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 <iostream>
#include <string>
#include <vector>

using namespace std;

#define REP(i,n) for(ll (i) = (0);(i) < (n);++i)
#define REV(i,n) for(ll (i) = (n) - 1;(i) >= 0;--i)
#define PB push_back

typedef long long ll;

void solve() {
	ll n;cin >> n;
	vector<ll> v(n);REP(i, n)cin >> v[i];
	string str;cin >> str;

	vector<ll> mp;
	REV(i, n){
		REP(j, mp.size())v[i] = min(v[i], v[i] ^ mp[j]);
		if(v[i] == 0)continue;
		if(str[i] == '1'){
			cout << 1 << endl;
			return;
		}
		mp.PB(v[i]);
	}
	cout << 0 << endl;
}

int main(){
	cin.tie(0);cout.tie(0);ios::sync_with_stdio(false);

	ll t;cin >> t;
	REP(i, t)solve();

	return 0;
}