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:
def msb(x):
    cnt = 0
    while x:
        x >>= 1
        cnt += 1
    return cnt


def solve(n, a, s):
    # dp[i] = (i回目時点で最終的に0にできる数の集合)
    dp = [[] for _ in range(n + 1)]
    # dp[n] = [0]
    for i in reversed(range(n)):
        if s[i] == '0':
            x = a[i]
            dp[i] = dp[i + 1].copy()
            dp[i].sort(reverse=True)
            for j in range(len(dp[i])):
                x = min(x, x ^ dp[i][j])
            if x != 0:
                dp[i].append(x)
        else:
            x = a[i]
            dp[i + 1].sort(reverse=True)
            for j in range(len(dp[i + 1])):
                x = min(x, x ^ dp[i + 1][j])
            if x == 0:
                dp[i] = dp[i + 1].copy()
            else:
                return '1'
        # print(i, a[i], s[i], dp[i])
    # print(n, a, s)
    # print(*dp, sep='\n')
    if len(dp[0]) != 0:
        return '0'
    else:
        return '1'


t = int(input())
for _ in range(t):
    n = int(input())
    a = list(map(int, input().split()))
    s = input()
    ans = solve(n, a, s)
    print(ans)