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(clippy::many_single_char_names)]

// language: Rust(1.42.0)
// check available crates on AtCoder at "https://atcoder.jp/contests/language-test-202001"
// My Library Repo' is at "https://github.com/Loptall/prcn_lib"

/*
    6月で水色になるぞ〜!!!
*/

// from std...
use std::cmp::{
    max, min,
    Ordering::{Equal, Greater, Less},
};
use std::collections::{BTreeMap, BTreeSet, BinaryHeap, HashMap, HashSet, VecDeque};
use std::mem::swap;
use std::ops::*;
use std::process::exit;
use std::{f32, f64, i128, i16, i32, i64, i8, isize, u128, u16, u32, u64, u8, usize};

// Dep' crates are...
use itertools::*;
use itertools_num::*;
use lazy_static::lazy_static;
use maplit::{btreemap, btreeset, hashmap, hashset};
use num_bigint::{BigInt, BigUint};
use num_complex::Complex;
use num_integer::{binomial, gcd, lcm, Integer};
use num_rational::Rational;
use num_traits::{One, Zero};
use permutohedron::Heap;
use petgraph::unionfind::UnionFind;
use proconio::{fastout, input, is_stdin_empty, marker::*};
use rand::random;

pub const MOD: usize = 1000000007;
pub const MAX: usize = 1usize << 63usize;
pub const MIN: i64 = i64::MIN;
pub const PI: f64 = f64::consts::PI;
pub const A: u8 = 'A' as u8;

// code...
// #[fastout]
fn main() {
    input! {
        t: usize
    }

    for _testcase in 0..t {
        // println!("testcase: {}", testcase);
        solve();
    }
}

fn solve() {
    input! {
        n: usize,
        a: [usize; n],
        s: Chars
    }

    if s[n - 1] == '1' {
        println!("1");
        return;
    }

    let mut z = vec![0usize];
    let mut o = vec![0usize];

    for (i, p) in s.iter().enumerate() {
        match p {
            '0' => {
                let mut add = Vec::new();
                for e in z.iter() {
                    add.push(*e ^ a[i]);
                }
                z.extend(add.iter());
            }
            '1' => {
                let mut add = Vec::new();
                for e in o.iter() {
                    add.push(*e ^ a[i]);
                }
                o.extend(add.iter());
            }
            _ => unreachable!(),
        }
    }

    if o.iter().all(|x| z.contains(x)) {
        println!("0");
    } else {
        println!("1");
    }
}