Problem: 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.

Example

Input

3
2
1 2
10
2
1 1
10
6
2 3 4 5 6 7
111000


Output

1
0
0

Solution (in PYTHON3):

Solution:
import sys,queue,math,copy,itertools,bisect,collections,heapq
import random
def main():
    sys.setrecursionlimit(10**7)
    INF = float('inf')
    MOD = 10**9 + 7
    LI = lambda : [int(x) for x in sys.stdin.readline().split()]
    _LI = lambda : [int(x)-1 for x in sys.stdin.readline().split()]
    NI = lambda : int(sys.stdin.readline())
    SI = lambda : sys.stdin.readline().rstrip()
    DD = ((1,0),(0,1),(-1,0),(0,-1))

    T = NI()
    for _ in range(T):
        N = NI()
        A = LI()
        S = SI()

        base = [0] * 60
        for i in range(N-1,-1,-1):
            x = A[i]
            if S[i] == '0':
                for j in range(60):
                    if base[j] > 0 and x & (1 << j):
                        x ^= base[j]

                for j in range(60):
                    if base[j] == 0 and x & (1<<j):
                        for k in range(60):
                            if base[k] & (1<<j):
                                base[k] ^= x
                        base[j] = x
                        break
            else:
                for j in range(60):
                    if base[j] > 0 and x & (1<<j):
                        x ^= base[j]
                if x > 0:
                    print(1)
                    break
        else:
            print(0)

if __name__ == '__main__':
    main()