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 "bits/stdc++.h"
#pragma GCC optimize "03"
using namespace std;
 
#define int long long int
#define ld long double
#define pi pair<int, int>
#define pb push_back
#define fi first
#define se second
#define IOS ios::sync_with_stdio(false); cin.tie(0); cout.tie(0)
#ifndef LOCAL
#define endl '\n'
#endif
 
const int N = 2e5 + 5;
const int mod = 1e9 + 7;
const int inf = 1e9 + 9;

int a[N];

signed main() {
	IOS;
	int t;	cin >> t;
	while(t--){
		int n;	cin >> n;
		for(int i = 0; i < n; i++)
			cin >> a[i];
		string s;	cin >> s;
		bool flag = 0;
		for(int b = 0; b < 64 && !flag; b++){
			int last = -1, p[2] = {0};
			for(int i = 0; i < n; i++){
				if((1LL<<b) & a[i]){
					p[s[i]-'0']++;
					last = s[i]-'0';
				}
			}
			if(last == -1)	continue;
			if(p[1] > p[0] || (p[1] == p[0] && last == 1))
				flag = 1;
		}
		cout << flag << endl;
	}	
	return 0;
}