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::io::stdin;

struct Tree {
    state: usize,
    player: Vec<usize>,
    moves: Vec<usize>,
    len: usize,
}

impl Tree {
    fn new(player: Vec<usize>, moves: Vec<usize>) -> Tree {
        let len = player.len();
        Tree {
            state: 0,
            player,
            moves,
            len,
        }
    }

    fn and_or_search(&mut self, t: usize) -> usize {
        if t == self.len {
            return if self.state > 0 { 1 } else { 0 };
        }

        let now = self.player[t];
        let mut winner = self.and_or_search(t + 1);
        if now != winner {
            self.state ^= self.moves[t];
            winner = self.and_or_search(t + 1);
            self.state ^= self.moves[t];
        }

        winner
    }
}

fn main() {
    let mut is = String::new();
    stdin().read_line(&mut is).ok();
    let t: usize = is.trim().parse().unwrap();
    for _ in 0..t {
        is.clear();
        stdin().read_line(&mut is).ok();
        let n = is.trim().parse::<usize>().unwrap();
        is.clear();
        stdin().read_line(&mut is).ok();
        let moves = is
            .split_whitespace()
            .map(|e| e.parse::<usize>().unwrap())
            .collect::<Vec<_>>();
        is.clear();
        stdin().read_line(&mut is).ok();
        is.pop();
        let player = is
            .chars()
            .map(|e| e.to_digit(2).unwrap() as usize)
            .collect::<Vec<_>>();
        let mut ans: usize = 0;
        let mut tree = Tree::new(player, moves);
        println!("{}", tree.and_or_search(0));
    }
}