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 PyPy3 (7.3.0) (judge verdict: Wrong Answer)

t = int(input())
cmpx = []
for h in range(t):
    n = int(input())
    a = list(map(int,input().split()))
    s = input()
    x = []
    y = []
    m = len(str(bin(max(a))))
    for j in range(n):
        if(s[j] == '0'):
            x.append(a[j])
        else:
            y.append(a[j])
    t1 = [0]*m
    l1 = [0]*m
    for i in range(len(x)):
        a1 = str(bin(x[i])[2:])
        for j in range(1,len(a1)+1):
            if(a1[-j] == '1'):
                t1[j-1] ^= x[i]
                if(t1[j-1]&t1[j-1]-1 == 0):
                    l1[len(bin(t1[j-1]))-3] = 1
    q1 = 0
    z1 = []
    for i in range(len(l1)):
        if(l1[i] == 0):
            q1 += 2**i
    for i in range(len(t1)):
        c = t1[i]&q1
        if(c&c-1):
            z1.append(c)
            
    t2 = [0]*m
    l2 = [0]*m
    for i in range(len(y)):
        a2 = str(bin(y[i])[2:])
        for j in range(1,len(a2)+1):
            if(a2[-j] == '1'):
                t2[j-1] ^= y[i]
                if(t2[j-1]&t2[j-1]-1 == 0):
                    l2[len(bin(t2[j-1]))-3] = 1
    q2 = 0
    z2 = []
    for i in range(len(l2)):
        if(l2[i] == 0):
            q2 += 2**i
    for i in range(len(t2)):
        c = t2[i]&q2
        if(c&c-1):
            z2.append(c)
    cmp = 0
    if(q1 <= q2):
        for j in range(m):
            if(l1[j] > l2[j]):
                cmp = 1
                break
    else:
        cmp = 1
    print(cmp)