, n + 1, x, res);
        res[n] = (0, format!("{:b}", x ^ a[n]));
        dfs(s, a, n + 1, x ^ a[n], res);
    } else {
        res[n] = (1, format!("{:b}", x));
        dfs(s, a, n + 1, x, res);
        res[n] = (1, format!("{:b}", x ^ a[n]));
        dfs(s, a, n + 1, x ^ a[n], res);
    }
}

fn main() {
    let t: usize = read();
    'outer: for _ in 0..t {
        let n = read();
        let a: Vec<usize> = (0..n).map(|_| read::<usize>()).collect();
        let s: Vec<char> = read::<String>().chars().collect();
        let mut bases = vec![];
        for i in (0..n).rev() {
            let mut cur = a[i];
            for &b in &bases {
                if cur ^ b < cur {
                    cur ^= b;
                }
            }
            if cur != 0 {
                if s[i] == '1' {
                    println!("{}", 1);
                    continue 'outer;
                } else {
                    bases.push(cur);
                }
            }
        }
        println!("{}", 0);
    }
}

// =========
#[allow(unused_imports)]
use std::cmp::{max, min};
#[allow(unused_imports)]
use std::collections::{HashMap, HashSet};
#[allow(unused_imports)]
use std::process::exit;

#[allow(dead_code)]
const MOD: usize = 1000000007;

fn read<T: std::str::FromStr>() -> T {
    use std::io::Read;
    let stdin = std::io::stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

// =========