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 Python (3.8.2) (judge verdict: Time Limit Exceeded)

# coding: utf-8
# Your code here!

t = int(input())

for i in range(t):
    n = int(input())
    a = []
    a = list(map(int,input().split()))
    s = input()
    sl = len(s)
    
    if s[sl-1] == '1':
#        print("saisyo")
        print(1)
    else:
        
        for i in range(1,2**sl):  # 空集合を除く場合はrange(1, 2**len(list1))
            list2 = []
            x = 0
            # 処理対象の数字を2進数に変換し、各桁のbitが１かどうかを判断する
            for j in range(sl):
#                print(s[j:sl])
    	        # 演算結果が1なら処理を行う
                if x == 0 and int(s[j:sl]) == 0:
#                    print(j,s[j:sl])
                    break
                elif (i >> j) &1 == 1 or (s[j] == '1'):
                    if (s[j] == '1') or(s[j] == '0' and x != 0):
                        x = x^a[j]
#                            print(str(i) + ':' + str(x))
                
            if x == 0:
                print(0)
                break
        else:
            print(1)