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;
const int maxn=2000;
int n,t;long long d;
long long a[maxn];
char str[maxn];
long long base[100];
int main()
{
	scanf("%d",&t);
	while(t--)
	{
		scanf("%d",&n);
		bool f=1;d=0;
		memset(base,0,sizeof(base));
		for(int i=0;i<n;i++) {
			scanf("%lld",&a[i]);while((1ll<<d)<=a[i]) ++d;}
		scanf("%s",str);
		for(int i=n-1;i>=0;i--)
		{
			if(str[i]=='0') {
				for(long long j=d;j>=0;j--)
					if(a[i]&(1ll<<j)) {
						if(base[j]>0) a[i]^=base[j];
						else {base[j]=a[i];break;}
					}
			}
			else 
			{
				for(long long j=d;j>=0;j--)
					if(a[i]&(1ll<<j)) {
						if(base[j]>0) a[i]^=base[j];
						else f=0;
					}
			}
			
		}
		if(f==0) printf("1\n");
		else  printf("0\n");
	}
	return 0;
}