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)

use std::collections::HashSet;
use std::error::Error;
use std::io;

pub fn main() {
    if let Err(_e) = run() {
        panic!("failed.");
    }
}

fn run() -> Result<(), Box<dyn Error>> {
    let mut input = String::new();
    io::stdin().read_line(&mut input)?;
    let t = input.trim().parse::<i32>()?;
    input.clear();

    for _i in 0..t {
        solve_each();
    }

    Ok(())
}

fn solve_each() -> Result<(), Box<dyn Error>> {
    let mut input = String::new();
    io::stdin().read_line(&mut input)?;
    let n = input.trim().parse::<usize>()?;
    input.clear();

    io::stdin().read_line(&mut input)?;
    let a_s: Vec<i64> = input
        .trim()
        .split_whitespace()
        .map(|s| s.parse::<i64>().unwrap())
        .collect();
    input.clear();

    io::stdin().read_line(&mut input)?;
    let s_s = input.trim().to_owned();
    input.clear();

    let mut s_s: Vec<char> = s_s.chars().collect();
    if *s_s.last().unwrap() == '1' {
        println!("1");
        return Ok(());
    }
    s_s.reverse();
    let mut one_variations: HashSet<i64> = HashSet::new();
    let mut zero_variations: HashSet<i64> = HashSet::new();
    for (index, &x) in s_s.iter().enumerate() {
        if x == '1' {
            let temp = one_variations.clone();
            for &one in &temp {
                let value = one ^ a_s[index];
                if !zero_variations.contains(&value) {
                    println!("1");
                    return Ok(());
                }
                one_variations.insert(value);
            }
            if !zero_variations.contains(&a_s[index]) {
                println!("1");
                return Ok(());
            }
            one_variations.insert(a_s[index]);
        } else {
            // x == '0'
            // one_variations.clear();
            for &zero in &zero_variations.clone() {
                zero_variations.insert(zero ^ a_s[index]);
            }
            zero_variations.insert(a_s[index]);
        }
    }
    println!("0");
    return Ok(());
}