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<iostream>
#include<algorithm>
#include<cstdio>
#include<cstring>
using namespace std;
const int M=60;
struct Basis{
	long long a[M+10];
	void clear()
	{
		memset(a,0,sizeof(a));
		return ;
	}
	void ins(long long x)
	{
		for(int i=M;i>=0;i--)
			if(x&(1ll<<i))
			{
				if(!a[i]){
					a[i]=x;
					return ;
				}
				x^=a[i];
			}
		return ;
	}
	bool check(long long x)
	{
		for(int i=M;i>=0;i--)
			if(x&(1ll<<i))
			{
				if(!a[i])return false;
				x^=a[i];
			}
		return true;
	}
}S;
long long a[210];
char str[210];
void solve()
{
	int n;scanf("%d",&n);
	for(int i=1;i<=n;i++)
		scanf("%lld",&a[i]);
	scanf("%s",str+1);
	S.clear();
	for(int i=n;i>=1;i--)
		if(str[i]=='0')S.ins(a[i]);
		else if(!S.check(a[i])){
			printf("1\n");
			return ;
		}
	printf("0\n");
	return ;
}
int main()
{
	int t;scanf("%d",&t);
	while(t--)
		solve();
	return 0;
}