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>

using namespace std;

long long a[201];
char s[202];
int main(){
	int t;
	scanf("%d",&t);
	for(int tt=1;tt<=t;tt++){
		int n;
		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(a[i]==0)continue;
			int u=60;
			while(!(a[i]>>u&1))u--;
			for(int j=i-1;j;j--)
				if(a[j]>>u&1)a[j]^=a[i];
		}
		int ans=0;
		for(int i=1;i<=n;i++)
			if(s[i]=='1'&&a[i])
				ans=1;
		printf("%d\n",ans);
	}
}