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:
#!/usr/bin/env python3
import sys
input = sys.stdin.readline

t = int(input())
for _ in range(t):
    n = int(input())
    a = [int(item) for item in input().split()]
    s = input().rstrip()
    if s[-1] == "1":
        print(1)
        continue
    group = []
    prev = "-1"
    for ch, num in zip(s, a):
        if prev != ch:
            group.append([])
        group[-1].append(num)
        prev = ch
    group.reverse()
    tools = []
    ok = True
    for itr, g in enumerate(group):
        if itr % 2 == 0:
            for item in g:
                tools.append(item)
        else:
            tl = tools[:]
            index = 0
            for i in range(64, -1, -1):
                flag = 0
                for j in range(index, len(tl)):
                    if tl[j] & (1 << i):
                        flag = 1
                        tl[index], tl[j] = tl[j], tl[index]
                        break
                for j in range(index + 1, len(tl)):
                    if tl[j] & 1 << i:
                        tl[j] ^= tl[index]
                if flag == 1:
                    index += 1
            for item in g:
                current = 0
                for val in tl:
                    index = len(bin(val)) - 3
                    if item >> index != current >> index:
                        current ^= val
                if current != item:
                    ok = False
    if ok:
        print(0)
    else:
        print(1)