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 Julia (1.4.0) (judge verdict: Runtime Error)

# Q.1
function A01(x,y)
    if count_zeros(y) > count_zeros(x)
        x = y
    elseif count_zeros(y) == count_zeros(x)
        xor(x,A[])
    end
    x
end

function A02(x,y)
    if count_zeros(y) > count_zeros(x)
        x = y
    elseif count_zeros(y) == count_zeros(x)
        x = y
    end
    x
end

function A11(x,y)
    if count_zeros(y) < count_zeros(x)
        x = y
    elseif count_zeros(y) == count_zeros(x)
        x = x
    end
    x
end

function A12(x,y)
    if count_zeros(y) < count_zeros(x)
        x = y
    elseif count_zeros(y) == count_zeros(x)
        x = y
    end
    x
end

function calc(A,S)
    let j=1
        x = Int128(0)
        while j<=length(S)
            jun = parse(Int128,S[j])
            #println(jun)
            y = xor(x,A[j])
            #println(count_zeros(y)," vs ",count_zeros(x))
            if jun==0
                if count_zeros(y) > count_zeros(x)
                    x = y
                elseif count_zeros(y) == count_zeros(x)
                    if count_zeros(xor(x,A[j+1])) < count_zeros(xor(y,A[j+1]))
                        x = y
                    end
                end
#                x1 = A01(x,y)
#                x2 = A02(x,y)
            else
                if count_zeros(y) < count_zeros(x)
                    x = y
                elseif count_zeros(y) == count_zeros(x)
                    if count_zeros(xor(x,A[j+1])) > count_zeros(xor(y,A[j+1]))
                        x = y
                    end
                end
#                x1 = A11(x,y)
#                x2 = A12(x,y)
            end

            #println("j = $j, turn: $jun, Aâ±¼ = $(A[j]), x = $x")
            j += 1
        end
        #println("xans = ",x)
        if x==0
            #println(0)
            ans=0
        else
            #println(1)
            ans=1
        end
        ans
    end
end

function calc2(A,S)
    let j=1
        x = Int128(0)
        while j<=length(S)
            jun = parse(Int128,S[j])
            #println(jun)
            y = xor(x,A[j])
            #println(count_zeros(y)," vs ",count_zeros(x))
            if jun==0
                if count_zeros(y) >= count_zeros(x)
                    x = y
                end
            else
                if count_zeros(y) <= count_zeros(x)
                    x = y
                end
            end
            #println("j = $j, turn: $jun, Aâ±¼ = $(A[j]), x = $x")
            j += 1
        end
        #println("xans = ",x)
        if x==0
            #println(0)
            ans=0
        else
            #println(1)
            ans=1
        end
        ans
    end
end

tmp=readline()
#println("Input: ",split(tmp))
T=parse(Int128,tmp)
let i=1
    while i<=T
        tmp=readline()
        N=parse(Int128,tmp)
        tmp=readline()
        A=parse.(Int128,split(tmp))
        tmp=readline()
        S=tmp
        #println("Input: $N, $A ,$S")
        #println(length(S))
        ans=calc(A,S)
        ans2=1#calc2(A,S)
        if ans==0 || ans2==0
            println(0)
        else
            println(1)
        end
        i += 1
    end
end