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>
#define re register
#define int long long
using namespace std;
inline int read(){
	re int t=0;re char v=getchar();
	while(v<'0')v=getchar();
	while(v>='0')t=(t<<3)+(t<<1)+v-48,v=getchar();
	return t;
}
int t,n,a[202],p[65];
char s[202];
inline void insert(re int x){
	for(re int i=62;~i;--i){
		if(x&(1ll<<i)){
			if(!p[i]){
				p[i]=x;
				return;
			}
			else x^=p[i];
		}
	}
}
inline int ask(re int x){
	for(re int i=62;~i;--i){
		if(x&(1ll<<i))x^=p[i];
	}
	return x;
}
signed main(){
	t=read();
	while(t--){
		n=read();
		memset(p,0,sizeof(p));
		re int ans=0;
		for(re int i=1;i<=n;++i)a[i]=read();
		scanf("%s",s+1);
		for(re int i=n;i;--i){
			if(s[i]=='0')insert(a[i]);
			else{
				if(ask(a[i])){
					ans=1;break;
				}
			}
		}
		printf("%lld\n",ans);
	}
}