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;
typedef long long LL;
const int N=200;
const int L=62;
const LL X=1LL<<L;
LL a[N];
char s[N];
LL x[L];
bool ins(LL v){
	for(int i=L-1;i>=0;i--){
		if((v>>i)&1){
			if(x[i]){
				v^=x[i];
			}
			else{
				x[i]=v;
				return true;
			}
		}
	}
	return false;
}
bool work(){
	memset(x,0,sizeof(x));
	int n;
	cin>>n;
	for(int i=0;i<n;i++){
		cin>>a[i];
	}
	cin>>s;
	for(int i=n-1;i>=0;i--){
		if(ins(a[i])&&s[i]=='1'){
			return true;
		}
	}
	return false;
}

int main(){
	ios::sync_with_stdio(false);
	int t;
	cin>>t;
	while(t--){
		puts(work()?"1":"0");
	}
	return 0;
}