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 CPP):

Solution:
#include <bits/stdc++.h>

#define pb push_back
#define F first
#define S second
#define all(x) x.begin(), x.end()
#define debug(x) cerr << #x << " : " << x << '\n'

using namespace std;

typedef long long ll;
typedef long double ld;
typedef string str;
typedef pair<ll, ll> pll;

const ll Mod = 1000000007LL;
const int N = 2e5 + 10;
const ll Inf = 2242545357980376863LL;
const ll Log = 30;

ll a[N];
vector<ll> V;
bool Add(ll x){
	for(auto y : V) x = min(x, x ^ y);
	if(x){
		V.pb(x);
		sort(all(V));
		reverse(all(V));
	}
	return (x > 0);
}
void Main(){
	int n;
	V.clear();
	cin >> n;
	for(int i = 0; i < n; i++){
		cin >> a[i];
	}
	str s;
	cin >> s;
	for(int i = n - 1; i >= 0; i--){
		if(s[i] == '0') Add(a[i]);
		else {
			if(Add(a[i])){
				cout << "1\n";
				return ;
			}
		}
	}
	cout << "0\n";
}

int main(){
	ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
	int tc;
	cin >> tc;
	while(tc --) Main();
	return 0;
}