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)

use proconio::marker::Chars;
use proconio::{fastout, input};

fn solve() {
    input! { in_n: usize, in_a: [i128; in_n], in_s: Chars};
    let mut nums = Vec::new();

    for i in (0..in_s.len()).rev() {
        if in_s[i] == '0' {
            let mut a = in_a[i];
            let mut j = 0;

            while a != 0 {
                if j == nums.len() {
                    nums.push(a);
                    a = 0;
                } else {
                    if a > nums[j] {
                        std::mem::swap(&mut a, &mut nums[j]);
                    }

                    let b = nums[j] ^ a;

                    if b < a {
                        a = b;
                    }

                    j += 1;
                }
            }
        } else {
            let mut a = in_a[i];

            for n in &nums {
                let b = a ^ *n;

                if b < a {
                    a = b;
                }
            }

            if a != 0 {
                println!("1");
                return;
            }
        }
    }

    println!("0");
}

#[fastout]
fn main() {
    input! {in_t: usize};

    for _ in 0..in_t {
        solve();
    }
}