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 = 1010, M = 64;
ll a[N];int n;char s[N];ll b[N];
 
ll insert(ll x){
	for(int i=60;~i;i--)if(1&(x>>i)){
		if(!b[i]){b[i]=x;break;}
		else x^=b[i];
	}
	return x;
}
 
void Main()
{
	for(int i=0;i<M;i++)b[i]=0;
	cin >> n;for(int i=1;i<=n;i++)scanf("%lld",&a[i]);
	scanf("%s",s+1);
	bool Ans=0;
	for(int i=n;i;i--){
		if(s[i]=='0'){
			insert(a[i]);
		}else{
			ll d=insert(a[i]);
			// cerr << d << "??" << endl;
			Ans|=d!=0;
		}
	}
	printf("%d\n",(int)Ans);
}

int main(){int T;cin >>  T;while(T--)Main();}