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 C++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <iostream>
using namespace std;
#include<string>
#define ll long long

#define fr(i,a,b) for(ll i=a;i<b;i++)
#define ffr(i,a,b) for(ll i=a;i>=b;i--)
#include<bits/stdc++.h>
#include<vector>
#define vl vector<ll>
//const ll N=1e5+5;




int solve(){
    ll n,x=0;
    string s;
    cin>>n;
    ll a[n];
    fr(i,0,n) cin>>a[i];
    cin>>s;
    fr(i,0,n){
        if(s[i]=='0'){
            if(x==0)
            continue;
            else
            x^=a[i];
        }
        else{
            if((x^a[i])!=0)
            x^=a[i];
            else
            continue;
        }
    }
    if(x!=0)
    cout<<1;
    else
    cout<<0;
    return 0;
}


int main(){
    ll t;
    cin>>t;
    while(t--){
        solve();
        cout<<'\n';
    }
	return 0;
}