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>
using namespace std;

long long t,n,v[205];
long long b[205];
string s;
bool fine;

bool check(long long num){
	
	for(int i=62;i>=0;i--){
		if(num&(1ll<<i))num^=b[i];
	}
	
	return num==0;
}

void add(long long num){
	for(int i=62;i>=0;i--){
		if(num&(1ll<<i)){
			if(b[i]==0){
				b[i]=num;
				break;
			}
			else{
				num^=b[i];
			}
		}
	}
}

int main(){

	ios::sync_with_stdio(false);
	cin.tie(0);

	cin>>t;
	
	while(t--){
		for(int i=0;i<205;i++)b[i]=0;
		fine=false;
		
		cin>>n;
		for(int i=0;i<n;i++)cin>>v[i];
		cin>>s;
		
		for(int i=n-1;i>=0;i--){
			if(s[i]=='0'){
				add(v[i]);
			}
			else{
				if(check(v[i])==false){
					cout<<"1\n";
					fine=true;
					break;
				}
			}
		}
		
		if(fine==false)cout<<"0\n";
	}

return 0;
}