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)

// This code is generated by [cargo-atcoder](https://github.com/tanakh/cargo-atcoder)
// Original source code:
/*
use competitive::prelude::*;
use rand::*;

fn main() {
    input! {
        t: usize,
    }

    for _ in 0..t {
        input! {
            n: usize,
            a: [u64; n],
            s: Chars,
        }

        let mut zero = true;

        for i in 0..8 {
            solve_reset();
            let a = a.iter().map(|&a| (a >> (i * 8)) & 0xff).collect_vec();
            zero &= solve(0, 0, &a, &s);
        }

        for _ in 0..32 {
            solve_reset();

            let mut bs = vec![];

            for _ in 0..8 {
                bs.push(rand::thread_rng().gen_range(0, 64));
            }

            let a = a
                .iter()
                .map(|&a| {
                    let mut t = 0;
                    for j in 0..8 {
                        t |= ((a >> bs[j]) & 1) << j;
                    }
                    t
                })
                .collect_vec();
            zero &= solve(0, 0, &a, &s);
        }

        if zero {
            echo!(0);
        } else {
            echo!(1);
        }
    }
}

#[memoise(cur, x)]
fn solve(cur: usize, x: u64, a: &[u64], s: &[char]) -> bool {
    if cur == a.len() {
        return x == 0;
    }

    let y = a[cur];

    if s[cur] == '0' {
        solve(cur + 1, x ^ y, a, s) || solve(cur + 1, x, a, s)
    } else {
        solve(cur + 1, x ^ y, a, s) && solve(cur + 1, x, a, s)
    }
}
*/

fn main() {
    let exe = "/tmp/binE3D1D698";
    std::io::Write::write_all(&mut std::fs::File::create(exe).unwrap(), &decode(BIN)).unwrap();
    std::fs::set_permissions(exe, std::os::unix::fs::PermissionsExt::from_mode(0o755)).unwrap();
    std::process::exit(std::process::Command::new(exe).status().unwrap().code().unwrap())
}

fn decode(v: &str) -> Vec<u8> {
    let mut ret = vec![];
    let mut buf = 0;
    let mut tbl = vec![64; 256];
    for i in 0..64 { tbl[TBL[i] as usize] = i as u8; }
    for (i, c) in v.bytes().filter_map(|c| { let c = tbl[c as usize]; if c < 64 { Some(c) } else { None } }).enumerate() {
        match i % 4 {
            0 => buf = c << 2,
            1 => { ret.push(buf | c >> 4); buf = c << 4; }
            2 => { ret.push(buf | c >> 2); buf = c << 6; }
            3 => ret.push(buf | c),
            _ => unreachable!(),
        }
    }
    ret
}

const TBL: &'static [u8] = b"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
const BIN: &'static str = "<base64-encoded ELF executable removed>";