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 JavaScript (Node.js 12.16.1) (judge verdict: Wrong Answer)

function Main(input) {
  let t = input.split("\n")[0], n , a = new Array(n), s = new Array(n), x = 0;
  
  for (let i = 0; i < t; i++) {
    n = input.split("\n")[i*3+1];
    a = input.split("\n")[i*3+2].split(" ");
    s = input.split("\n")[i*3+3].split("");

    let tmp;

    for (let j = 0; j < n; j++) {
      tmp = x ^ a[j];
      
      if (s[j] == 0) {
        if (tmp == 0) x = tmp;
      } else {
        if (tmp != 0) x = tmp;
      }
    }
    
    if (x == 0) {
      console.log(0)
    } else console.log(1);
    
    x = 0;
  }
}

Main(require("fs").readFileSync("/dev/stdin", "utf8"));