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 Ruby (2.7.1) (judge verdict: Accepted)

t = gets.to_i

t.times do
    n = gets.to_i
    a = gets.split.map(&:to_i)
    s = gets.chars

    dp = [0]
    (n-1).downto(0) do |i|
        if s[i] == ?0
            dp.each {|e| (x = a[i] ^ e) < a[i] and a[i] = x}

            if a[i] != 0
                dp.map!{|e| (x = e ^ a[i]) < e ? x : e}
                dp << a[i]
            end
        else
            a[i] = dp.inject(a[i]) {|r,v| (x = r ^ v) < r ? x : r}
            next if a[i] == 0
            p 1
            break
        end
    end and p 0
end