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<cstdio>
#include<cstring>
#include<algorithm>
#include<vector>
#include<string>

using namespace std;

#define ll long long

const int N = 5e3;

void solve(){
	ll n,a[N];
	string s;	
	cin >> n; 
	for(int i = 0; i < n; i++) cin >> a[i];
	cin >> s;
	vector<ll> p;
	for(int i = n-1; i >= 0; i--){
		int len = p.size();
		for(int j = 0; j < len; j++){
			//cout << *j; 
			a[i] = min(a[i],a[i]^p[j]);
		}
		if(a[i]){
			if(s[i] == '1'){
			cout << 1 << endl;
			return;
		}
		p.push_back(a[i]);
	}
}	
	cout << 0 << endl;
}

int main(){
	int t;
	cin >> t;
	while(t--) solve();
}