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)

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

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

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

        let mut vs = vec![];
        let mut ans = 0;

        for i in (0..n).rev() {
            if s[i] == '0' {
                vs.push(a[i]);
            } else {
                if !check(a[i], &vs) {
                    ans = 1;
                    break;
                }
            }
        }

        echo!(ans);
    }
}

fn check(b: u64, vs: &[u64]) -> bool {
    let n = 64;
    let m = vs.len();
    let mut a = vec![vec![0; m + 1]; n];

    for i in 0..n {
        for j in 0..m {
            a[i][j] = (vs[j] >> i) & 1;
        }
        a[i][m] = (b >> i) & 1;
    }

    for i in 0..min(n, m) {
        'outer: for i2 in i..n {
            for j2 in i..m {
                if a[i2][j2] == 1 {
                    for k in 0..n {
                        let t = a[k][i];
                        a[k][i] = a[k][j2];
                        a[k][j2] = t;
                    }
                    a.swap(i2, i);
                    break 'outer;
                }
            }
        }

        if a[i][i] == 0 {
            break;
        }

        for j in i + 1..n {
            if a[j][i] == 1 {
                for k in 0..m + 1 {
                    a[j][k] ^= a[i][k];
                }
            }
        }
    }

    for i in 0..n {
        if a[i][m] == 1 {
            if i >= m || a[i][i] == 0 {
                return false;
            }
        }
    }

    true
}
*/

fn main() {
    let exe = "/tmp/bin3CCFBEF9";
    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>";