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<cstdio>
typedef long long ll;
const int N=203,K=60;
int n,k;ll a[N],f[K];char s[N];
inline void Insert(ll a){
	for(int j=K-1;~j;j--)if(a>>j&1)
	  if(f[j])a^=f[j];
	  else{f[j]=a;return;}
}
inline bool Find(ll a){
	for(int j=K-1;~j;j--)if(a>>j&1)
	  if(f[j])a^=f[j];
	  else return 0;
	return 1;
}
int main(){
	int T;scanf("%d",&T);for(;T--;){
	k=0;
	for(int i=0;i<K;i++)f[i]=0;
	scanf("%d",&n);
	for(int i=1;i<=n;i++)
	  scanf("%lld",a+i);
	scanf("%s",s+1);
	for(int i=n;i;i--){
	  if(s[i]=='0')Insert(a[i]);
	  if(s[i]=='1'&&!Find(a[i])){puts("1");goto Brk;}
	}
	puts("0");
	Brk:;
	}return 0;
}