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 C (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <stdio.h>

void test() {
   int i,n,x;
   long long a[200],mx,k;
   char s[201];

   scanf("%d",&n);
   for (i=0;i<n;i++) {
      scanf("%lld",&a[i]);
      if (mx<a[i]) mx=a[i];
   }
   scanf("%s",s);
   k=1;
   while (k<=mx) {
      x=0;
      for (i=0;i<n;i++)
         if (s[i]=='0') {
            if (x==1 && (a[i]/k)%2==1) x=0;
         } else {
            if (x==0 && (a[i]/k)%2==1) x=1;
         }
      if (x==1) {
         puts("1");
         return;
      }
      k*=2;
   }
   puts("0");
}

int main(){
   int i,t;

   scanf("%d",&t);
   for (i=0;i<t;i++) test();
   return 0;
}