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>
#include <algorithm>
#include <cstring>
using namespace std;
typedef long long ll;
const int maxn=205;
ll a[maxn],p[maxn];
char s[maxn];
int n,m;

void solve(){
	int T;
	scanf("%d",&T);
	while(T--){
		scanf("%d",&n);
		for(int i=1;i<=n;i++)	scanf("%lld",&a[i]);
		scanf("%s",s+1);
		if(s[n]=='1')	printf("1\n");
		else{
			int flag=0;
			memset(p,0,sizeof(p));
			for(int i=n;i>=1;i--){
				if(s[i]=='0'){
					ll tmp=a[i];
					for(int j=62;j>=0;j--){
						if((1ll<<j)&tmp){
							if(!p[j]){
								p[j]=tmp;break;
							}
							tmp^=p[j];
						}
					}
				}
				else if(s[i]=='1'){
					ll tmp=a[i];
					for(int j=62;j>=0;j--){
						if((1ll<<j)&tmp){
							if(!p[j])	break;
							tmp^=p[j];
						}
					}
					if(tmp){
						flag=1;break;
					}
				}
			}
			printf("%d\n",flag);
		}
	}
}
int main(){
	solve();
	return 0;
}