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=205,p=998244353;
int read(){
	int f=1,g=0;
	char ch=getchar();
	for (;!isdigit(ch);ch=getchar()) if (ch=='-') f=-1;
	for (;isdigit(ch);ch=getchar()) g=g*10+ch-'0';
	return f*g;
}
int T,n;
ll a[N];
char s[N];
struct asd{
	ll f[61];
	void clear(){memset(f,0,sizeof(f));}
	void add(ll x){
		for (int i=60;i>=0;i--)
		if (x&(1ll<<i)){
			if (!f[i]) {f[i]=x;return;}
			else x^=f[i];
		}
	}
	bool find(ll x){
		for (int i=60;i>=0;i--)
		if ((x^f[i])<x) x^=f[i];
		return (x==0);
	}
}f;
int main(){
//	freopen("a.in","r",stdin);
//	freopen("a.out","w",stdout);
	T=read();
	while (T--){
		n=read();int fl=0;
		f.clear();
		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'){
			f.add(a[i]);
		}
		else{
			if (!f.find(a[i])){fl=1;break;}
		}
		printf("%d\n",fl);
	}
	return 0;
}