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: Wrong Answer)

#[allow(unused_imports)]
use itertools::Itertools;
use proconio::input;
#[allow(unused_imports)]
use proconio::marker::*;

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

    for _ in 0..t {
        input! {
            n: usize,
            a: [i64; n],
            s: Chars,
        }
        let mut c0 = [0; 64];
        let mut c1 = [0; 64];
        for i in 0..n {
            for j in 0..64 {
                if a[i] >> j & 1 == 1 {
                    if s[i] == '0' {
                        c0[j] += 1;
                    } else {
                        c1[j] += 1;
                    }
                }
            }
        }

        if (0..64).any(|i| c1[i] != 0 && c0[i] == 0) {
            println!("1");
            continue;
        }
        if s.last() == Some(&'1') {
            println!("1");
            continue;
        }

        println!("0");
    }
    // println!("Yes");
    // println!("No");
    // println!("{}", );
}