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.



Sample input:
3
2
1 2
10
2
1 1
10
6
2 3 4 5 6 7
111000


Sample output:
1
0
0

Submission status: Runtime Error

Solution code:
#!/usr/bin/env python3


def num2bin(n):
    return tuple(int(d) for d in "{:010b}".format(n))


def can_reach_zero(n, bs, s):
    bins = [num2bin(b) for b in bs]
    max_len = len(bins[0])
    score = [[0 for _ in range(max_len)] for _ in range(2)]
    for i, player in enumerate(s):
        for j, c in enumerate(bins[i]):
            if c == 1:
                score[player][j] += 1
    for s0, s1 in zip(score[0], score[1]):
        if s0 < s1:
            return False
    else:
        return True


def main():
    t = int(input())
    for _ in range(t):
        n = int(input())
        bs = [int(b) for b in input().split()]
        s = [int(d) for d in input()]
        if can_reach_zero(n, bs, s):
            print(0)
        else:
            print(1)


if __name__ == '__main__':
    main()

Submission status: Runtime Error

Solution code:
import sys
from collections import deque

sys.setrecursionlimit(10**6)
readline = sys.stdin.readline
#read = sys.stdin.buffer.read

def main():
    T = int(readline())
    for _ in range(T):
        N = int(readline())
        A = list(map(int, readline().split()))
        S = list(readline()[:-1])
        human1 = set(); human0 = set()
        for i, s in enumerate(S):
            if s == '1':
                human1.add(A[i])
            else:
                human0.add(A[i])
        nexts = deque(list(human1))
        flag = False
        used = set()
        for _ in range(pow(10, 6)):
            nxt = nexts.popleft()
            used.add(nxt)
            for h0 in human0:
                tmp = nxt^h0
                if tmp in human0:
                    human0.add(nxt)
                    break
                elif tmp in human1:
                    print(1)
                    flag = True
                    break
                elif tmp in used:
                    break
                else:
                    used.add(tmp)
                    nexts.append(tmp)
            if flag:
                break
            if len(nexts) == 0:
                print(0)
                break

if __name__ == "__main__":
    main()

Submission status: Runtime Error

Solution code:
t = int(input())

for i in range(t):
  n = int(input())
  a = []
  alpha = list(map(int, input().split()))
  a.append(alpha)
  x = 0
  for j in range(len(a)):
    x = x ^ a[j]
  if x == 0:

Submission status: Runtime Error

Solution code:
import