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:
mod = 1000000007
eps = 10**-9


def main():
    import sys
    input = sys.stdin.readline

    for t in range(int(input())):
        N = int(input())
        A = list(map(int, input().split()))
        S = input().rstrip('\n')
        A.reverse()
        S = S[::-1]

        A0 = [0] * 60
        A1 = [0] * 60
        zero = 0
        one = 0
        for i, a in enumerate(A):
            if S[i] == "0":
                for j in range(60):
                    A0[j] ^= ((a >> j & 1) << zero)
                zero += 1
            else:
                for j in range(60):
                    A1[j] ^= ((a >> j & 1) << one)
                one += 1

        B = [0] * 60
        for i in range(60):
            B[i] = A0[i] + (A1[i] << zero)

        rnk = 0
        for i in range(zero):
            #print(B)
            for j in range(rnk, 60):
                if B[j] >> i & 1:
                    B[j], B[rnk] = B[rnk], B[j]
                    b = B[rnk]
                    #print(b)
                    for jj in range(60):
                        if jj == rnk:
                            continue
                        if B[jj] >> i & 1:
                            B[jj] ^= b
                    rnk += 1
                    break

        cnt0 = 0
        cnt1 = zero
        r = -1
        win = 0
        for s in S:
            if s == "0":
                if r+1 >= len(B):
                    break
                if B[r+1] >> cnt0 & 1:
                    r += 1
                cnt0 += 1
            else:
                rr = -1
                for j in range(60):
                    if B[j] >> cnt1 & 1:
                        rr = j
                if rr > r:
                    win = 1
                    break
                cnt1 += 1
        print(win)


if __name__ == '__main__':
    main()