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 PHP (7.4.4) (judge verdict: Time Limit Exceeded)

<?php
$t  = trim(fgets(STDIN));
$ret = [];
for ($i = 0; $i < $t; $i++) {
	$n     = trim(fgets(STDIN));
	$array = explode(' ', trim(fgets(STDIN)));
	$s     = trim(fgets(STDIN));

	$p0 = [];
	$p1 = [];

    for ($j = 0; $j < $n; $j++) {
		$a = $array[$j];

		$p = substr($s, $j, 1);
		if ($p == '0'){
			$p0[] = $a;
		} else {
			$p1[] = $a;
		}
	}
	
	$patterns = userOne($p1);
	$diff  = userZero($patterns, $p0);
	$ret[] = (0 < count($diff) ? 1 : 0);
}

for ($i = 0; $i < count($ret); $i++) {

	echo "{$ret[$i]}\n";
}

function userOne(array $p1): array
{
	$patterns = [0];
	for($i = 0; $i < count($p1); $i++){
		$a = $p1[$i];
		if(in_array($a, $patterns)){
			continue;
		}

		$newPattern = [];
		for($j = 0; $j < count($patterns); $j++){
			$x = $patterns[$j];
			$x = $x ^ $a;
			if(in_array($x, $patterns)){
				continue;
			}
			$newPattern[] = $x;
		}
		$patterns = array_merge($patterns, $newPattern);
	}

	return $patterns;
}

function userZero(array $patterns1, array $p0): array
{
	$patterns = userOne($p0);

	$diff = array_diff($patterns1, $patterns);

	return $diff;
}